ENDOWMENTS, INEQUALITY, AND AGGREGATION:

AN INQUIRY INTO THE FOUNDATIONS

AND METHODS

OF DISTRIBUTIVE JUSTICE

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF PHILOSOPHY

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Daniel Kearney Halliday

April 2011

This dissertation is online at: http://purl.stanford.edu/pq098zk0542

© 2011 by Daniel Kearney Halliday. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

ii

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Joshua Cohen, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Nadeem Hussain

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Debra Satz

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

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Abstract

This dissertation is organised around the development and defence of a novel

distributive principle and its philosophical foundations. This principle serves as a

refinement of the view that distributive justice requires the mitigation of endowment

differences, which otherwise stand to make some people worse off than others. The

principle of distribution itself is extensionally intermediate between Utilitarian

principles of distribution, and principles that have (typically) been offered as

expressing the idea of giving priority to the worse-off.

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Acknowledgements

In writing this dissertation, I have accrued a substantial number of debts,

intellectual and otherwise. The largest of these is to Joshua Cohen, who served as my

principal advisor. Josh spent many hours guiding the project along, past several false

starts and yet more false continuations, and often at odd hours from across several

time zones. What was eventually produced was at least better than what was earlier

produced, thanks largely to Josh. The other members of my committee, Debra Satz

and Nadeem Hussain, provided substantial additional support and often a novel angle.

For this I am also very grateful.

One of the many nice things about Stanford has been the amount of support I

have had, in addition to the generous amount provided by my committee. I should like

to thank literally all members of the Stanford philosophical community, including (but

not restricted) members of its philosophy department. At the same time as thanking all

in general, I would like to acknowledge, as valuable participants in conversations and

seminars that helped shape this dissertation, the following individuals, each of whom

had some affiliation with Stanford during my time: Jesse Alama, Lanier Anderson,

Sam Asarnow, Ralf Bader, Will Beals, Chris Bobonich, Michael Bratman, Rahul

Chaudri, Luis Cheng-Guajardo, Mark Crimmins, Matt Darmalingum, Marcello

DiBello, Daniel Elstein, Tal Glezer, Paul Gowder, Amanda Greene, Lauren Hartzell,

Nicole Hassoun, Wes Holliday, Tomohiro Hoshi, Allistair Isaac, Agnieszka Jaworska,

Pedro Jimenez, Sara Kerr, Krista Lawlor, RJ Leland, Brad McHose, Alan McLuckie,

Jeremy Meyers, Ben Miller, Teru Miyake, Sara Mrsny, Kieran Oberman, Ӧzlem

Ӧzgur, Marc Pauly, Govind Persad, Philip Pettit, John and Tomer Perry, Angela

Potochnik, Kristin Primus, Tamar Schapiro, Tobey Scharding, Assaf Sharon, Adam

Simon, Quayshawn Spencer, David Taylor, Han van Wietmarschen, Donovan

Wishon, Johanna Wolff, and Ben Wolfson. Tom Dougherty was added to this

community towards the end of my enrolment at Stanford, but I have been highly

fortunate to know Tom for some years now, and probably started benefitting from his

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thoughts on moral and political philosopher earlier than I started talking about such

things with anyone else mentioned here. Value was added to these interactions by

shared participation at Antonio’s Nuthouse, as well as through the now flourishing

Society of the Dirty Leviathan, which helped us appreciate what California has to

offer besides Silicon Valley (for example, Sacramento).

In the early stages of the writing phase, I was lucky enough to spend the best

part of the 2008-09 academic year visiting John Broome in Oxford. John kindly

arranged visiting membership of his college and then provided hours of feedback and

pedagogy that helped overcome initial ineptitude with technical approaches to

distributive principles, and replace this with something at least approaching

competence. I’m grateful to him for this. Whilst in Oxford, I was fortunate enough to

also to interact with a number of other philosophers or philosophically-minded

economists. I’d now like to thank Jonathan Bateman, (the) Courtney Cox, Roger

Crisp, Raissa Fabregas, Richard Kraut, Mara van der Lugt, Gaurav Khanna, and last

but in fact probably most, Gerard Vong. Other members of the MCR at Corpus Christi

College added to a community in which a work/life balance was nicely realised.

Thanks extend beyond the Silicon and Thames valleys. Further

acknowledgement is due to individuals fruitfully encountered in the course of talks

given on this material, shared hiking/conference attendances, or just my wanderings

into their geographical vicinities. Here I’d like to thank David Benatar, Luc Bovens,

Matthew Braham, Tim Clarke, Axel Gosseries, Johann Frick, Jeff McMahan, Larry

Temkin, and Alex Voorhoeve. Gustaf Arrhenius was kind enough to share drafts of his

forthcoming book and to provide substantial written comments on some drafts of what

became chapter five. Anna Wilkinson’s contribution was the most important one

during many challenging phases, and her proofreading at the end helped mitigate my

tendency to produce typographical errors.

Lastly, I thank my family - David, Patricia, Theresa, Sheila and Stuart - for the

reasons people normally thank their families (these being love, support, and patience,

among other things).

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Preface

The sub-title of this dissertation makes reference to “the foundations and

methods of distributive justice”. For the purposes of summarising the aims and content

of what follows over the course of the following chapters, it is perhaps easiest to begin

by unpacking this sub-title rather than the actual title. In any case, the latter merely

follows the norm of supplying some conjunction of concepts.

Roughly speaking, questions about the foundations of distributive justice ask

which considerations are fundamental in determining persons’ respective entitlements,

when assessing how some relevant good is distributed. Of course, the question of

which good is relevant in the first place may depend, although is not exhausted by,

how such questions are answered. Numerous types of answer have been given to the

foundational question. One type appeals to the idea that a person’s material shares

should reflect their choices, not merely their circumstances. It has been said, for

example, that a fundamental aim of justice is to eliminate involuntary disadvantage1.

This may favour removing material inequalities that can be blamed on unavoidable

personal misfortune, whilst allowing certain other inequalities to remain. Another type

of view says that justice requires the protection of personal freedom, or certain rights

of the individual. It has been said, for example, the persons have a fundamental right

of self-ownership2. Accordingly, persons are entitled to whatever they can produce for

themselves, or gain through voluntary exchanges with others. This view may imply a

much higher tolerance of material inequality than other foundational conceptions. A

third answer to the foundational question says that we should be guided by principles

of co-operation that we would agree to in a situation where we are ignorant of various

1 The phrase here is G.A.Cohen’s (1989: 916). I should note that Cohen presents this idea as a

fundamental egalitarian aim, which one might think counts as a fundamental aim of justice only if equality is itself fundamental to justice. 2 This is one way of representing the position of Robert Nozick (1974).

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biases3. This view will have yet different implications for the regulation of material

inequality

Each of the above foundational positions will be subjected to some discussion

in what follows. Here I just want to establish the way in which they contrast with what

I mean by the ‘methods’ of distributive justice. Crudely put, what I have in mind when

using the two expressions in the sub-title is a distinction between work that aims to

defend of a foundational conception against competing positions, and work that

concentrates more on the refinement and articulation of one such conception4. More

precisely, what I call the methods of distributive justice pertains to the sort of

theorising that reasons from some foundational view, towards a more precise set of

principles that have more definite implications for the regulation of actual material

inequalities. Understood in this way, work on the methods of distributive justice is

concerned with settling on a more committed, less unambiguous presentation of some

foundational ideal. The results of this second sort of work may still fall some way

short of anything that can provide full, immediate guidance with respect to issues that

society must currently address. Nevertheless, a project focusing on the methods of

distributive justice may be taken to represent an attempted step in this direction.

During the programme of research that eventually led to the writing of this

dissertation, I gained the sense that work on the foundations of distributive justice has

become rather weakly connected with the sort of philosophical work on distribution

that might be regarded as more precise and committed. Nowadays, contributions to the

latter category have chiefly been made not within the scope of work distributive

justice, but in areas such as population ethics. Philosophers who produce this sort of

work have somewhat different ambitions from those working on the foundations of

distributive justice. In the work of such authors, one at any rate finds some attempt to

3 This alludes to the position of John Rawls (esp 1999) and, to some extent, the Social Contract tradition

on which it builds. 4 I do not affirm that the distinction is sharp, or separates wholly independent relata. After all, refining

various foundational ideals will often contribute to any effort to work out which is the most plausible. What makes it useful to distinguish between foundations and methods is that, as I describe below, foundational work in political philosophy has drifted away from the discussion of precise principles of distribution, which itself has ended up being more often discussed by authors less exercised by the same distinctively political concerns.

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distance the project of evaluating principles of distribution from the sort of political

concerns that might otherwise inform such evaluation. Some authors claim to be

engaged in the project of evaluating different possible distributions having stipulated

that there are no differences between persons in the distribution other than what their

material shares actually are5. These claims are different ways of articulating a shared

assumption that work on principles of distribution can be driven by the aim of

evaluating states of affairs in their own right6.

Now, this concern with the ‘betterness’ of distributions is distinct from the

foundational question of the source of material entitlements. This is reflected by the

fact that political philosophers, working on the foundational question, have often

rejected the description that any sense can be made of which possible distributions are

independently ‘better’ than which others7. Independent of this idea is the view that

questions of justice only arise when there is the sort of scarcity that leads to the need

for principles that can resolve the resulting conflicts of interest in ways that are

morally defensible8. Respectively, these features give distributive justice a different

aim from, and a narrower scope than, any fully general evaluation of distributions. The

point here is not an evaluative one, it is just that the project of (mainstream,

cotemporary) distributive justice is importantly different from the project occupying

Parfit, Broome and others. Nevertheless, a difference in substance is compatible with a

shared aim of evaluating distributions for some reason or another. Indeed, part of what

guides the arguments in this dissertation is the view that progress in distributive justice

can be helped along if better use is made of the kind of techniques employed in the

moral ‘axiological’ work recently done on principles of distribution.

5 This is how Derek Parfit explains his reasons for setting aside certain foundational views in political

philosophy, which might otherwise have a bearing on his discussion. (2001: 82) 6 See for example Broome (2004, esp Ch.1).

7 For example, John Rawls has written: “A distribution cannot be judged in isolation from the system of

which it is an outcome…If it is asked in the abstract whether one distribution…is better than another, then there is simply no answer to this question” (1999: 76). As well as leaving it open whether Rawls was right to make these remarks, I also do not take a stance on whether what he rejects is exactly what authors like Broome and Parfit are committed to when talking about the betterness of states of affairs. I offer some further thoughts about the independent evaluation of distributions in Appendix A. 8 Versions of this idea are adopted by Rawls (1999: 109-112) and Hume (3.2.2. of the Treatise, (2000:

311-322). For further exegesis and comparison between their respective positions, see Barry (1989: 152-163, 179-183).

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Work done in what is now becoming known as ‘population axiology’ pays far

greater attention to the form of principles of distribution than does the vast majority of

work that is motivated by foundational questions in distributive justice. By the ‘form’

of a principle of distribution, I mean the properties that distinguish it extensionally

from other principles. This pertains to the way in which such a principle is able to

make comparisons between different possible distributions. More technically, the form

of a distributive principle is the function that it states from the facts about persons’

respective shares within a distribution, to the value of that distribution (vis a vis other

distributions). A principle’s form, therefore, is sort of thing that manifests itself in the

shape of the graph that might represent that function. All of these relatively technical

details will be studied more extensively in later chapters. The point for now is just to

understand that properties relating to form are to be distinguished from whatever

foundational considerations count in favour of one principle of distribution, or (more

likely) some set of principles that need to be assessed as to which gives the relevant

foundational conception its best representation. Work in population axiology is full of

sophisticated attempts to compare principles with different forms. In the literature on

distributive justice, however, talk about the formal properties of distributive principles

is increasingly left out of serious articulation of authors’ views, or relegated to

footnotes or afterthoughts. At any rate, political philosophers who have something

substantive to say about questions to do with form do not develop these ideas as fully

as they might.

My view is that this ought to be changed. The project of investigating and

developing the form of a distributive principle is what represents the methods of

distributive justice, at least when this project is guided by the aims motivating existing

foundational theorising about justice. Study of the methods of distributive justice, so

defined, has somewhat fallen by the wayside: Political philosophers increasingly stay

within the scope of foundational discussion, thereby limiting the degree to which their

views can be developed and tested. Those who do work on the form of distributive

principles have less investment in the aims of distributive justice, and their proposals

reflect this. The result is not only that the literature on justice has remained more

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restricted than it might be; it is also fair to say that certain areas of logical space have

been left relatively unexplored at the level of form. In what follows I try to do

something about both of these shortcomings. In due course, I will develop a principle

of justice that offers a new way of articulating a foundational position about justice.

This principle also counts as novel among the various positions that have already been

discussed by the population axiologists, even though it is, I suspect, less interesting

from the perspective of those invested in axiological debates.

Overall, I’ve come to see the project as partly an attempt to reclaim the

methods of distributive justice from more detached parts of moral philosophy. To

reiterate an earlier point, the use of the word ‘reclaim’ is not meant to imply that what

is reclaimed has been languishing in the wrong place. The choice of words reflects the

fact that I am concerned ultimately with addressing problems about justice, but in

ways that are informed by the techniques used by others with rather different aims.

The explanation given so far of how these foundations and techniques are related is

supposed to do no more than to show that they are distinct, insofar as they may be

(and have in fact come to be) studied in relative isolation from each other. This

explanation is designed to give some account of where the following work fits into

existing work on distribution generally and distributive justice in particular. In so

doing, it is meant to account also for the distinction drawn in the dissertation’s sub-

title.

*

In what remains of this preface, I will provide an outline of the chapters that

make up the dissertation. Chapter one begins with something of a survey of well-

known foundational positions. Theories of justice are construed as expressing different

kinds of response to the effects of inequalities in endowments. Roughly speaking,

endowment inequality is just the phenomenon whereby some of us start off life with

better expectations than others. Some people have richer parents than others, some

people are just more talented than others, and you could go on at some length. Among

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the notable features of endowment inequality is its strong tendency to bring about

material inequality, at least when left unchecked. Theories of justice all embody some

sort of view about the extent to which the effects of endowment inequality ought to be

regulated.

Now, as I present things in chapter one, theories of justice line up on a sort of

spectrum. At one end, there is the extreme view on which endowment inequality is

perfectly innocent and should not be interfered with. This is a view associated with

Libertarians. At the other end, you have the view that endowment inequality should

have no effect on the material distribution. This is a view associated with Luck

Egalitarianism. In between these two extremes lies room for various intermediate

positions. Following John Rawls, we might think that justice requires the mitigation of

endowment differences. Now, Rawls was led to this claim as result of conceptually

prior commitments to a sort of social contract theory. This is reflected in the way in

which he cashes out the idea with his own theory. The Rawlsian view has come in for

serious criticism, particularly in the form of G.A.Cohen’s critique of the way in which

Rawls affirms the existence of permissible (material) inequality. Given that some

theory corresponding to the ‘mitigation’ of endowment differences is still desirable,

Cohen’s critique calls for an alternative to the Rawlsian position, one shorn of the

commitments to contract-theoretic commitments to ideals like fraternity and

reciprocity between citizens. The main point at the end of chapter one is that it’s

possible to explore the mitigation idea independently of social contract theory, and

that we might well end up with a different principle of distribution from Rawls if we

do so.

The positive proposal of this dissertation is sketched in chapter two. Here is

where I begin to call on methods of representation more often used in the literature on

population ethics (or ‘axiology’) as opposed to distributive justice. After some

exposition on these techniques, I introduce a principle of distribution that I call a

piecewise-linear function. The function is so named because its graph is made up of

separate linear pieces. To use a description that philosophers will be more familiar

with, the principle is extensionally intermediate between Utilitarian and so-called

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‘Prioritarian’ principles of distribution. Indeed, when first presenting this idea to

audiences, I labelled the principle as a sort of logically weakened Prioritarianism.

This, however, proved problematic, since people (I discovered) tend to make strong

assumptions or inferences about what an author’s motivations are, upon being

presented with what is described as a form of Prioritarianism. Either that, or audiences

were insufficiently appreciative of what is implied by the formal differences between a

piecewise-linear function and more standard representations of Prioritarianism

(particularly, forms of strictly concave function). Although the distinction between

Prioritarian and Utilitarian principles is supposed to be purely extensional, my

experience suggests that it seems to have gathered much more baggage. So I switched

to the mathematical name instead, and have got on better since. However, if the

concept of Prioritarianism is permitted to remain purely extensional, then the

piecewise linear function may be regarded as a species of that position.

The middle part of chapter two distinguishes the piecewise-linear function

from other possible principles of distribution. Among other things, a core feature of

my own principle is that it combines a distinctive Egalitarian dimension with

important elements of indifference. What the function says is that we should carry out

transfers only from persons located above the threshold to persons located below.

Once there is no longer any deviation on one side of the threshold, any residual

deviation on the other side will be tolerated. In other words, there has to be deviation

on both sides for a transfer to be appropriate. Where the function is indifferent is

chiefly as to whether there are inequalities among the badly off or among the well-off.

Nothing is bad about these inequalities, qua inequalities. In addition, the function is

indifferent as to who below the threshold gets the most priority, and who above the

threshold has to shoulder the burden of redistributive transfers. This is all spelled out

more fully in chapter two.

The foundational case for the piecewise-linear function is laid out towards the

end of chapter two, and defended more fully in chapter three. Like other theories of

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justice, use is made of the theoretical device of a hypothetical scenario9. Of particular

significance in connecting the principle with this concept is a function’s threshold.

As I explain in (2.7), this threshold is located at what would be the average level of

welfare in a scenario where endowment differences are the only thing that affects

persons’ material shares. This requires imagining a set of circumstances where there

are not morally interesting differences between how people have made choices based

on their endowments, like they do in the real world. The point is that whenever

someone is better off than someone else, this is purely because they had a better start

in life. When its threshold is set at the average level the application of a piecewise-

linear function to a distribution will have the effect of wholly equalising material

shares. As such, the piecewise linear function represents a view on which, were

endowment differences the sole factor in shaping the material distribution, then perfect

equality would be what justice required. Now, in the real world, there’s more to what

shapes the distribution than endowments. But, because real average welfare is almost

certainly going to differ from the hypothetical average, the function is going to have

rather different implications when applied in real-world contexts.

This foundational point segues into chapter three. Assuming that the function’s

threshold is at a level other than actual average welfare, it follows that there are going

to be some permissible inequalities. Which inequalities are permissible is equivalent to

the question of who among the better off gets to be exempt from providing in such

transfers, or who among the badly off isn’t made a beneficiary of such transfers.

Because the function does not tell us the answer to these questions, there’s plenty of

room for ‘historical’ factors to come into play as a determinant of entitlements. The

main point I want to make in connection with this is that we’ve managed to avoid the

sort of conflict that Robert Nozick discussed when he said that historical principles of

justice were incompatible with end-state principles. The piecewise-linear function can

be considered an end-state principle, but it’s open to historical considerations having

force. Indeed, the idea of including elements of indifference in the function is what

confers such force on historical factors. This is not to say that Nozick wouldn’t have 9 This technique is employed, in very different ways, by Rawls (1999) and Ronald Dworkin’s (2000)

version of ‘Luck Egalitarianism’.

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other reasons for rejecting the view, but those are separate issues. A further advantage,

also spelled out in chapter three, is that we avoid the very rigid view associated with

Luck Egalitarianism, which serves as the basis for recent criticism of that view. The

piecewise-linear function allows us to be neutral as to whether a person’s being worse

off as a result of their own choices never entitles them to any redistributive

compensation, regardless of how badly off they are. Many philosophers’

dissatisfaction with Luck Egalitarianism stems from the fact that it appears to abandon

the badly off whenever their predicament cannot be blamed on their start in life. As I

explain in chapter three, the piecewise-linear function has properties that allow it us to

simultaneously attach greater importance to the effects of unsought risks (or ‘brute bad

luck’), without washing our hands of the victims of avoidable (and indeed rationally

sought) risks.

In this way, chapters two and three the piecewise-linear function serves to

refine a certain foundational conception, that being the need to ‘mitigate’ the effects of

‘morally arbitrary’ differences in endowment. Chapters four and five are less focused

on concerns at the heart of distributive justice. In fact, it is in these chapters that there

might be something of interest to those who work on principles of distribution in their

more ‘axiological’ setting. Chapter four is concerned, albeit somewhat indirectly, with

the distinction between welfare functions that are strongly separable and principles

that are not. This distinction closely resembles the more informal one separating a

concern about persons’ absolute positions in a distribution, and concern about the

relations between their positions. This issue is approached via an analysis of

G.E.Moore’s principle of organic unities, which states that the value of a whole cannot

be assumed to vary in proportion with the sum of the values of its parts. Ultimately,

axiological claims about the importance of relations between persons’ respective

positions amount to the view that distributions satisfy Moore’s principle. It is therefore

possible (in principle) to test these claims by way of filling out Moore’s view so that

the plausibility of non-separable welfare functions may be ascertained. This is what I

try to do in chapter four.

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Chapter five discusses the long-standing problem posed by distributions

containing different numbers of people. Again, this issue has been somewhat set aside

by participants in the debate about theories of distributive justice, although it surely

needs to be looked at as part of any assessment of justice between generations.

Accordingly, this chapter is more closely related to the literature in axiology. Setting

aside the question of how this topic relates to intergenerational justice, the chapter’s

main argument shows that the piecewise-linear function is of some use in balancing

the various competing intuitions that axiologists worry about when trying to say

plausible things about variable population size. As I argue, the route to a compromise

lies in discounting the value of benefits to existing people as they become better off

(ex ante), but not to such a degree that the value of adding lives to a distribution is

allowed to swamp the former value. One way of limiting the discount is to adopt a

function that tends towards linearity at higher welfare levels, which is precisely what

the piecewise linear function does.

This concludes the chapter breakdown. There are also some appendices. The

sole justification for these is that I had some ideas that I wanted to include in earlier

chapters. These ideas turned out to be irrelevant, but I wanted to keep them.

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CONTENTS 1 Endowments 1.1 The theoretical primacy of endowment inequality...........................1 1.2 Major positions in distributive justice...............................................4 1.3 Rawlsian claims................................................................................9 1.4 Contract theory and its problems....................................................13 1.5 Outline of a positive framework and its methodology....................20 2 Methods of aggregation 2.1 Aggregation: Some preliminaries...................................................24 2.2 Seven presuppositions regarding the concept of an ordering.........27 2.3 Separability and linearity................................................................33 2.4 Utilitarian theories..........................................................................35 2.5 Egalitarian theories.........................................................................38 2.6 Prioritarian theories.........................................................................41 2.7 The piecewise-linear function.........................................................45 2.8 The concept of sufficiency..............................................................51 3 Aggregation and justice 3.1 The problem of the bare self...........................................................55 3.2 More on the idea of a baseline........................................................58 3.3 History versus pattern.....................................................................64 3.4 On brute and option luck.................................................................70 3.5 Further remarks on Luck and Egalitarianism .................................74 4 Holistic approaches to aggregation 4.1 Some motivations recalled..............................................................77 4.2 G.E.Moore on parts and wholes......................................................80 4.3 Two distinctions .............................................................................83 4.4 Evaluative priority and explanatory priority...................................85 4.5 Why the material distribution is not an organic whole...................88 4.6 Summary comments on non-separable aggregation.......................91

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5 Population size 5.1 Adding lives versus improving lives...............................................94 5.2 Refining the common sense view ..................................................96 5.3 Trouble with the common sense view............................................98 5.4 Lines of response..........................................................................100 5.5 The piecewise-linear function, again............................................106 5.6 Concluding remarks......................................................................110 Appendix A: Speaker-relativity, normativity and incentives..................114 Appendix B: Scepticism about the betterness of outcomes....................118 Appendix C: The inequality relation.......................................................125 Bibliography............................................................................................128

1

Chapter One: Endowments

1.1 The primacy of endowment inequality

Theories of distributive justice provide principles for regulating the social

distribution of welfare, or the distribution of some other relevant set of goods.

Theories of this kind work from some conception of how persons come to be entitled

to certain distributive shares. The principles they provide aim to guide efforts to bring

persons’ actual shares into greater conformity with their respective entitlements. That

is to say, defending some conception of the source of entitlements, and identifying a

principle of distribution reflecting it, may be regarded as a first approximation of what

it is to conduct theorising in distributive justice.

A host of factors may be regarded as part of what determines any person’s

entitlements. Among these factors are persons’ endowments, which we may single out

for special attention. The idea of ‘endowments’ to be employed here is meant to align

with more colloquial talk about the quality of a person’s start in life. Thus, included

among a person’s endowments are the financial circumstances of their family, the

wider socio-economic context in which they find themselves, and the aspects of their

psycho-physiological condition that we often call ‘native talents’. The boundaries

separating endowments from other factors are bound to be vague, and developing an

exhaustive account of what distinguishes endowments from non-endowments may be

beyond us. Nevertheless, the reasons for directing a certain theoretical focus towards

endowments (or, more accurately, on the way they are unequally distributed) are

sound ones, and I shall begin by highlighting what some of these reasons are.

To begin, endowments have a sort of primary efficacy in affecting a person’s

material shares, when compared with the other factors that may exercise some

influence. That is to say, there is a sense in which one’s endowments make the first

contribution to how one fares in life. The space in which other factors can operate,

such as a person’s choices, efforts and ways of co-operating with other people, is to

2

some extent defined by (or limited by) the quality of this person’s endowments. This

favours a search for principles of justice that begins with an analysis of how

entitlements are related to endowments, ahead of any analysis of other determinants.

This is based on a plausible, abstract presumption: If the operation of some morally

relevant factor is determined in some way by the operation of some other morally

relevant factor, then an account of the former factor’s moral relevance risks being

incomplete, or incorrect, unless it is guided by an account of the latter’s moral

relevance.

Another reason for focusing on endowments is the sheer extent of their causal

power. The distribution of endowments is highly unequal. Endowment inequality is

largely to blame for the substantial material inequality and poverty that currently

exists. Certainly, the effect of having had a bad start in life is defeasible, insofar as

hard work and wise choices may overturn an initially unfavourable set of expectations.

(The expectations associated with a good start in life is, of course, also defeasible,

albeit rather less so.) In spite of what is often said in public political discourse, serious

academic research suggests that it is difficult to exaggerate the significance of having

a favourable or unfavourable set of endowments10. In the setting of distributive justice,

we are concerned to ask whether the distribution of goods stands in violation of some

compelling principles, even if we are as yet undecided as to what these principles must

be. An answer to this question will include some evaluation of whatever it is that

actually influences the distribution of goods, in the absence of this distribution being

regulated by the terms of a plausible theory. Since the effects of endowment inequality

are, in fact, largest among such influences, this in itself counts as some reason to give

them priority as an object of analysis.

A third reason for giving prominence to the concept of endowments is its

ability to play an important taxonomic role. As a matter of fact, points of disagreement

between major theories of distributive justice can be most readily seen if such theories

are regarded as specifying different responses to the effects of endowment inequality.

10

For something approaching a survey of the sociological literature, see McNamee (2009).

3

This approach does not just give a good sense of which possible views have already

been articulated. As I shall explain, the focus on possible responses to endowment

inequality also helps indicate the sorts of approaches that have not yet been proposed

in distributive justice. As such, giving primacy to endowment inequality provides a

foothold on which to build some novel proposals.

I should qualify these three points in several ways. None of them, especially

not the second two, are meant to express the view that any claim about endowment

inequality serves as a fundamental normative ideal in distributive justice. Certainly,

assigning such status to the endowment distribution might be favoured. Indeed, I shall

later commit myself to a version of this view. However, there are plenty of other

candidates for what counts as fundamental to distributive justice11. I do not mean to

express prejudice against any of these alternatives views by talking of the ‘theoretical

primacy’ of endowment inequality. This may sound in conflict with my claim that the

influence of non-endowments is in some way dictated by whatever endowments

already attach to the person in question. The point of this claim, however, is merely

that one cannot take a view about the significance of non-endowments without also

having decided on the significance of endowments. Accepting this would not stop one

from denying that endowments relate to entitlements at all, or that their contribution to

entitlements can be reduced to the significance of some other fact. In other words, the

sense in which endowment inequality enjoys at least some kind of priority over other

factors is that one could, if one wished, formulate a view about endowments’

contribution to entitlements whilst postponing any analysis of how other factors add

their own contribution. With respect to the other two points, all I mean by the

‘primacy’ of endowment inequality is that it counts as a useful organising concept,

attention to which is also supported by a strong causal connection with the material

inequality that theories of justice aim to regulate.

11

One view, favoured by Rawls, is that justice is fundamentally about fair terms of co-operation (2001: 5). Certain Libertarians have attached fundamental status to freedom from interference with personal choices (e.g. Friedman 2001: ch10). Some of these views are described more fully below.

4

For now, then, what I have called the ‘primacy’ of endowment inequality is

meant in a more methodological sense than any substantive, conceptual sense. And,

after all, any theorising about distributive justice must start somewhere. If primacy

were not given to endowment inequality, we would still need a case for whatever else

we might give it to.

1.2 Some main theoretical positions in distributive justice

In due course, I shall present a positive proposal about how endowment

inequality is related to the regulation of material inequality. One way of working

towards any positive proposal about justice is to gain a sense of some of the more

prominent and complete proposals already in existence. As I have said, theories of

justice can be treated, at least extensionally, as specifying different reactions to the

influence of endowment inequality. More helpfully, it is possible to arrange the most

influential positions in contemporary distributive justice along a certain sort of

spectrum: At one end of this spectrum is the idea that the influence of any differences

in endowments ought to be entirely eliminated. At the opposite extreme is the view

that endowment inequality is a perfectly legitimate phenomenon which cannot, at least

on its own, have unjust effects on the material distribution. Two well-known positions

occupy these two extremes. The view commonly known as Luck Egalitarianism has

been associated with the conviction that it is “unjust for any person to be worse off,

through no fault of their own”12. A particularly influential refinement of this idea says

that entitlements should be strongly connected to choice, rather not circumstance. In

connection with this idea, much has been made of Ronald Dworkin’s distinction

between what he calls “brute luck” and “option luck”. The latter refers to the effects of

“deliberate and calculated gambles”, which the subject “should have anticipated and

might have declined”13. Brute luck is to serve as a label for whatever sorts of fortune

12

I think the first occurrence of this sort of slogan is in Nagel (1991: 123). A similar remark appears in Temkin (1993: 200). It should be said, though, that the emphasis on the choice/circumstance distinction is older than this, and also that neither Nagel nor Temkin subscribe to all elements of Luck Egalitarianism as popularly understood. 13

I am using Dworkin’s own phrasing (2000: 73-74). Other classic statements of the Luck Egalitarian position include Arneson (1989) and G.A.Cohen (1989). For something of an up-to-date survey of the

5

do not satisfy this description. Clearly, one’s endowments, favourable or otherwise, do

not result from chancy processes that one could have done anything to anticipate,

much less avoid exposure to. The crucial element of the Luck Egalitarian view, at least

as it is normally interpreted, is that entitlements to benefit from any redistributive

policy exist only if one has been victim to the effects of bad brute luck.

So stated, the Luck Egalitarian position is in need of elaboration. Some

baseline needs to be established, against which the badness of any brute luck can be

measured. And it also needs to be established, perhaps via the same method, with

whom the redistributive burden lies. Members of the Luck Egalitarian programme

differ as to how the basic view is to be refined. What should be clear is that there is a

strong aversion to any distributive inequalities that can be blamed solely on

endowment inequality, or any other effect of brute luck (we may set aside the question

of what counts as an effect of brute luck if it is not the effect of an endowment). This

is the strongest possible response to the question of what justice requires by way of

intervention with the effects of endowment inequality.

Libertarian views tend to oppose the regulation of material distribution,

particularly when such regulation would be guided by the aim of reducing any effects

of the unequal endowment distribution. There are various ways of motivating this

view. It has been said that redistributive taxation is on a par with forced labour, in the

sense that it gives the state a property right in those who are taxed14. Another view is

that the capacity to make one’s own choices is part of what is special about being a

human being. On this view, state interference aimed at adjusting the results of such

choices (perhaps regardless of the conditions under which they had to be made) does

something to undermine this value15. Perhaps Libertarians can coherently accept that

an unequal endowment distribution, and its effects on the material distribution, may be

now very large literature, see Arneson (2011). I shall discuss some important contributions to this literature over the course of this dissertation. 14

This is an element of Robert Nozick’s view (1974, esp. 167-74). 15

This approximates, in my view, Milton Friedman’s position (2002, esp. Ch. 10). Overall, Friedman’s Libertarianism seems to be motivated by an aversion to paternalism, to which a concern for property rights is secondary.

6

in some respects objectionable from the point of view of justice16. But what they are

committed to is that there exist other important values, such as freedom and/or self-

ownership, which cannot be properly respected unless we allow people to do what

they choose with their endowments17. Indeed, the proper exercise of personal freedom

and a right to choose is just part of what happens when the distribution of endowments

is allowed to influence the distribution of welfare or goods, irrespective of what these

effects turn out to be.

The Libertarian view is associated with some more particular claims about

endowment inequality. Libertarians have made the point that a person’s start in life is

often the result of choices that their predecessors made, and is therefore not an isolable

object of evaluation18. This might suggest a conflict with my earlier claim that the role

of factors such as voluntary choice is in some way secondary to the influence of

endowments. More accurately, what Libertarians can perhaps say is that endowments

have the relevant causal priority within the life of a single person, but have no such

priority across persons (or, perhaps better, along generations). A more general

Libertarian claim is that theories become friendly to redistributive regulation only by

regarding injustice as attaching to ‘end-state’ distributions, rather than through an

assessment of the processes by which such end states are reached. Libertarians have

urged that if we focus on how persons have gained their distributive shares, rather than 16

This is not true for all Libertarians. F. A. Hayek seems to believe that we should celebrate the fact that there is some amount of endowment inequality, calling it “one of the most distinctive facts about the human species”. Hayek is then led to claim: “From the fact that people are very different it follows that, if we treat them equally, the result must be inequality in their actual position” (1960: 86-87). Hayek’s view may converge somewhat with Friedman’s: there is something valuable about the kinds of things that humans are, in ways that makes it objectionable to try to eliminate the differences between them. 17

My discussion here is not inclusive of so-called ‘Left Libertarians’, who aim to reconcile ideas about self-ownership with the case for some sort Egalitarian redistribution. Such views do not lie at the extreme end of the spectrum that I have described. The Left-Libertarian approach depends on a certain way of redeveloping traditional Libertarian views about acquisition. Since I lack the space to discuss these background matters, I shall also leave Left Libertarianism undiscussed. For a sense of the issues at stake, see the exchange between Fried (2004) and Vallentyne et al (2005). 18

An application of this point can be found in Libertarian opposition to inheritance tax. Milton Friedmand gives similar emphasis to the idea that one person’s endowment is often intended consequence of another’s choice: “it seems illogical to say that a man is entitled to what he has produced by personal capacities or to the produce of the wealth he has accumulated, but that he is not entitled to pass any wealth on to his children; that he may use his income for riotous living, but may not give it to his heirs” (2002: 164). The abstract point is also gestured at in Nozick (1974: 167-68).

7

what their shares are, then we will be in a better position to observe what justice

requires. But construction of rigid principles of distribution, Egalitarian or otherwise,

is never going to provide the right kind of sensitivity to ‘historical’ factors. Now, both

of these Libertarian claims have some plausibility, and need to be taken seriously. I

shall return to these issues in chapter three, where I shall explain why neither is

obviously incompatible with a certain aversion to an unfettered influence of

endowment inequality, so long as this aversion is formulated in a certain way.

Between the possibilities of ignoring and eradicating the effects of the

endowment distribution there may be found any number of more moderate,

intermediate positions. Here I mean to use ‘intermediate’ in the extensional sense

mentioned earlier, on which the implications of the relevant views sit somewhere

between those of Luck Egalitarianism and Libertarianism. By way of referring to

theories in this intermediate range, it might be said (to use an expression from John

Rawls19) that they seek to “mitigate” the effects of endowment inequality on the

material distribution. Within this range of intermediate positions, a variety of

theoretical frameworks are available. One is a version of social contract theory.

Another is the view I mean to develop myself.

One might think that an intermediate position could be formulated on

intuitionistic grounds alone. It is easy to imagine a hybrid that simply incorporates the

rationales of the Libertarian and Luck Egalitarian extremes. On such a view, some

weight would be given to placing limits on material inequality caused by the operation

of bad brute luck, and some simultaneous weight given to removing limits on free

choice (or some other factor with a tendency to cause material inequality). One trouble

with hybrids such as these is their tendency to require apparently arbitrary decisions

about how to trade-off the multiple values at stake. A further, perhaps deeper,

difficulty lies in explaining how the values concerned admit of any trade-off in the

first place. As I have said, part of the Libertarian view is the idea that values such as

choice or freedom are inviolable, such that accepting some sort of trade-off might

19

See for example (1999: 63).

8

simply misunderstand the values in question. In any case, one might take issue with

the decision to compromise competing values rather than work harder to find fault

with one and thus fully embrace the other. In this way, hybrids are rather like

ambiguity theories that are sometimes offered in the philosophy of language as a

response to some linguistic category that resists a unified account. Such theories have

been described as a “lazy” concession to challenging data, when the right response is

to work out which data can be discounted20.

Of course, hybridising the commitments of two extreme positions is not the

only way of arriving at a view that is extensionally intermediate. One way in which

one might be led to mitigate the effects of endowment inequality is by adopting the

theory of Justice as Fairness that Rawls defended himself21. A guiding idea of

Rawlsian theory is that distributive shares be regulated in ways that permit material

inequalities where these benefit the worst-off, subject to certain constraints regarding

fair equality of opportunity, and the protection of some set of equal basic liberties22.

The fact that the view tolerates some material inequality means that some persons may

become better off than others, even if superiority in endowment enters into the causal

explanation of why such inequalities could become generated in the first place23. The

condition that injustice typically attaches to inequalities not benefitting the worse off

is intended to satisfy certain background ideas about reciprocity and fraternity among

citizens, and be something that citizens would rationally agree to in Rawls’s

hypothetical contract situation, whilst ignorant of what their actual social position

(including their set of endowments) would be.

20

The allusion is to Saul Kripke’s claim that “it is very much the lazy man’s approach to philosophy to posit ambiguities when in trouble” (1977: 243). 21

See Rawls (1999). I shall make more focused references below. 22

I leave it open whether these constraints merely reduce the number of occasions on which benefits to the worst-off render an inequality permissible, or whether they also qualify certain other inequalities as permissible even if these do not improve the position of the worst-off. 23

Rawls is also reluctant to deny the Libertarian platitude that a person’s endowments are her own and there is thus some pressure to allow her to make the most of them (see below). This reflects a methodology within which intuitionistic judgments are not entirely abandoned, but where an emphasis is placed on finding a “conception of justice that...tends to make our considered judgments of justice converge” (1999: 39-40). See also the description of Reflective Equilibrium (1999: 42-45).

9

Rawlsian theory offers one example of how one might defend the mitigation of

endowment inequality’s influence over material shares, without simply combining

elements of the Luck Egalitarian and Libertarian alternatives. The aim in this

dissertation is to explore the prospects for how we might arrive at an intermediate

position without adopting the core commitments of a Rawlsian view. In due course,

this will lead to a principle of justice with its own set of interesting properties and

applications. What I shall do in what remains of this first chapter is lay out the

foundations of my own position, and motivate the departure from the Rawlsian

approach. This will clear the way for the statement of an alternative positive view

about how to mitigate the effects of endowment inequality.

1.3 Rawlsian ideas

I will expand my discussion of the Rawlsian approach both to highlight some

of the problems with it, and to highlight ways in which it is similar to and different

from the view I shall go on to develop myself. At this stage, no argument is given for

what is common between the Rawlsian view and my own, namely, the position that

mitigating the effects of the endowment distribution is preferable to ignoring or

eradicating those effects instead. The case for this view is one that will emerge more

gradually over the following chapters. In chapter three I will begin to explain what it is

about the Luck Egalitarian and Libertarian approaches that make them inferior to a

theoretical position that is intermediate between them, at least on the specific

intermediate proposal that I shall be concerned to develop. These arguments, however,

cannot easily be given without having the positive proposal in place beforehand. In

any case, there is something to be said for putting the positive element of a

philosophical project towards the early part of its execution.

As I have said, the reference to mitigating the effects of endowment inequality

is one that I have taken from Rawls himself. Rawls makes repeated use of the term

“mitigation”, but does not give it any free-standing analysis. Indeed, Rawls’s claims

about endowment inequality are somewhat complicated, even given a full

understanding of Justice as Fairness. This is partly because Rawls’s references to

10

endowments underwent a certain amount of alteration as his writings developed, and

were among what was revised in the second edition of A Theory of Justice. Care is

needed when interpreting Rawls’s position, but a careful analysis still leaves some

unanswered questions. What I shall aim to do is highlight what I take to be the main

problems with the Rawlsian approach. This in itself will not consist in any new

arguments being offered. What I do want to emphasise, however, is a certain diagnosis

of why these main problems with Rawlsian theory arise. The main objections to Rawls

do not indicate any difficulty with the search for a moderate treatment of endowment

inequality, but to features not essential to this end. In particular, as I shall explain, the

main objections to Rawlsian theory gain their force from the fact that Justice as

Fairness is a version of social contract theory.

One of Rawls’s better-known claims about endowments is that they are

“morally arbitrary”. This claim first occurs in the following passage:

The existing distribution...is the cumulative effect of prior distributions of natural assets –

that is, natural talents and abilities – as these have been developed or left unrealized, and

their use favoured or disfavoured over time by social circumstances and such chance

contingencies as accident and good fortune. Intuitively, the most obvious injustice of [this

system] is that it permits distributive shares to be improperly influenced by factors so

arbitrary from a moral point of view.24

These remarks invite certain questions as to exactly what sort of evaluation is being

made. Rawls goes on to say that there is nothing just or unjust about the distribution of

endowments per se: “These are simply natural facts. What is just and unjust is the way

that institutions deal with these facts”25. Similarly, Rawls claims that persons’

24

(1999: 62-63). 25

(1999: 87). One might ask why it might not still be compatible with the requirements of justice to affect the sort of endowments persons have in the first place. Scientific advances may allow certain genetic interventions that pre-empt endowment inequalities. If this can have the same sort of consequences as the relevant institutional responses that Rawls favours, then why is there any special reason to delay so as to let institutions respond to endowment inequalities, rather than set up other institutions that pre-empt such inequality? I raise this question largely to leave it. But it is worth noting that questions such as these are gaining an increasing amount of attention within moral philosophy (see for example McMahan 2005a), and may in due course need to be addressed by those working in distributive justice.

11

differing endowments are “accidents”, which a theory of justice should enable us to

“leave aside”26. This sort of language falls short of any suggestion that it would be

appropriate for endowments to be made perfectly equal. Most explicit is the remark

that justice “does not require society to even out handicaps”27. All of these remarks

reflect one important fact, which was that when talking about the moral arbitrariness

of native endowments, Rawls’s analysis was purely negative. That is to say, the

reference to moral arbitrariness is merely the denial of any claim that an unequal

distribution of endowments could be favourable from a moral point of view. This is

really not a very strong view at all. It establishes little more than the view that, as

Rawls observed, we cannot plausibly say that anyone deserves their particular set of

endowments, whether they be favourable or unfavourable28.

By offering a negative evaluation when making claims about the moral

arbitrariness of endowments, Rawls merely expresses the view that it is an open

question as to how endowment inequality can justly affect a material distribution. His

point is largely that the question remains open chiefly because there is no possible

appeal to certain moral concepts, like desert, that could close it. Some commentators

have reacted to the quoted passage in a different way. It has been said, for example,

that Rawls was in fact something of an incipient Luck Egalitarian, and that, when fully

developed, his views on the moral arbitrariness of endowment inequality would favour

its nullification. Luck Egalitarianism is thus sometimes presented as a ‘successor’ to

Rawlsian theory29. If Rawls’s references to moral arbitrariness are understood in the

negative way described above, then it is wrong to interpret Rawls as being on any sort

of Luck Egalitarian ‘trajectory’. This has been pointed out by those who have argued

26

(1999: 14). 27

(1999: 86). 28

(1999: 88). It is worth registering the fact that Rawls uses ‘desert’ as a technical term, meant to exclude certain colloquial uses. On this usage, ‘deserving’ something is just meant to mean being legitimately entitled to it (see 2001: 72-79). 29

See for example Kymlicka (1990: 70-76). Susan Hurley also presents Rawls as a “luck neutraliser” (2003: 133-36). Based on this, Hurley claims that Rawls’s position on endowments is in tension with his idea that concepts such as desert and responsibility should play no role in a theory of justice. The tension emerges only if Rawls thinks that we should neturalise effects of luck on grounds that people are not responsible for such effects. The reason the tension is not genuine is the fact that Rawls did not hold the “luck neutralising” view attributed to him by Hurley.

12

against the Luck Egalitarian interpretation of Rawls. According to these authors, the

fundamental element of Rawlsian theory is not any view about endowments, but a

commitment to the importance of certain contract-theoretic concepts, such as

reciprocity and fraternity mentioned above30.

Now, on the balance of textual evidence, the interpretation of Rawls as having

a tendency towards Luck Egalitarian is the weaker one. And given the fuller

theoretical framework of Justice as Fairness, there is undoubtedly more going on than

could be derived from a simple appeal to the moral arbitrariness of endowments, even

if one forces a reading that goes beyond the negative claim. Nevertheless there is an

element of truth in the Luck Egalitarian interpretation. First, it should be noted that

even if some freestanding concern about endowment inequality is not the core

foundation of justice as fairness, it may still be present in Rawls’s view without being

derived from some more fundamental premise, and may even make some contribution

to the view’s appeal31. There are some threads of textual evidence which hint at the

idea that there is something objectionable about endowment inequality itself32. One

thing usually not observed is that the term ‘mitigation’ is itself essentially evaluative

in a way that ‘eradication’ is not. Specifically, one cannot propose to mitigate the

effects of some phenomenon without the presumption that some of these effects are in

some way bad. Thus ‘mitigating’ is not merely a weakened analogue of ‘eradicating’

in a way that, say, ‘reducing’ is. The point I wish to make is just that there are echoes

of some free-standing evaluation of endowment inequality, or of its effects, within the

Rawlsian position. This much is not ruled out by the fact that the driving force in

Justice as Fairness comes from elsewhere.

30

This is emphasised in Freeman (2007: ch4) and Scheffler (2003). A nice explanation of how Rawls’s claims here are merely negative is given by Arneson (2008: 383-384). 31

This is not to say that the distance between Rawls and Luck Egalitarianism is quite as great as some have said. I think Samuel Scheffler goes too far when claiming “the best explanation of the fact that Rawls’s theory of justice does not respect the distinction between choice and circumstances is that Rawls is not attempting to respect it. He simply does not regard the distinction has having the kind of fundamental importance that it has for Luck Egalitarians” (2003: 11). I think that Rawls does respect the distinction, in ways that motivate his own position. The difference is, perhaps, that Rawls does not make the distinction exhaustive of the requirements of justice in the way that a Luck Egalitarian might be seen as doing. But a consideration may be non-exhaustive and yet still fundamental. 32

Discussed by Parfit (2000: 90-91).

13

The lesson of this, I think, is not that there is any enduring push towards Luck

Egalitarianism within the Rawlsian theory. Rather, the right observation is that it is

hard to completely disconnect a theory of justice exhibiting default redistributive

tendencies, from the idea that there is something objectionable about endowment

inequality, or its effects on material shares. As such, the statement of the Rawlsian

view, for all its other sources of inspiration, never manages to fully exclude the sort of

evaluation that is much more fully endorsed by the Luck Egalitarians. In my view, this

suggests that such a severance isn’t really available. Still, none of this counts against

Justice as Fairness, at least not vis a vis the Luck Egalitarian View.

1.4 Contract theory

Rawls tells us that Justice as Fairness reflects an aim to “generalise and carry

to a higher order of abstraction the traditional theory of the social contract”33. In

accordance with this description, the abstract idea of social contract theory might be

identified with the view that requirements of justice rest on ideas where social co-

operation, and hence the proper distribution of its products, are guided by principles

reflecting mutual respect between citizens. The Rawlsian idea of principles being of a

sort that citizens would agree to behind a veil of ignorance counts as one refinement of

this idea34. Contract theory, at least of the Rawlsian thought, does not sit in a very

straightforward relation with the conception of a theory of justice as an expression of

what to do about the effects of endowment inequality

Part of the idea of an agreement to Rawlsian principles when in the original

position is an idea that as part of regarding each other as free and equal, citizens would

agree to regard the distribution of endowments as analogous to a common asset. This

is a hard claim to make sense of, but Rawls apparently regards it as essential to the

distinctiveness of Justice as Fairness. A particular difficulty is of how literally this

claim is meant to be read. It has been said, by some of Rawls’s readers, that the better-

33

These remarks occur in the preface to the (1971) edition. 34

The abstract remarks offered here are also guided by those offered by Rawls in the preface to the revised edition (1999: xv).

14

endowed do not own their talents. Instead, such individuals are to be regarded as a

“guardian or repository”, for what is collectively owned35. More dissenting critics find

the view incompatible with Rawlsian claims about the separateness of persons (on one

understanding of this idea), or simply intolerable in its own right36. All of these claims

might be said to take Rawls too literally. Or, at least, the literal reading is especially

disqualified by the way in which Rawls phrases his views in later writings. Rawls

placed increasingly greater emphasis on the idea that the distribution of endowments

is to be regarded as a common asset, not the endowments themselves37. In the revised

version of A Theory of Justice, we are told that the agreement behind the veil of

ignorance is one that “in effect” regards endowments as “in some respects” a common

asset38. Rawls also makes explicit the view that “should [questions of ownership]

arise, it is persons themselves who own their endowments”39.

It is all very well making the assertion that one’s theory is compatible with

persons owning their endowments, or their own selves (insofar as these are distinct;

see chapter three). However, it is not clear how else to interpret the references to

common assets that Rawls continued to make, notwithstanding the heavy

qualifications. At times, one is led to wonder what difference is made by what can

look like little more than the addition of hedge terms. At any rate, the issues

surrounding Rawls’s claims about endowments as a common asset are certainly

underworked. Rawls did not do enough to fully assuage the doubts raised by critics of

35

This description is found in Sandel (1998: 70). On this interpretation, Rawls’s commitment goes deeper than the claim that assets are owned collectively. Roughly, Sandel’s view is that the boundaries between different members are blurred, in ways that give rise to a single, intersubjective self. According to Sandel, this gives content to the Rawlsian claim that “in justice as fairness men agree to share one another’s fate” (1971: 102). It is perhaps worth noting that this is one of the phrases replaced in the revised edition with one tied more closely to the difference principle itself: “men agree to avail themselves of the accidents of nature and social circumstance only when doing so is for the common benefit” (1999: 88). 36

On the separateness of persons see Nozick (1974: 228). David Gauthier expresses the view that “for Rawls morality demands the giving of free rides; no other interpretation can be put on the insistence that talents be treated as a common asset” (1986: 220). This formulation is, however, question-begging: The denial that the poorly-endowed gain free rides is precisely what would follow from claims about endowments being in some way commonly owned. 37 (2003: 75). 38

(1999: 87). 39

(2003: 75).

15

his earlier statements of the idea, and no one among his followers has made any

sustained attempt to give a defensible account of what an improved version of the

critics’ interpretation is. Faced with these facts, the Rawlsian commitments on this

matter should continue to be regarded as a weakness in the Rawlsian view.

There is one matter that has received far more sustained and careful attention

than the idea of the endowment distribution as a common asset. This is the relation

between Rawls’s views and the provision of incentives. Any theory of justice that

aims to do less than eradicate the effects of endowment inequality is committed to the

view that some material inequality may occur without any injustice. As I have said,

the Rawlsian view holds that inequalities may be permissible when the worst-off

would be even more badly off if the relevant inequalities had not been allowed to

obtain. This suggests the view that incentives may be offered to the better-endowed, in

return for greater levels of production40. In a sense, endowments just are certain

capacities to produce. The provision of an incentive can be understood as that which

permits the bearer of an endowment to retain a disproportionate share of their

productive activity41, so long as at least some share accrues to the worst-off. (For

simplicity, the worst-off may be regarded as roughly co-extensive with those who are

poorly-endowed and, as such, less able to produce.)

The above sketch alludes to an apparently coherent expression of when certain

inequalities are permissible. However, there may be serious tensions between Rawls’s

willingness to permit inequality, and other aspects of his overall view. The idea, to

repeat, is that inequalities are permissible when they are necessary for certain benefits

to accrue to the worst-off. But, as G.A.Cohen has asked, we might pause to ask what

the nature of this necessity really is: why is it that the worst-off are able to benefit 40

For his most explicit endorsement of permissible inequality described in this way, see Rawls (1975: 257). 41

Care will be needed in defining what ‘disproportionate’ comes to. It cannot mean merely a greater share than whatever would be retained by a source of productive activity if their product was distributed equally, or in ways that aim to reduce inequality by prioritising the worst-off. Often, a productive individual’s share may need to be enhanced merely to provide a means to their productive activity, or, more likely, to compensate them for the costs of that activity when it is particularly onerous. The idea of an incentive to be productive must mean that a person’s retention of their product is allowed to be greater than what would merely compensate them.

16

from the production of their better-endowed counterparts only if the latter are allowed

to retain a greater share of what they can produce? The only available answer seems to

be that the better-endowed would, in fact, be unwilling to use their capacities so fully,

absent such special permissions to retain a grand share of the benefits42. If the better-

endowed were differently motivated, then they might be willing to put their capacities

to the fullest use, and yet allow the benefits to be shared among members of society in

ways that improved the position of the worst-off, but in ways that reduced material

inequality overall. An extreme version of a productive member so motivated, might be

prepared to receive no benefits from their activity, if this does the most to allow the

worst off to rise to a position closer to that which he enjoys. The important question

raised by Cohen’s criticism is this: The fact that the better-endowed are motivated as

they actually are is a merely contingent fact. In being actually motivated, they might

also be less justly motivated than if they were differently motivated. Incentive-

demanding behaviour looks rather like mere self-promotion. Why is a concession to

the relatively selfish motivations of the better-endowed compatible with justice?

Granted, prudence might entail that we ought to adopt policies granting incentives to

the better-endowed, given that their psychology is the way that it is. But the prudential

‘ought’ is not the same as the moral ‘ought’43. The case for permitting incentives is not

so much a requirement of justice as a required sacrifice.

All of this is laid out in much more detail by Cohen himself, and has generated

a growing literature44. I lack the space to go through all of the details, but will register

some further elements that are of importance. First, the criticism does not gain its

force entirely from the presentation of incentive-demanding behaviour as crudely

selfish. By being disposed to full activity only when offered incentives, the better-

endowed act against core values of Rawlsian justice, notably relations of reciprocity

42

It is of course possible that such inequalities are necessary in a stronger sense of the term. As Cohen argues, however, it is hard to believe that such necessities actually occur. 43

Cohen summarises his criticism in terms of the distinction between what is just and what is “sensible” in the preface to his recent book (2008: xv). 44

Cohen’s line of criticism has been laid out over several years, sometimes presented as an attack on incentive-provision in actual society, rather than just a critique of Rawlsian theory in particular. Important publications include Cohen (1992), (2000), (20008).

17

and fraternity that are supposed to extend between them and their fellow citizens45.

What’s more, Cohen points out, Rawls’s own distributive principle does not licence

inequality in the way that Rawls requires, at least when read strictly. The principle in

question, the famous Difference Principle, has the form of a maximin rule on which

changes in the position of the worst-off have lexical priority over any other alterations

to a distribution. This aspect of a maximin rule means that it favours large inequalities

if they are accompanied by even the smallest increase in the position of the worst-

off46. In this way, a maximin rule appears to have the right sort of structure to operate

within a framework designed to permit certain inequalities. However, whilst the form

of a maximin rule implies that creating inequalities can improve a distribution, such

rules also imply that the improvement will be even greater if the inequality is

subsequently reduced by transferring from the better-off to the worst-off, even if it

would be inefficient to do so. The basic point is that even if inequalities confer

benefits on the worst-off, it is usually possible to benefit the worst-off even more, in

ways that do not involve creation of the inequality47. Any maximin principle will

prefer the latter improvement, even if it is the less efficient overall. As Cohen points

out, there is an argument for incentive inequality only when “the attitude of talented

people runs counter to the spirit of the Difference Principle itself”48. This is one way

in which any argument for incentives might be regarded as concessionary in ways that

make it merely prudential, rather than based on premises about what justice really

requires. For reasons such as these, Rawlsian theory is in a particularly difficult

position to justify incentive-demanding behaviour, even if it is possible that some

other moderately Egalitarian theory could do so.

45

See e.g. (2008: 68-86) 46

Because of this feature of maximin principles, is sometimes suggested that Rawls’s position is consequently not as strongly egalitarian as Rawls claimed it to be (see e.g. Temkin (2001: 134)). However, it is important to remember that Rawls’s use of a maximin rule is meant to be constrained by the other elements of Justice as Fairness. Very large inequalities that would be tolerated by the Difference Principle in isolation would likely by incompatible with the Principle of Fair Equality of Opportunity, for example. 47

This presentation of the criticism fits the argument of Cohen (1995). 48

(2008: 32).

18

Attempts have been made to respond to Cohen on Rawls’s behalf. One

assumption in Cohen’s critique is that requirements of justice can be incompatible

with certain sorts of behaviour, or psychological states, of citizens. However, one

feature of the Rawlsian view is that theories of justice regulate institutions, not the

way that individual people think or act. On its own, however, it’s not obvious how this

removes the conflict between incentive-demanding behaviour and ideals such as

reciprocity and fraternity. Cohen’s attack suggests that justice might not be so easily

dissociated from the direct regulation of individuals, especially given adherence to

these ideals. Authors aiming to defend Rawls on this point have thus emphasised the

idea that regulation of institutions counts among the better ways in which to instil the

sort of egalitarian ethos within which the better-endowed will not be disposed to

increase production only if offered incentives49. Cohen’s counter-reply is to point out

that this is merely a causal claim, at best establishing that regulation of institutions is a

means of ultimately regulating personal behaviour50.

The dialectic on incentive inequality is rather detailed and subtle, and the

above remarks only sketch some of the lines of argument. It is worth mentioning one

more dialectical move, which involves criticising Cohen’s view on its own terms. It is

plausible to say that the requirements of justice may simply be too demanding if

citizens are not permitted to give some special weight to their own interests. A

disposition to work only for incentives is one way in which citizens’ behaviour may

reflect this51. In addition, the abstract elements of Cohen’s criticism are rather under-

worked. Cohen appeals to the idea that when an individual “makes true” a premise in

an argument, this places a justificatory demand on that individual52. Incentive-

demanding behaviour is presented as an instance of an argument of this sort, where

better-endowed individuals are apparently unable to meet this demand. However, we

might wonder exactly why there is this relation between making an argument’s

premise true, and having to justify having done so. Whether or not these quibbles are

49

See for example Joshua Cohen (2001). 50

(2008: 377-81). 51

A point made by Estlund (1998). 52

Cohen describes this abstract point is the “interpersonal test” for normative arguments (2008: 35-38).

19

well-founded does not actually have much significance so far as the current dialectic is

concerned: Such responses to Cohen only show that some incentive inequality is

compatible with certain possible views about justice. It would take a different

argument to show that such inequality is compatible with Rawlsian justice. Such an

argument would have to do something to remove the tension between incentives and

particular Rawlsian values targeted by Cohen’s critique. Notwithstanding attempts by

Rawlsians to provide such an argument, Cohen’s criticism has considerable bite.

To summarise the argument of this section, the Rawlsian approach can be

regarded as subject to two difficulties. One of these, focused on incentives and

permissible inequality, has been relatively well-explored and will probably continue to

be written about. The other, concerning Rawls’s likening the endowment distribution

to a common asset, remains relatively unexplored. Both, however, are serious enough

to have doubts about whether Rawlsian theory offers the best prospects for a moderate

approach to endowment inequality. They warrant some search for an alternative

theory, given the possibility that other alternatives may occupy the logical space on

the spectrum between Libertarian and Luck Egalitarian responses to endowment

inequality. The important point to make here is that neither of the difficulties

discussed in this section are attached to the idea of endowment-mitigation as such.

Rather, they can be blamed on the presence of contract theory. It is the contract-

theoretic aspect of the Rawlsian view that explains both the presence of the values like

reciprocity and fraternity, and the talk about the distribution of endowments being

something like a common asset. Both of the criticisms we have seen are ones that

question whether these are plausible features of Rawls’s theory, and in particular

whether they are compatible with the possibility that some inequalities are

permissible. This compatibility is crucial to whether the Rawlsian approach

successfully describes how principles of justice guide the mitigation of endowment

inequality’s effects on the material distribution. Justice as Fairness remains, in many

ways, a rich and attractive position. But since it is our aim to find principles that

20

provide this particular sort of guidance, there is a strong case for wanting more than

what is offered by Rawlsian theory53.

1.5 Outline of a positive framework and methodology

When discussing Rawls’s Difference Principle, Robert Nozick offers the

following remarks about material equality:

If things fell from heaven like manna, and no one had any special entitlement to any

portion of it, and no manna would fall unless all agreed to a particular distribution, and

somehow the quantity varied depending on the distribution, then it is plausible to claim

that persons placed so that they couldn’t make threats, or hold out for specially large

shares, would agree to the difference principle rule of distribution. But...why think the

same results should obtain for situations where there are differential entitlements as for

situations where there are not?54

Nozick’s critique of Rawls was left out of the previous section on account of the fact

that, as an assessment of Rawlsian ideas in particular, it is too full of defects to be

worth an extended discussion55. In spite of this, Nozick’s political philosophy is full of

insightful remarks that ought to guide our thinking about distributive justice, several of

which I shall take guidance from in the course of this dissertation. The quoted passage

is the first such case, even if the guidance I shall take from it is not that which Nozick

intended, and of a sort that will only be more fully spelled out in later chapters.

Nozick’s claims focus on Rawls, but they contain a more general point.

Crudely speaking, Nozick’s concession is that a strongly egalitarian principle would

be plausible, but for the fact that other factors create the “differential entitlements”

that cannot be simultaneously honoured by Egalitarian redistribution. Now, Nozick

meant his remarks to convey the idea that the desirability of material equality is in

some sense ‘left behind’, or overruled by whatever generates entitlements that is not 53

Other criticisms of Rawls exist, besides those discussed in this section. Notable for being also related to the contract-theoretic spirit of Justice as Fairness are certain problems posed by intergenerational justice (see for example Barry (1989: 189-203). I discuss certain other problems relating to future generations in chapter five. 54

(1974: 198). 55

For an argument for this, see for example Kukathas & Pettit (1990: ch5).

21

itself some concern for equality. (This is in accordance with the general description of

Libertarian values given earlier on.) Nozick makes things sound as if a concern for

material equality could be upheld only in fantastically unrealistic conditions.

However, it is not the case that his remarks establish such a pessimistic conclusion,

even if perfect material equality itself could only be justified under unrealistic

conditions. The fact that it would take a fantastic situation for a certain value to be

decisive does not mean that the influence of this same concern can’t still be present in

what justice requires about a real state of affairs, where entitlements are substantially

affected by other factors. What I now want to explain is how we can agree with

Nozick's remarks (even if not his wider set of views), in ways that turn out to have

implications close to the sort he would have rejected56.

The core claims on which I wish to build are these. Suppose, as is in fact true,

that the material distribution arose from an unequal distribution of endowments. In

addition, suppose, as is in fact false, that the subsequent material distribution were a

perfect mirror of the endowment distribution. More precisely, suppose that any other

morally relevant factors, such that respective persons’ free choices, efforts, and so on,

simply cancel each other out, with respect to the entitlements that they generate. In

other words, imagine that, for any person in a distribution, factors besides endowments

either did not operate in ways different from those of other persons, or at least did not

differ in ways that would make interesting different contributions to entitlements.

Justice would require that, in this sort of case, distributive shares were made perfectly

equal. This would be due to the fact that material inequalities could be blamed on

endowment inequalities alone. As Nozick suggests, there is nothing to prevent the just

redistribution of such a material inequality apart from the moral relevance of other

factors. But such factors are, by stipulation, inert in the imagined case. No doubt this

state of affairs has a fictional air about it. Nozick’s wording implies as much.

56

It should be stressed that agreeing with what’s expressed in the passage would not imply agreement with Nozick’s overall position. Nozick’s view was that persons are entitled to their endowments, which would block the idea that Egalitarian redistribution would be appropriate even if endowment inequality were the only factor. At least part of Nozick’s rationale for this view is the fact that some endowments are conferred as a result of the choices of others (see above).

22

However, there is nothing objectionable about the use of hypothetical or fictional

cases to guide the development of abstract theories. After all, this has been done

before. What matters is that a view developed in this way can be made amenable to

more realistic situations by being sensitive to the sort of morally relevant features that

distinguish them from hypothetical cases.

What I am proposing suggests the following particular methodology. Its

features will become clearer in the next chapter, but some preliminary remarks may be

made here. One way of identifying a plausible principle of distribution is to search for

whatever principle may satisfy the hypothetical condition just outlined. In so doing, a

principle may be reached that permits sensitivity to whatever considerations, besides

facts about endowments, enter into the determination of persons’ differing

entitlements. Of course there are objections to the idea that other values can be

handled in this way, and these will need to be discussed in due course. For now, I want

to emphasise merely that by following a methodology such as this, novel content may

be given to the idea that justice requires the mitigation of the effects of endowment

inequality. What I shall try to show is that work on distributive justice has simply not

yet exhausted the question of whether a concern to restrict the impact of persons’

unequal endowments may be combined with proper attendance to other factors.

This concludes the brief statement of the strategy that will be executed over the

following chapters. As stated in this section, the strategy is undeniably abstract and

one might have doubts about whether it can yield results. Nevertheless, a novel

distributive principle does emerge as a direct result of an inquiry into what satisfies the

requirements of justice in the described hypothetical scenario. This is demonstrated in

the next chapter. And, if the arguments of the following chapters are cogent, then this

is a principle that may be combined with a serious sensitivity to the importance of

personal choice, responsibility, and effort in determining what persons are entitled to.

In so doing, a case may be made for how it might be possible to attend to the

apparently competing requirements of justice all at once, without relying on

intuitionistic trade-offs, and without relying on the introduction of substantive

23

controversial techniques that are apt to generate the sort of internal tensions we see in

Rawls.

24

Chapter Two: Methods of Aggregation

I shall now begin working towards a refinement of the general strategy that

was given a cursory sketch at the end of chapter one. To do this, I will need to

introduce a variety of concepts and techniques employed in more formal

representations of principles of distribution. With the help of these devices, I will

present a particular distributive principle that will be offered as a framework for a

theory of justice. At times, the level of detail that is introduced may seem more than

what is required to fill out the proposal of the last chapter. The reason is that I am

concerned to do rather more with the principle presented here than use it to develop

the ideas in chapter one. Later chapters will engage with further philosophical issues

about distribution, which have been studied somewhat separately from the classical

questions of distributive justice. The type of work done in this chapter completes

much of the spadework that will allow the presentation of later arguments to run more

smoothly.

2.1 Aggregation: Some preliminaries

My first aim in this chapter is to gain an understanding of the various methods

of aggregation that can be used to represent certain principles for regulating

distributions. In the most abstract sense, a method of aggregation is any means by

which a value is assigned to a whole, according to some way of processing the values

of the parts of that whole. This does not itself presuppose anything about the way in

which such processing occurs. I am therefore not using ‘aggregation’ as a narrow term

that merely means ‘addition’, as philosophers sometimes do. When applied to

distributions of welfare or goods, it may be said that a method of aggregation

evaluates a distribution according to facts about the lives lived by the persons in that

distribution. In other words, the parts of a distribution of welfare may be identified

with the welfare levels of its members.

25

At this point it is worth registering an important point about the way in which

we construe lives in a distribution as being better or worse than each other.

Throughout chapter one I talked, somewhat loosely, of persons as having different

levels of ‘distributive shares’, or of certain variations in the ‘material distribution’.

Both of these expressions were designed to be vague as to how persons are identified

as having better or worse social positions. Many more precise bases of interpersonal

comparison are available. It is possible to construe a distribution in terms of well-

being in a strict sense, that is, the literal quality of persons’ lives. Material shares may

also be identified with arguably more tangible goods, such as resources, income,

capabilities, or some hybrid. There has been much debate over which of these

‘metrics’ is the most plausible57. However, I intend to set this matter aside. It is

certainly true that the selection of a basis for interpersonal comparisons is going to

affect the implications of the relevant principle of distribution. However, this is

separate from the matter of what form of distributive principle is most plausible. In

fact, there is a strong degree of independence between these two questions. Since I am

interested, here, in the form of a principle of distribution, I will say nothing very

substantive about the ‘metric’ question. I will, however, have something to say about

it when discussing Luck Egalitarian views in chapter three.

Nevertheless, some basis of interpersonal comparisons needs to be assumed,

just to make it possible to talk more precisely about persons being better or worse off

than each other. The literature on methods of aggregation tends to assume that human

well-being is to serve as the basis for interpersonal comparisons. So that I can more

easily engage with the work that has been done on aggregation, I shall make this

assumption as well, but merely for convenience.

It is important to separate two senses in which the lives in a distribution have a

‘value’. First, a life has a value that can be identified with the overall lifetime well-

being of the person who lives it. We may refer to this first sense as a life’s personal

57

Some classic discussions are Sen (1979) and Rawls (1982). Cohen (2004) demonstrates the way in which stances in this debate have guided ways of refining the Luck Egalitarian view.

26

value. (We might say that a life’s personal value corresponds to how worthwhile it

would be to live this life.) Second, a life has what might be called its contributive

value58. This expresses what difference is made to the value of that distribution, by the

presence of that life in it. We may use the distinction between personal and

contributive value to improve on the abstract definition of aggregation that was given

above: Methods of aggregation assign a value to a distribution by first converting the

personal values of its lives into some set of contributive values, and then adding these

contributive values together.

The above definition helps us give a precise account of how different methods

of aggregation will disagree. Generally speaking, methods can be separated from each

other due to the different ways in which they convert personal values into contributive

values. Depending on the method of aggregation used, improving a life’s personal

value by n need not mean that its contributive value improves by n as well59. In other

words, personal and contributive value may not increase or decrease at the same rate.

A second way in which personal and contributive value may come apart concerns the

location of the zero on their respective scales: When the personal value of a life is zero

(the life might be said to be neither worth living nor worth not living) it does not

follow that the contributive value of this life is also zero. The fact that personal and

contributive value can come apart in these two ways means that many different

principles could be formulated.

I have said that methods of aggregation assign values to distributions. We can

extend this description by saying that such methods generate orderings of

distributions. This is just to say that distributions can be arranged into an ordering

according to what their respective assigned values are. The idea of an ordering can be

identified with a comparative relation of some sort. Very often, methods of

aggregation are normally understood as providing ‘betterness’ orderings of

58

This phrase is due to Arrhenius (2010: 8) 59 A life’s personal value could turn out to be the same as its contributive value. There is no incoherence in this. But (as we shall see) all methods of aggregation besides Classical Utilitarianism draw some distinction between these two values.

27

distributions60. On this view, distributive principles can be viewed as specifying which

distributions are better than which, which are worse than which, and which are equally

as good as each other. Such talk of the ‘betterness’ of distribtions is sometimes

claimed to be metaphysically or linguistically incoherent61. Political philosophers have

expressed related worries, even when they make use of principles that may order

alternative distributions in the way just described62. This suggests that it might be

possible to treat references to the ‘betterness’ of distributions as a shorthand for some

more complicated claims about the degree to which a material distribution matches the

entitlements of those living within it. When discussing Rawlsian claims in (1.3), I said

that it is hard to maintain any aversion to the influence of endowment inequality whilst

completely abandoning the idea that consequences may be made the object of

independent evaluation. Given this, there is some pressure to regard talk of the

betterness of outcomes as literal, even if reducible to claims about entitlements.

However, I shall proceed as if such talk really is just shorthand for something less

controversial. Appendix B examines whether a strong case has really been made for

the incoherence of ‘betterness’ claims in the relevant contexts.

2.2 Seven presuppositions regarding the concept of an ordering

I shall now work through some further presuppositions about aggregation.

These need to be registered in any serious work about aggregation even if they are not

always regarded as important by those working on distributive justice. Some of the

presuppositions I shall make are controversial ones. I shall not give full defence of

them here. The best I can do is gesture at possible routes of defence, cite defences

provided by others, or show that the assumptions are convenient rather than essential.

The following presuppositions are, however, all quite general: they are required by

any principle that could be used to compare any possible pair of distributions. When

discussing some particular methods of aggregation later on, further assumptions will

60

See Broome (2004a: 20-23). 61

See for example J.J. Thomson (1997). 62

Here I will again quote a remark from Rawls that I referenced in the preface: “A distribution cannot be judged in isolation from the system of which it is an outcome…If it is asked in the abstract whether one distribution…is better than another, then there is simply no answer to this question” (1999: 76).

28

sometimes be required. But these are best left until discussion of the relevant theory is

reached.

(i) The primacy of lifetime well-being

As I have said, distributions can be individuated as sets of lives, each subject to

a level of personal value, which a method of aggregation converts into a contributive

value. A first assumption is that the personal value of a life can be identified with the

overall lifetime well-being of the person concerned. Lifetime well-being can be

distinguished from well-being at some point in a life, or during some period within a

life63. It is a standard view that methods of aggregation process information about

lifetime well-being. This is natural enough. Intuitively, what really matters is how

some person’s life goes overall. Of course, wellbeing during or at a time does not get

ignored, since it still makes some contribution to lifetime well-being. I will not say

any more about the relation between these ways in which we might refer to a person’s

well-being64. Nor will I have anything to say about what well-being’s content is –

whether increased well-being consists in the satisfaction of certain desires, being

subject to certain experiences, or any other view65.

(ii) Distributions as possible worlds

A second assumption is that distributions are eternal. That is to say, a

distribution is a set of all lives that will ever be lived, not as some set of lives being

lived at a particular time. Different distributions therefore correspond to different

possible worlds. Although this ‘eternity’ assumption is standard in the literature on

aggregation, it can seem strange given the language normally associated with ideas

63

Following Arrhenius (2010: 7-8) personal value can thus also be distinguished from various other senses of the value of a life, such as its aesthetic value, or the moral worth of the person who lives (insofar as this comes apart from lifetime well-being). 64

These include so-called ‘shape of life’ questions as discussed by Velleman (1991), or how to weigh longevity, something discussed in different ways by Arrhenius & Rabinowicz (2005) and Broome (2004b). 65

This question may not even arise (or at least be less difficult) on a non-welfarist metric. However, the distinction between the lifetime quality of a life and its quality at or during a time is one that remains irrespective of the basis of interpersonal comparison.

29

about justice and redistribution66. In particular, it is often natural to talk of

redistribution as something that alters a distribution of welfare, or turns one

distribution into another. Such talk is odd if distributions are eternal; one cannot

‘move’ from one possible world to another. Fortunately, there is no incompatibility

between distributions construed eternally and the language of changing a distribution

by redistributing among the lives in it. The reason is that many eternal distributions are

identical up to a certain point in time. Thus, the idea of ‘moving’ from one distribution

to another can just be understood in terms of one eternal distribution being actualized,

rather than some other eternal distribution being actualized, when both distributions

are identical up to the point in time at which the ‘change in distribution’ takes place.

This fits with possible-worlds talk, whereby the actual world mirrors several possible

worlds up to a certain point in its history, after which it is identical with just one of

these worlds. All subsequent talk of ‘altering’ the distribution should be understood as

convenient shorthand for actualising one eternal distribution rather than another.

(iii) Anonymity

A third assumption is that orderings of distributions are anonymous. Roughly

speaking, this means that the evaluation of a distribution is independent of the

identities of the persons in it. For any two distributions, whether one is better than the

other is unaffected by the degree of overlap between the identities of their respective

members. In effect, the anonymity assumption just means that information about

welfare is all that matters. A more intuitive way of understanding why we might make

the assumption is this: If we adopt some distributive ideal such as, say, concern about

people being badly-off, this may count as an aversion to the fact that some people are

badly-off, or an aversion to the fact that those who are in fact badly-off just happen to

be the ones who are badly-off. Evidently the first view would, as a default, be the

more plausible: Aiming to improve the welfare of the badly-off is not just the aim of

66

It is shared by Arrhenius (2010: 32) and Broome (2004a: 19). I should say that my use of the word ‘distribution’ is equivalent to Arrhenius and Broome’s use of the word ‘population’.

30

improving the position of those who just happen to be badly-off, but to make it the

case that no (other) person satisfies the description of being badly off67.

The extended rationale for anonymity is just the need to compare distributions

that do not contain all the same people68. Very often policies that affect a material

distribution will also affect the identities of who will live in the future. But this does

not serve as any reason to not evaluate such policies69. The fact that affecting a

distribution may also affect who exists has been much discussed. In the course of such

discussions, certain authors have casted doubt on the need for anonymous principles of

distribution. However, the work of such authors has been criticized elsewhere, and I

can’t think of anything worth adding to what has already been said70. In light of this

fact, I will just proceed with the anonymity assumption in place.

(iv) Comparability

I shall now move on to the first really controversial assumption. Attaching a

personal value to each life in a distribution includes the assignment of a numerical

value to that life. This presupposes an ability to compare different live’s lifetime well-

being very precisely. Specifically, it requires that welfare can be compared on a ratio

scale. The idea of ratio scale measurement is that we may say such things as ‘this

person’s life is n times better than that person’s life’. Notice that this claim is stronger

than any assertion about how large the gap is between the welfare levels of two

persons, (this presupposes what is known as an interval scale). Use of a ratio scale

requires that a zero be set for welfare (an interval scale does not). Without a ratio

scale, we cannot say what total or average welfare is. Now, just about any existing

method of aggregation presupposes a ratio-scale. As such, this dissertation could not

be written without including the assumption that welfare can be measured in this way.

67

This point is often not made very clear in the literature, but Rawls realized the anonymity of distributive principles when he denied that the badly off be identified independently of their shares, by way of claiming that “least advantaged” is not a rigid designator (2001: 59fn). 68

Derek Parfit described this as the need to solve what he called the “non-identity problem” (1984: ch 16) 69

This approximates to what Parfit called the “no difference view” (1984: 366-71). 70

See, for example, McMahan (1998).

31

As I have said, such a precise assumption is controversial. The most I can say in its

favour is that there exist serious attempts to defend it in the literature71.

(v) Transitivity

The next assumption is that the ‘better than’ relation is transitive. This

assumption implies that if one distribution is better than a second, and the second

better than some third, then the first distribution is therefore better than the third one.

Transitivity is commonly exhibited by comparative relations; relations that are non-

transitive tend to be non-comparative. Some claim that transitivity is an analytic

feature of comparative relations72. Transitivity can fail in weak or strong ways. A

strong failure is for an ordering to be ‘cyclical’, in which case the ‘better than’ relation

orders a series of items such that the first member in this series eventually re-enters

this series lower down in the ordering: A may be better than B, B better than C, and C

better than A). The weak failure does not imply a cycle: A may be better than B, B

better than C, and C not worse than A). Some authors have argued that the transitivity

of ‘better than’ can fail in the weak sense73. Since the arguments of these authors take

some time to lay out, I will rely on the replies that others have made on behalf of

transitivity74. So I shall make the assumption without (additional) defence.

(vi) Completeness

I assume, also, that on any distributive principle, the ordering of distributions

is complete. An ordering may be said to be complete when any two items in its field

are such that one is better than the other, or else they are equally as good as each other.

In the current context, the completeness assumption states that no two distributions are

incommensurable. A standard definition of incommensurability is just the idea of two

items being neither better nor worse than each other, nor equally good75. The

71See the exchange between Bradley (2008) Broome (2008). For a much more detailed discussion of aggregation and measurement than the one I have given here, see Arrhenius (2010). 72

E.g. Broome (2004: 50). 73

The most active proponent of this view is Larry Temkin, see e.g. (1996). 74

E.g. Binmore & Voorhoeve (2003), Broome (2004a: 50-63) 75

Raz (1986: 322).

32

completeness assumption can seem very strong. Why think that the values of two

distributions can always be compared? Some reasons for denying completeness tend to

arise only once a certain method of aggregation has been selected76. A general point

about incompleteness is that certain complications attach to the idea that distributions

may sometimes be incommensurable. Arguments for completeness, which make use

of difficulties with incommensurability, can be found elsewhere77.

(vii) Non-relativity

My final assumption concerns whether to accept relativism about the ‘better

than’ relation. One possibility is that a distribution can only be considered better than

another relative to some standard, or point of view78. Various sorts of relativism are

possible. The most plausible form of relativism is a version of one on which the value

of a distribution is relative to who exists. Its rationale comes from a sort of intuitive

asymmetry between prospective and retrospective evaluations of some person being

caused to exist. Very often, we will say that it may be a bad thing for some child to be

born, based on knowledge about what this child’s life would be like. But should it

happen that such a child is born, we do not like to claim that this child’s existence is a

bad thing79. Relativism can be invoked as an attempt to make these asymmetric

attitudes compatible with each other. If the value of the distribution containing this

child is conditional on whether this child exists, then both prospective and

retrospective evaluations may be true80. I believe we should reject relativism.

Although I share the asymmetric intuitions that motivate it, relativism accommodates

these intuitions at a cost. The basic problem with relativism is the implication that

some policy might have a good (bad) outcome, even though we will know that once

76

Amartya Sen has claimed that attempts to find an Egalitarian method of aggregation counts against the completeness assumption. See for example (1992: 48). 77

See Broome (2004a: 168-71). This argument is closely related to one of Broome’s that I discuss in chapter five. 78

This is not the same view as the one on which the ‘better than’ relation needs to be three place (see above, and also appendix B), although this might be viewed as a form of relativism. 79

This case was first discussed by Parfit (1984: 360). 80

Some attempt to vindicate the discrepancy of intuitions attaching to prospective and retrospective evaluations can be found in McMahan (2005b) and Velleman (2008).

33

this outcome obtains, it will be true to say that the policy has brought about a bad

(good) outcome. This is implausible, particularly if one wants to arrive at views that

will guide the regulation of distribution. My view is that we should give up the

retrospective intuition, or at least reinterpret it. If a child is born with a condition that

grounded an earlier aversion to this child’s birth, then our evaluation of the child’s

existence should not change afterwards. The intuition that we should change our mind

arises, I suggest, out of our confusing the contributive value of a life and the extent to

which a life matters, or is some object of value or importance in itself. Instead, we

should distinguish the value of a life from the value of the person who lives it. To

claim that a life has a negative contributive value does not, although it can seem as if it

does, imply that whoever lives this life is less valuable in themselves. Relativism is

worthy of further discussion than this, but this is as far as I shall go81.

2.3 Separability and linearity

There exist three broad classes of theory among the various methods of

aggregation that are possible. These are Utilitarian, Prioritarian and Egalitarian types

familiar from both the formal and informal literature. Other classes are sometimes

introduced but, as I shall argue, their introduction is not really helpful. I shall argue

that members of each of the three classes can be separated according to whether they

bear one or another combination of just two properties. The work of this section will

establish a sort of taxonomy that I will make use of at various stages in later chapters.

The two properties on which I want to focus are separability and linearity. A

theory is Prioritarian, Utilitarian, or Egalitarian according to whether it bears one,

both, or neither of these two properties. The property of separability can be understood

in connection with the idea of atomism about value. Speaking very roughly, atomism

is the view that the value of a whole (e.g. a distribution) can be derived by processing

the value of its parts, so to speak, one part at a time. Atomistic views are represented

by non-separable functions. More formally, a function G is strongly separable if and

81

As it happens, further discussion reveals further problems: see Schroeder (2007).

34

only if it can be applied to a distribution (w1, w2,…wi) such that the value of this

distribution is equal to G(w1) + G(w2) + … + G(wi)82. A non-separable function is any

that does not satisfy this definition. Utilitarian and Prioritarian functions tend to be

strongly separable. Egalitarian functions tend to be non-separable. Whilst separability

can be understood in terms of value-atomism, non-separability can be associated with

the idea of value holism. Roughly speaking, holism is the view that the value of a

whole cannot be inferred by way of a process where the contributive value of each part

holds irrespective of the relation between that part and other parts. (It is sometimes

said that holism excludes the idea that the whole’s value is equal to the sum of the

values of its parts. As I shall explain in chapter four, holism excludes more than this.)

The important point, for now, is just that a non-separable method of aggregation tends

to make the value of a distribution sensitive to certain relations between the well-being

of different lives in that distribution.

The property of linearity is rather more straightforward than separability.

Linearity can be understood in terms of what a theory implies about redistributive

transfers. For a method of aggregation to be strictly linear, it must exhibit a perfect

indifference to transfers. Utilitarianism is the only theory that is strictly linear. It is

sufficient, given the purpose at hand, to define a strictly linear function as any function

that is incompatible with a weak formulation of the well-known Pigou-Dalton

condition:

The Weak Pigou-Dalton condition

A distribution <(n+½m), (n+½m)> is better than a distribution <n,

(n+m)>, for at least some positive values of n and m.

This condition just says that some transfers are a good thing. It is neutral as to which

transfers are good and which (if any) are not good. The scope of the condition is also

restricted to transfers that do not affect total welfare, and where population size is held

82

For a fuller account of separability see Broome (1991: ch4, esp 68-70). The definition I have used corresponds to what Broome calls ‘additive separability’. He also defines a number of weaker forms of separability, but the relevant distinctions do not matter here.

35

fixed. Obviously, there are different ways in which the Pigou-Dalton condition could

be strengthened, up to the point that all transfers are favoured. I shall have reason to

come back to stronger versions of the condition later on. But the weak formulation just

given says enough to tell us what linearity amounts to.

2.4 Utilitarian theories

There exist several Utilitarian methods of aggregation. According to Classical

Utilitarianism, any set of distributions can be ordered according to the respective total

welfare of the distributions in that set: The higher the total, the better the distribution

(the higher its place in the ordering). Classical Utilitarian theories can be written as the

following function:

∑

i

iw )(

This function says that the value of a population is the sum of the welfare, w, of each

member, i, of that particular population. It is possible to represent this function using

the following graph:

36

The horizontal axis serves as a scale for welfare, and the vertical axis acts as a scale

for contributive value. The graph has a perfectly straight line. This reflects the fact

that, on Classical Utilitarianism, the value of any change in a distribution of welfare is

equal to the size of that change (i.e. its effect on total welfare). Any fixed-size move

along the horizontal axis, wherever it occurs, corresponds to a fixed-size move along

the vertical axis. Thus, adding n units of welfare to someone whose welfare is very

low counts for the same as adding it to someone whose welfare is higher. Distributing

the addition of n units amongst several people will also have no effect on the value of

this addition.

An alternative to the Classical Utilitarian view is a method of aggregation

commonly known as Critical-Level Utilitarianism (CLU). I will get round to singling

out CLU for some special discussion in chapter five, and will just give it a short

introduction now. CLU can be written as the following function:

∑ −i

i Lw )( where L > 0.

In other words, the value of a distribution is the sum of the welfare of each person,

once some critical level is subtracted from that person’s welfare. This critical level is

some welfare value located some distance above the point at which a life is worth

living (i.e., zero welfare). A graph for CLU is depicted on the next page:

37

Like the classical one, CLU’s function is strictly linear. The difference between CLU

and Classical Utilitarianism is that the zero for welfare is no longer at the same level

as the zero for contributive value. As I have indicated in the graph’s labelling, it is

now located at, -n, which stands for some unspecified negative contributive value83.

The intersection of the lines is now at the zero for contributive value and the critical

level L. An interesting consequence of this difference is that, according to CLU, the

addition of a person is not as highly valued as an improvement of an existing life

when total welfare would be increased by the same amount in either case.

Another Utilitarian theory is Average Utilitarianism. This theory is actually

quite different, structurally speaking, from other forms of Utilitarianism. Its principal

difference, it will turn out, is that Average Utilitarianism has a non-separable function.

This makes writing a graph for it less straightforward; non-separability means that

contributive value cannot be ‘read off’ personal value. But it is clear that Average

Utilitarianism violates the Weak Pigou-Dalton Condition: no transfers among a fixed

number of lives, when total welfare is held constant, will affect average welfare.

Accordingly, Average Utilitarianism attaches no value or disvalue to transfers, just

like other versions of Utilitarianism. 83

A purely technical point might be made here: It is standard practice in the aggregation literature to write graphs such that the line goes through the origin. We could instead leave the axes alone, and move the line downwards/to the right. This would be another way in which the zero for personal and contributive value could be made to not coincide, although it would still be true that the graph’s axes intersect at the zero point on both scales.

38

2.5 Egalitarian theories

Roughly speaking, Egalitarian methods of aggregation attach some negative

weight to inequality between the personal values of lives: More intuitively, a theory is

strictly Egalitarian if and only if the value of a distribution increases whenever the

degree of inequality in it decreases, other things being equal. The presence of the

‘other things being equal’ clause indicates an important fact about Egalitarian theories:

they cannot plausibly make the value of a distribution sensitive to inequality and

nothing else. If inequality were all that mattered, then two distributions would be

equally good even if everyone led equally wonderful lives in the first and everyone led

equally horrible lives in the second: Because this sort of view is so implausible,

proponents of Egalitarian aggregation generally do not present themselves as pure

Egalitarians84. Instead, they favour a view on which the disvalue of inequality is

weighed against some other value, typically total welfare. This is reflected in the way

that Egalitarian methods of aggregation are formulated. A simple formulation is this

one:

Ι−

∑i

iw )(

According to this function, the value of a distribution is equal to its total welfare

minus the present degree of inequality, denoted by I. It is, of course, possible to weigh

inequality against something other than total welfare. However, no points I am going

to make about Egalitarianism are affected by this. Therefore, I will make the

simplifying assumption that total welfare is the only other input attached to Egalitarian

methods of aggregation. Now, the Egalitarian function is non-separable. This is

because the value of the distribution does not depend merely on the repeated 84

See Hirose (2009), Temkin (1993).

39

application of some function to the welfare of each life in the distribution. The

presence of I is a reflection of this85.

In chapter four, I shall develop some general doubts about non-separable

methods of aggregation. I shall register a couple of other problems related to

Egalitarian methods in particular now. A first point is that inequality’s badness might,

so to speak, already be ‘factored in’ to the welfare information about the various lives

in a distribution. This is a possibility that John Broome refers to as “dispersion”86.

Dispersion is particularly plausible if the badness of inequality consists in its being

unfair, or involving persons being treated badly in some way (just because a life

containing unfair treatment is, other things being equal, a worse life for that). If the

badness of inequality is dispersed among the lives within a distribution, then it is

possible that the Egalitarian welfare function commits a fallacy of double-counting.

A second challenge for Egalitarians is to identify a measure of inequality that

can occupy the position of I in the Egalitarian welfare function. Even if it can be

maintained that inequality of welfare is bad in itself (not dispersible), an account needs

to be given of what an increase or decrease in inequality consists in. Sometimes it is

clear which of two possible distributions has the greater inequality. But often it is not.

This shows that a full set of conditions under which inequality increases or decreases

is difficult to indentify. The following set of distributions makes this difficulty more

visible. (Since the example concerns inequalities, use of numerical values will make

things less cumbersome.)

Person A Person B Person C Person D

Distribution J 10 50 50 90

Distribution K 20 20 80 80

Distribution L 25 25 25 125

85 Even if the function were written out such that some fraction of I was applied to each life separately (perhaps 1/n where n is the number of lives), then varying the welfare of one life would affect the value of I, and hence the contributive value of other lives. 86

(1991: 110-1). Arrhenius (2009: 229-330) provides a very succinct explanation of how inequality’s disvalue may plausibly be dispersed.

40

Each population here is subject to the same total welfare. Therefore, if the Egalitarian

welfare function is to be used, J, K and L must be ordered according to the facts about

their respective inequalities. However, it is not obvious which population is subject to

the largest inequality. In population K, for example, the gap between the top and

bottom (often called the range of inequality) is smaller than in J. In this sense, K has

less inequality than J. However, J also has fewer people at the extremes than K does,

which suggests a respect in which K has more severe inequality. In distribution L,

everyone is at one extreme or the other, but more people are at the lower extreme than

the upper (or, to put it another way, the greater portion of total welfare is more

‘concentrated’ among the best-off). On some other measures, this makes the inequality

in L greater than that in J or K (though no one in L is as badly off as the worst off in

both J and K?). I will not bother to go through the various statistical measures of

inequality and demonstrate how they disagree as to an ordering of J, K and L. This

would take a long time87. It is clear enough that, although there is obviously some

inequality in each of the populations, it is not easy to say in which it is the greatest.

The fact that Inequality is subject to multiple dimensions has led some to question the

possibility of a complete Egalitarian ordering of distributions. Amartya Sen writes:

[Egalitarian theories] are inherently defective since inequality as a notion does not

have any innate property of completeness…the concept of inequality has different

facets which may point in different directions, and sometimes a total ranking can not

be expected to emerge.88

Sen thinks that we might be able to make Egalitarian comparisons of distributions that

differ only with respect to one dimension of inequality. But an attempt to go beyond

this will require a way of combining measures which Sen thinks are, in some sense,

incommensurable. In other words, Sen’s view is that there is nothing that could play

the role of I. Some have argued that Sen’s strong scepticism is unwarranted, but

concede that the multi-dimensional nature of inequality makes it hard to construct a

87

For a thorough philosophical discussion of measures of inequality, see Temkin (1993: ch.5) 88

(1997: 47-48)

41

workable Egalitarian theory89. At least, the problem of a choice between multiple

dimensions of measurement is not one faced by other theories. As long as we want a

theory to equip us with the ability to compare any possible pair of distributions,

Egalitarians will need to solve the problem of identifying I. This is not something I

will make a sustained attempt to do. I do, however, discuss one possibility in

Appendix C.

2.6 Prioritarian theories

I will now turn to Prioritarian forms of aggregation. Prioritarianism is so-called

because it reflects the idea of giving priority to those who are worst off. Derek Parfit

identifies this view with the claim that “benefiting people matters more, the worse off

these people are”90. In the literature on aggregation, there is general agreement that

Prioritarians should aggregate by summing a concave transformation of the welfare

levels within a distribution91. This method of aggregation can be written like this:

∑i

iwV )(

The parameter V acts such that the contributive value of a life is a strictly concave

transformation of its personal value, w. (A parameter can be defined as any element of

a function that manipulates some sort of input variable, without being an input

variable itself). Roughly speaking, a transformation is strictly concave when its output

value increases at a steadily lesser rate than its input value. In other words, each time

the input is raised by some constant amount, the output also increases, but by some

increasingly smaller amount. The effect of evaluating distributions with the use of a

concave transformation like V is that greater weight is given to improving the welfare

of people, the lower their welfare ex ante. This all becomes more visible with the help

89

This, for example, is Temkin’s view. 90

(2001: 101) 91

E.g. Arrhenius (2010), Broome (1991: 178-79, 216), Blackorby et al (2005), McCarthy (2008) Rabinowicz (2002).

42

of a graphical representation of a strictly increasing, strictly concave function. Here is

a graph for standard Prioritarianism92:

The fact that the graph gradually becomes less steep means that fixed-size movements

along the horizontal (welfare) axis produce gradually larger movements up the vertical

(value) axis, the further left on the horizontal axis they occur. This captures the

Prioritarian slogan that benefits count for more, the worse off their beneficiary.

The curve of the graph reflects the way in which Prioritarian functions favour

transfers. It is possible to label the graph in ways that help demonstrate this:

92 This graph assumes no particular identity for V. But, bearing in mind that many different devices of transformation exist, it should be noted that different ones will generate slightly different curves.

43

It can be seen that changing a better-off person’s welfare by n units counts for more

than changing the welfare of a worse-off person by the same amount. The value v*

represents the value of the change in the better-off person’s welfare, whilst v

represents the value of the change in the worse-off person’s welfare. The fact that v >

v* indicates that the disvalue of lowering a better-off person’s welfare by n is

outweighed by the positive value of increasing a worse-off person’s welfare by the

same amount. This is how a concave function favours transfers. Indeed, the fact that

the graph curves demonstrates that the Prioritarian function is non-linear.

We can illustrate Prioritarian aggregation further by examining a particular

example of V at work. A familiar example of what could play the role of V is the

square root93. Use of square roots would allow us to write the Prioritarian method of

aggregation like this:

∑i

iw )(

It is easy to explain how use of roots captures the broad Prioritarian idea. The gap

between the square roots of 10 and 20 is larger than the gap between the square roots

of 70 and 80, even though the gaps between the numbers themselves are of the same

size. This means that an increase in welfare of 10 units is worth more when given to

someone living at the level of 10 than it is when given to someone living at the level

of 70. A benefit is therefore most valuable when it accrues to whichever person is

worst-off.

Prioritarianism satisfies the Pigou-Dalton condition in an entirely unrestricted

form, not just the weakened form mentioned above. It is easy to see how: The move

93

As a matter of fact, √ is not regarded as a good candidate for V because it cannot be used to transform negative welfare levels, which is a problem if we believe that there is no lower bound of well being (in which case negative numbers will need to be used to represent some welfare levels). A better, but more complicated concave function makes use of logarithms. The issues here can become quite technical and, since distinctions between different concave functions do not bear hugely on the issues I want to discuss, I will set them aside.

44

from <n, (n+m)> to <(n+½m), (n+½m)> involves raising one person’s welfare and

lowering another’s, by the same margin. Since the raising accrues to the worse off

person, its positive value is greater than the disvalue of lowering the other person’s

welfare. Therefore, the overall value of the change is positive. Using the example of a

square root, for any positive values of n and m, it will be true that (√(n+½m) +

√(n+½m)) > (√n + √(n+m)). The fact that the values of n and m do not matter is what

confirms that a fully strong Pigou-Dalton condition is satisfied.

The standard Prioritarian function is strongly separable. This is clear from the

fact that the contributive value of each life in a distribution is gained just by taking

some transformation of it, where this transformation is independent of the facts about

the welfare of others. This fact helps explain the contrast with Egalitarianism in a

more principled way. Derek Parfit says that, according to Prioritarianism:

What is bad is not that…people are worse off than others. It is rather that they are

worse off than they might have been.94

Based on this claim, Parfit adds the following remarks:

The chief difference [between equality and priority] is this. Egalitarians are concerned

with relativities: with how each person’s level compares with the level of other

people. On the Priority View, we are concerned only with people’s absolute levels.

This is a fundamental structural difference.

Parfit’s reference to absolute levels corresponds roughly with the property of

separability introduced to at the start of this chapter. This is easy to see: the

Prioritarian function applies a concave transformation V to each person’s welfare,

taken on its own. For the welfare level of any single person within a distribution, the

result of this transformation will be the same regardless of what the welfare of other

persons is, or how many other persons there are. Thus, V satisfies the description of G

that formed part of the definition of strong separability given earlier on. It should be

noted, though, that the relation between separability and a concern for absolute levels

94

(2000: 104)

45

is not one of identity: Views that allow a life’s contributive value to be defined in

ways guided by what the average is count as non-separable, because the average

depends on the welfare of all lives in the distribution. However, it can still be accurate

to describe such a view as being unconcerned with relations between levels.

To summarise what I have said over the last four sections: We now have a

means of separating three different classes of aggregation. Whether a theory counts as

Utilitarian, Egalitarian, or Prioritarian depends on what combination it exhibits of the

properties of linearity and separability. I have described both of these properties

formally and informally. The main point of making these distinctions lies in their

being useful as a means of assessing theories that depart from the more

straightforward statements of the three distributive ideals already discussed. In

particular, the method of categorizing theories according to ideas of linearity and

separability will be helpful in assigning a more precise content to some of the informal

ideas in the literature, and in determining the extent to which certain proposals

represent very novel ways of ordering distributions. It is now time to return to chapter

one’s main idea.

2.7 The piecewise-linear function

Consider now another function:

46

Unlike the constant curve of the standard Prioritarian function, we now have a sort of

‘kinked’ line. The function is not strictly linear, but not strictly concave either. It

‘curves’ insofar as it is made up of straight segments of differing steepness. As such, it

is what is known as a piecewise-linear function. Piecewise linear functions have not

yet been subjected to any detailed discussion in the literature on aggregation or

distribution, or for that matter the literature on distributive justice95.

The method of aggregation identified with a piecewise-linear function, such as

that above, can be written like this:

{ }{ }∑ ∑< ≥

−+−Lww Lww

ii wLBLwA )()( where A > B > 0, and L > 0

Here is what the above formalization says: There exists some fixed threshold L,

identified with some positive level of welfare. There also exist two parameters; the

linear weightings A and B. These parameters do not transform welfare levels. Instead,

they transform the gap between a person’s welfare and the threshold L. Which

parameter gets used depends on whether the relevant life’s personal value is at least as

high as the threshold, L. The method of aggregation gives greater weight to deviations

below L than to deviations above. That is to say, if a person’s welfare is less than L,

then the weaker parameter B is used to transform this deviation. The fact that the

parameters are of different strengths is what accounts for the graph having a steeper

lower segment than its upper segment. The steeper segment is that corresponding to

the range of welfare levels that deviate below L and thus fall within the scope of the

stronger parameter A. It follows from this that the graph’s kink is located at the level

of welfare identified with L.

Before explaining how the piecewise-linear function relates to the ideas of

chapter one, I shall make two clarifications. First, any recourse to the idea of a

threshold when presenting views about distribution tends to stimulate certain reactions 95

A piecewise linear function is identified as a possible view in the literature on welfare economics – see Blackorby et al (2005: 36).

47

about what the use of thresholds is motivated by, or committed to. Most common is

the view that the location of L must be identified with some idea of a ‘sufficiency’

level, or point at which we might say that a person ‘has enough’. This reaction is to be

discouraged. The concept of sufficiency does not play any role in the motivations for

the piecewise-linear function or in its development. The location of L is, of course, a

crucial matter, which I shall soon address. I want to set aside any pre-occupation with

‘sufficiency’ before doing so. It is true that one could formulate a piecewise-linear

function whose threshold was understood in terms of sufficiency, but this would make

for a different project from the one in which I am engaged. None of this is to say that

nothing interesting could be said about sufficiency, however, and I will offer some

remarks in the chapter’s final section.

A second point relates to the fact that, extensionally speaking, the function

proposed might be viewed as a variation on the Prioritarian one. Recall, the informal

Prioritarian idea states that benefits count for more, the worse off the beneficiary is.

The function that I have just presented is a non-linear, and it is also, at least in

principle, a strongly separable function. This means it could be viewed as an

alternative refinement of the informal Prioritarian slogan: The piecewise-linear

function implies that some fixed-size benefits count for more than others, and that a

benefit can be made to count for more only by lowering the welfare of its recipient ex

ante. The function just falls short of saying that benefits always count for more when

the recipient is made worse off by some amount, as on a strictly concave function.

Now, another aspect of my experience, in presenting the piecewise-linear function to

others, is that philosophers have an urge to categorise it under Prioritarianism or at

least one of the main taxonomic categories. One reason why I wish to resist labelling

the view as a weakened Prioritarianism (in anything other than an extensional sense) is

the fact that it is not being motivated purely by some primitive or intuitionistic desire

to promote the well-being of the worse-off for its own sake. Indeed, it is doubts about

such motivations that sometimes lead people to reject the piecewise-linear function,

upon having decided that it is a version of Prioritarianism. All of this assumes,

wrongly, that the function is being motivated by intuitions about the allocation of

48

benefits comparable to those offered in favour of Prioritarianism. On the contrary,

however, part of the point of distributive justice is that there is rather more to the

regulation of material shares than questions about optimal allocation96.

In chapter one, I proposed a view about distributive justice that can be

summarised in the following way: A plausible principle for regulating material

inequality will satisfy the condition that, were endowment inequality the only factor

affecting material shares, then this principle would recommend the equalisation of all

shares. A piecewise-linear function would favour a fully equalising series of transfers

under exactly one set of circumstances, which may be regarded as very unlikely to

occur, even in principle. The relevant circumstances would obtain when there is equal

total deviation on either side of the threshold L. In other words, such circumstances

can be identified with any material distribution in which the total amount by which

persons’ welfare falls below L is an exact mirror of the total amount by which other

persons’ welfare exceeds the level of L.

The limited range of situations in which the function favours such equalisation

can be regarded as identical with the idealised scenario, discussed at the end of chapter

one. This is the imagined case in which inequality of endowments are the only factors

that make a difference to the material distribution. This identification can be secured

by setting the location of L in an appropriate way. Specifically, L can be understood as

located at the average level of expected welfare, given endowments alone. Now, to

say that L is identical with average welfare in a certain hypothetical scenario leaves

certain questions unanswered. For example, we might wonder exactly what is meant

by the idea of inequality of endowments being the ‘only’ factor making a difference to

the material distribution. More specifically, we might wonder what else is being held

96

Discussions of Prioritarianism, and indeed much work on methods of aggregation, seem to be linked more closely to what Rawls called “allocative justice”, than to distributive justice. For Rawls, allocative justice concerned the narrower, more theoretical problem of “how a given bundle of commodities is to be distributed, or allocated, among various individuals...who have not co-operated in any way to produce those commodities” (2001: 50). In distributive justice, entitlements are sensitive to much more than this, and principles suitable for allocation problems may not be plausible in a distributive setting. The restricted context of allocative justice is noted by Parfit (2001: 82), but the Rawlsian distinction is not often acknowledged in recent work on principles of distribution.

49

constant. There are logically stronger and weaker answers to this question. To see this,

realise that two people may be equally badly off because of having equally bad

endowments, but still differ as to their preferences, dispositions to choose wisely or

poorly, willingness to take on the burdens associated with the sorts of occupations that

superior talents would have made optional, and so on. These other factors may in fact

be causally inert, but they might be thought to affect entitlements nonetheless:

Someone could be badly off in ways that their poor endowments prevent them from

doing anything about. However, it may be true of such an individual that, were they to

have been better endowed, they would have been poor at converting these superior

endowments into a better material position. For this reason, we might wonder whether

their entitlements to compensation are weaker than those who might have done more

with a superior set of endowments. I do not mean to take a stance on whether this is

so. The possibility being mentioned is one that allows clarification of the hypothetical

scenario as involving more than the mere causal inefficacy of non-endowment facts.

What is being claimed about the hypothetical case is this: For any person

worse off than some other better endowed person, the worse off person would have

been just as materially well off as their better endowed counterpart in fact is, were

they to have had the same, superior endowments as that counterpart. This claim is not

obviously part of the prior claim that facts about endowments exhaust the explanation

of how well off different people are. Its presence is therefore required to secure the

idea that facts about endowments are the only facts that vary in morally relevant ways

across different people. More generally, the hypothetical situation being considered

needs to be understood as one in which not only are non-endowment factors causally

neutral. In addition, it is stipulated that differently endowed people would still not

have differed with respect to the facts about non-endowment factors in their lives

(their willingness to work, disposition to accept gambles, etc.), had there not been any

difference between their endowments. In this way, the hypothetical scenario is perhaps

more distantly abstract than it would otherwise be, but this does not undermine the

theoretical role it is intended to play. Overall, the rationale for setting the threshold at

the average expectation given endowments is that we thereby gain a principle of

50

distribution that is guaranteed to eliminate material inequality only in a case where

endowment inequality is the sole determinant of the material inequality that exists

(and where other determinants are rendered inert in the strong sense described above).

We may now focus on how the piecewise-linear function provides guidance for

the regulation of non-hypothetical, real material distributions. In real cases, the

coincidence of L’s location and the actual average welfare level will typically not

obtain. This is how the piecewise-linear function will allow for a substantial range of

permissible inequalities whilst still identifying impermissible ones in ways that track

the presence of endowment inequality, whilst providing a framework than can

accommodate the relevance of other factors in the calculation of entitlements. It is the

primary virtue of the piecewise-linear function that it can combine an egalitarian

response to endowments with room for these other elements. In so doing, it provides a

novel way in which we may develop a moderate position, exhibiting the focus on

mitigating the effects of endowment inequality described more abstractly in chapter

one.

Now, the way in which the piecewise-linear function can accommodate the

moral relevance of factors beyond endowment inequality is something I have not yet

said anything substantial about. I shall concentrate on exploring this issue in the next

chapter, and will extend the study of the function in chapters four and five. What I

have done in this chapter is give the main positive rationale for the piecewise-linear

function, having earlier laid out the conceptual background. To some extent, the

arguments of later chapters will consist in comparing the framework offered by this

function with dominant alternatives in distributive justice, such as Luck

Egalitarianism. If the argument of this chapter is cogent, then the piecewise-linear

function provides a sound way of taking positive guidance out of the independently

plausible, but abstract, platitude that material inequality would be unjust, but for the

presence of other factors. The message to be taken into later chapters is that, whilst

conceding that other factors may rule out the injustice of material inequality as a

general rule, this does not mean that such factors trump the significance of endowment

51

inequality. Instead, a distributive principle has been identified that may continue to

regulate material shares, whatever the identity and importance of other factors may

turn out to be. Furthering the positive case for this view will depend on the

comparisons that I will later make with other views about justice.

2.8 Some remarks on the concept of sufficiency

I mentioned, earlier on, that it has become customary to associate the idea of a

threshold with the concept of ‘sufficiency’, or ‘having enough’. The pre-occupation

with sufficiency has given rise to the label of ‘Sufficientarianism’, which has been

attached to threshold-oriented theories, and is often presented as a fourth fundamental

category of theory. However, in spite of the fact that Sufficientarian ideas have been

discussed at some length, there does not exist a representative method of aggregation

that is subject either to wide endorsement or of the sort that obviously captures the

appeal of sufficiency thresholds97. Authors such as Paula Casal have made some

attempt at rectifying this:

[Sufficientarian] principles do not favor the elimination of inequality, nor do they

regard benefiting the less well off as generally more important than benefiting the

better off. Instead they insist that when evaluating different distributions what matters

is whether individuals have enough not to fall below some critical threshold.98

This definition does not, however, describe a complete view. Even if an emphasis is

placed on whether individuals have enough, it remains unclear how to compare

distributions in which different numbers of people fall below the threshold, or

distributions in which people fall below the threshold to different degrees. Casal goes

on to further define Sufficientarianism as the conjunction of what she calls the

“positive” and “negative” theses. The positive thesis “stresses the importance of

people living above a certain threshold, free from deprivation”, whilst the negative

97

This problem of a lack of consensus as to how to define Sufficientarianism is noted by Meyer (2008: fn34). 98

(2007: 297)

52

thesis “denies the relevance of additional distributive requirements”99. However, a

phrase such as ‘to stress the importance of people living free from deprivation’ is not

precise enough to suggest any kind of welfare function. Moreover, since the extension

of the negative thesis is parasitic on the meaning of the positive thesis (“additional

distributive requirements” must refer to requirements not implied by the positive

thesis), it is also hard to understand. Unfortunately, Casal does not settle on anything

more precise. What she does claim, however, is that “sufficiency, equality, and

priority are not mutually exclusive principles but might instead be combined in hybrid

views”. Her explication of this view does reveal further precision in her definition of

Sufficientarianism, but reveals a problem with attempts to isolate an independent class

of Sufficientarian theories.

An example of a theory that Casal treats as a hybrid is that of Roger Crisp.

Roughly speaking, Crisp’s theory assigns lexical priority to benefitting those below

the threshold over those above100. It is made complete by assigning a form of weighted

priority to benefitting those further below the threshold over others who are also below

it. Casal claims that it is the second component of this theory that makes it a hybrid.

Casal’s view must be, therefore, that a Sufficientarian theory becomes hybrid as soon

as it starts making claims about how to compare the value of benefits accruing to

people below the threshold. However, if a pure Sufficientarian theory must remain

silent on these sorts of claims, then it will be impossible for it to generate a complete

order of distributions. It follows from Casal’s claims that it is impossible for a

complete ordering of distributions to be purely Sufficientarian. If Sufficientarianism is

supposed to be a genuine class of theory, then this is implausible.

The reason that is tempting to call views such as Crisp’s hybrids of

Sufficentarianism and Prioritarianism is the fact that it makes use of a threshold whilst

having a clearly Prioritarian element. But it is most accurate to describe Crisp’s view

as Prioritarianism that has been restricted by the insertion of a particular device,

99

(2007: 297-98) 100

(2003a).

53

namely a sufficiency threshold. Casal was right to treat Crisp’s view as a form of

Prioritarianism. But Casal was wrong to also distinguish Crisp’s theory from an

imagined class of purely Sufficientarian theories. Really, there is no such distinction at

the level of theories, because there is no such theory as ‘Sufficientarianism’.

Thresholds merely modify the scope of the theory to which they are applied.

Thresholds are best viewed as a device with which we may depart from the most

straightforward versions of Utilitarianism, Prioritarianism, and Egalitarianism.

Viewed in this way, we may better understand the way in which a threshold is

employed in the method of aggregation I will now propose.

The concept of sufficiency offers one idea that might be used to motivate a

certain principle of distribution that is not exactly Prioritarian, Egalitarian, or

Utilitarian. But it makes only a limited contribution to the extensional content of a

distributive principle. The fact that some contribution can be made, however, is worthy

of some comment, since it bears on the way in which thresholds relate to the

taxonomic concepts discussed in this chapter. Earlier, I distinguished between

separable and non-separable methods of aggregation. Roughly speaking, what

separates these two categories is a matter of whether the contributive value of a life

can be inferred entirely from what I called its personal value, or lifetime well-being.

Egalitarian theories are non-separable, because the contributive value of a life depends

(in part) on relations between that life and other lives in that distribution. I also

described how there is a sense in which the piecewise-linear function can be likened to

a logically weaker version of Prioritarianism. Now, the Prioritarian function is

strongly separable. However, the piecewise-linear function is only strongly-separable

on a precise way of defining separability.

It is certainly possible for functions to be clearly non-separable even though

some role is assigned to a threshold. For example if L were simply defined as average

actual welfare, then it would not be known whether a given life was above or below L

unless the average welfare level was known. This would require knowing the facts

about other lives’ welfare in order to know the contributive value of a particular life.

54

If, on the other hand, L was located at an independently-defined ‘sufficiency’

threshold, then the theory might be strongly separable, so long as this threshold did not

move in accordance with any facts about how well-off persons actually were101. So a

piecewise-linear function could, in principle, being separable or non-separable,

depending on facts about the welfare of lives in a distribution is included among the

determinants of L. Now, it is not immediately obvious which description is right for

the view laid out in this chapter. I have said that the location of L is determined by

certain expected levels of welfare. It might turn out that it is impossible for actual

levels of welfare to radically change without expectations having therefore changed as

well. This would suggest that the function is non-separable. On the other hand, it’s not

as if the explanation for why L might vary from one distribution to the next is ever one

that depends on variation between the respective actual welfare levels in these

distributions. What ultimately matters is whether we decide to regard a theory as non-

separable when a life’s contributive value depends on facts about other lives in a

distribution, or when it is merely the case that a life might change its contributive

value when certain changes are made to the welfare of other lives. On the view that I

have proposed, the former description is not satisfied. I prefer to regard the piecewise-

linear function as strongly separable in the guise that I wish to use it. In chapter four I

will turn to examine the sort of value-holism that is behind non-separability, and ask

whether holistic views are plausible in the context of principles of distribution. For

now, though, we may set this issue aside.

101

This matter is more fully explored by Amartya Sen in a well-known paper about poverty lines (1983), which might be regarded as analogous to sufficiency thresholds. Sen’s view is that a poverty line may be absolute or relative, depending on what sort of goods we are interested (specifically, ‘poor’ as a financial concept is relative, whereas a more strictly welfarist conception of poverty lines suggests that they are absolute). What I say here makes sense so long as ‘sufficiency’ is constant with respect to some goods, as Sen suggests it must be.

55

Chapter Three: Justice and Aggregation

This chapter explores the way in which a piecewise-linear function can

contribute to our thinking about distributive justice. Particular focus will be on various

comparisons between the approach defended in the last chapter, and the well-

developed alternatives in the literature. This will give a sense of some of the

philosophical resources gained by adopting the framework that I have presented. To

some extent, the arguments in this chapter make use of features of the piecewise-linear

function that have already been highlighted in chapter two. The aim here is to

demonstrate why these features have interesting implications in political philosophy,

and where they connect with some topics that have recently received attention in the

literature. Overall, the argument of this chapter aims to establish the potential for

useful, interesting further theorising about distributive justice, and to take some small

steps in filling out this potential.

3.1 The problem of the bare self

I shall begin with a problem that has been raised against the possibility of there

being a baseline from which we can measure the extent to which a person’s material

shares have been influenced by the extent to which they possess favourable or

unfavourable endowments102. According to some philosophers, there is no such

baseline. This claim gains its plausibility from certain views about the relation

between a person’s endowments and their actual self. But it is possible to raise doubts

about the integrity of this distinction. As Robert Nozick has said, the more reliance

that is placed on a separation of the person and their talents, abilities, and so on, the

less we seem to have any person left over, metaphysically speaking103. This gives rise

to the so-called ‘bare self problem’. As with many ideas in Nozick, the point is made

102 I first mentioned this in (1.2), above. 103 See (1974: 228).

56

fleetingly104. It might be true that there is no way of fully separating the self from

certain endowments, but it’s not clear how this is instructive. Certainly, it’s not

obvious how the relevant inseparability entails, in itself, the further claim that a

person’s endowments make no contribution to their entitlements. Any causal claims

about the way in which endowments substantially influence material shares seem just

as defensible as they were before. Nevertheless, it is worth spending some time on this

matter, if only because a developed version of the bare self problem helps make clear

some of the advantages of the piecewise linear function and how its employment may

compare with other views about justice.

Fortunately, Nozick’s point is given an effective development by Susan

Hurley105. The crucial point, as Hurley points out, is that the bare-self threatens the

possibility of what she calls a “luck-neutral baseline” from which to measure the

distorting influence of endowments106. The real problem, then, is one of counterfactual

indeterminacy. The inseparability of selves and their endowments means that there is

no answer to the question of how well-off one would have been (materially speaking),

were it not for the influence of one’s endowments. Because of the incoherence of the

bare self, there is no fact of the matter as to how well one would have done, other than

in ways influenced by a set of endowments107. What this means is that it is impossible

to measure the degree to which one’s material position is attributable to the effects of

having had a more or less favourable place in the endowment distribution. The

impossibility of separating endowments from the self is thus the impossibility of the

required baseline with which to carry out this sort of measurement.

Hurley goes on to make a variety of diagnostic claims regarding the relation

between justice and luck. (Recall, from chapter one, that the effects of endowments

104 Nozick does get round to discussing the idea of an Egalitarian baseline at (1974: 216-224). Hurley’s analysis is, however, clearer, and less bound up with a (questionable) construal of Rawlsian theory as its target. 105 Hurley repeats Nozickean claim about the bare self at (2003: 121). See also (2003: 177-78). 106 (2003: 164). 107 Here I am paraphrasing Hurley’s description of the “indeterminacy problem” (2003:164-68). Hurley does not claim that the indeterminacy problem is arrived at by more carefully analysing the bare self problem, but it seems to me that the two problems are so related.

57

may be regarded as a subset of the effects of brute luck.) The most important of these

claims is just an application of her understanding of the bare-self problem: No

distributive principle can carry out a “luck-neutralising” role. Bringing material shares

into conformity with whatever would be optimal on an Egalitarian, Prioritarian, or

Utilitarian function offers no guarantee of producing a set of shares that is any less a

matter of luck. Due to the indeterminacy attaching to how one would have fared ‘but

for one’s endowments’, there exists no pattern of material shares that can be identified

with how people would have fared if their shares could have been distributed

independently of the effects of endowments. According to Hurley, the search for

distributive principles that might eradicate the effects of bad luck is vulnerable to what

she calls the “Egalitarian Fallacy”: It may be true that an unequal material distribution

can be blamed on the effects of luck (in particular, endowments being differently

distributed among that distribution’s members). But it does not follow from this claim

that, were material shares more equally distributed, then the material distribution

would be any less a matter of luck.

The problem of the bare self can look like it has considerable force108. But it

does not have force against any view embodying some sort of aversion to the

influence of endowment inequality. The first point to emphasise is that the

inseparability of the self and its endowments does not in itself show the moral

irrelevance of endowments, or the moral irrelevance of how they are distributed. At

most, it shows that we cannot remove the effects of endowments on material shares

(this is Hurley’s point). Part of what prevents this point from lacking force is the fact

108 In a reply to Hurley, Richard Arneson (2001) explains how the Dworkinian framework may not be vulnerable to the dependence on counterfactuals that the bare-self objection exploits, even though the view officially gives primacy to the choice/circumstance distinction. Indeed, Dworkin (2000) emphasises that the baseline against which entitlements are to be measured is not how someone would have fared in the absence of the causes of bad brute luck, but whether they would have purchased insurance against such effects in a scenario of resource-equality (see also Rakowski (1991) for a slightly different version of the insurance idea within a Luck Egalitarian framework). This view may avoid the problem of counterfactual indeterminacy that results from any reliance on how a person would have fared if not for the effects of endowments. However, the question of what a person’s preferences would have been in such a hypothetical situation may be just as indeterminate, albeit not for such metaphysical reasons. In any case the use of the insurance model may not turn out to be of much use against the other objections to the Luck Egalitarian view (see the discussion of Anderson and Dworkin in a later footnote).

58

that we are more concerned with removing the effects of endowment differences. For

example, we might think that it is unjust for men to be paid more than women, simply

because they are men. But to say that women need to be compensated does not require

us to imagine how anyone would have fared if they were ‘neither a man nor a woman’.

With its focus on the inseparability of selves and endowments, this is what the bare-

self problem seems to target. What instead matters is that the difference between being

a man and a woman does not (on its own) account for a difference in persons’

respective material shares. This does not require us to inquire as to how well off

people would have been if genderless. Instead, it requires us to search for some other

baseline that might represent how well off people would have been if the endowment

difference were prevented from having the effect it in fact has. Certainly, searching for

this answer has its challenges, but the bare-self problem does not add to these.

Notice, also, that the bare self problem could only present an issue for views

on which justice requires the eradication of any effects of the unequal endowment

distribution. Eradicating the effects of endowments is equivalent to any end of

neutralising their effects, which is precisely what Hurley targets as impossible.

However, the idea of mitigating the effects of endowment inequality need not be

undermined at all. If all that distinguished ‘mitigation’ and ‘eradication’ were a

difference of degree, then the bare self problem would be no easier to ignore.

However, as I explained in the last chapter, the idea of mitigating the influence of

endowment inequality is not intended to be a simple weakening of the eradication of

such influence109.

3.2 More on the idea of a baseline

The diagnosis of what is wrong with the bare self objection can be extended,

by focusing precisely on how it is ignored by the view being proposed in this

dissertation. In chapter one I explained how the mitigation of endowment inequality

109 A difference of degree might be what describes some of the intuitionistic hybrids alluded to in chapter one, where the value of eradicating the effects of endowment inequality is simply traded-off against values that count against such eradication. These hybrids may be regarded as inheriting a vulnerability to the bare-self problem.

59

may be independently motivated by searching for a principle satisfying little more

than the widely-endorsed hypothetical that equalisation of material shares would be

just if material inequality could be attributed to endowment inequality and nothing

else110. In chapter two, I presented the piecewise-linear function that satisfies this

claim whilst still having definite implications for the regulation of a material

distribution. This principle is intermediate between positions that would favour either

eradicating or ignoring the effects of way in which endowments are unequally

distributed. This is to say that it embeds a significant preference for redistributive

transfers, but simultaneously embeds a certain amount of indifference to such

transfers. Now, endorsement of chapter one’s hypothetical does not require any

reliance on counterfactual claims approaching how well-off any individual would be if

were not for the presence (or more accurately, the effects) of endowment inequality.

Moreover, no dependence on such forms of counterfactual analysis is introduced when

the piecewise-linear function is adopted as a principle with which more precise

commitments can be identified. Freedom from the relevant dependence on

counterfactuals entails freedom from the various problems relating to the bare self.

We are now in a position to introduce an important abstract distinction, which

completes the demonstration of how to mitigate the effects of endowment inequality

whilst avoiding worries about the bare self. When theorising about the relation

between endowments and justice, two strategies may be discerned111. The first strategy

aims to take guidance from what things would be like if endowments had no effect on

the material distribution. The second strategy seeks initial guidance from how things

would be like if endowments were the only effect on a material distribution (or at least

the only affect that led to material shares being any different from one person to

another). Now both of these strategies make use of counterfactuals in some way. But

110 Recall that this didn’t require the idea that no other factors influence material shares, as may be a conceptual impossibility, but merely that the inequality of shares, and the fact that shares would not be in full conformity with entitlements, can be blamed wholly on facts about the endowment distribution. 111 I don’t mean that no other strategy exists. There is at least one, namely the Rawlsian view on which the endowment distribution is likened to a common asset, as discussed in chapter one. Here I am just trying to emphasise the contrast between the strategy I favour and the one guiding the end of eradicating the effects of endowments.

60

only the former one requires that endowments be separated from the self in ways that

are problematic. The second strategy, the one I am concerned to exploit, invokes a

different sort of counterfactual. This one only requires the separation of endowments

from other effects on material shares. This separation is not prone to the same sort of

metaphysical difficulties as the first. As such, the relevant worries do not arise.

I have taken the bare-self problem relatively seriously. In accordance with the

response I have given, it is worth emphasising the limits on what the problem might

show about the relation between justice and luck. It remains an uncontroversial truth

that some become better off than others, and some become simply very badly off in an

absolute sense, in ways that depend largely on the facts about their endowments. The

bare self problem may show an impossibility of measuring how substantial this

influence is. But this impossibility, whether conceptual or epistemic112, should not

encourage us to wholly abandon idea that the material distribution should be regulated

in ways guided by the facts about unequal endowment distribution. To think otherwise

is to radically exaggerate the otherwise important lesson of the bare self problem. This

lesson is that we cannot respond to the significance of a distorting factor by seeking to

neutralise the influence of that factor. But the lesson does not extend to discounting

the factor’s significance altogether. We might instead seek alternative ways in which it

might guide our thinking about justice, such as those presented in this dissertation.

In the previous section, I explained why a principle of distributive justice does

not need to adopt a ‘luck neutralising’ baseline in order to address the type of concern

about endowment inequality that motivates such a baseline. One thing that is implied

by the argument of the last section is that a distributive principle doesn’t really need

any sort of baseline at all. At least, no such requirement exists if what is being pursued

is an end more moderate than that of eradicating the effects of endowment inequality.

The pre-occupation with baselines actually hinders our understanding of the idea that

redistribution may justly proceed in ways sensitive to endowment inequality. The

argument of this section is concerned with establishing why this is so, and why a 112 Hurley registers this question but is non-committal on it (2003: 167). I think the question can be left open without affecting the basic significance of the bare self problem.

61

redistributive baseline is not a necessary element of the mitigatory framework being

proposed.

Robert Nozick asks “why think there ought to be any particular pattern in

holdings? Why is equality the rest (or rectilinear motion) position of the system,

deviation from which may only be caused by moral forces?”113. This question occurs

as part of what is presented by Nozick as a fairly general critique of Egalitarian theory.

And although the question might be a good one to ask, it presupposes a feature of such

theories that is only exhibited by views other than the framework that I have proposed.

One claim implied by Nozick’s question is the view that any programme of

redistributive activity must be guided by some conception of what the ideal, or most

just, material distribution would be. (This is the ‘rest position’, to which Nozick

refers.) The idea that endowment-sensitive redistribution must have a baseline is

closely related to this conception of distributive principles being the sort of thing that

express a target, ‘ideal’ distribution at which the regulation of a material distribution is

to aim. Nozick’s question is motivated by doubts about why there has to be such an

ideal. It is doubtful, however, that a principle of distribution must adhere to Nozick’s

conception.

Most of the methods of aggregation laid out in chapter two satisfy Nozick’s

view of a patterned principle that aims at some ideal state. Each of these principles in

some way aims to promote a single distributive trend, where some optimal distribution

is whatever results from promoting this trend as much as possible. The piecewise-

linear function, however, is rather different. As I have said before, part of what makes

this function distinctive is the fact that it exhibits a degree of general aversion to

material inequality, whilst embedding certain elements of indifference to inequality.

Roughly speaking, the indifference arises in two ways. First, the function is indifferent

to any inequalities arising within certain ranges of welfare levels. Specifically, it

displays no aversion to inequalities among the badly-off and among the well-off, no

matter how large. This is not to say that the degree to which a person is well-off or

113 (1974: 222-23).

62

badly-off is entirely irrelevant. It will often be more appropriate, for example, to

benefit the more badly-off so long as the benefits concerned do more to reduce sub-

threshold deviation than when conferred on the less badly-off. Whether this is so will

depend on the size of the benefit in question, and how it compares with the degree to

which those among the badly-off happen to be differently situated below the level of

welfare associated with the function’s threshold114.

Part of the point here is just that there is no value attached to making transfers

among the individuals in these respective groups. Value is only attached to transfers

from the well-off to the badly-off. The value of these transfers varies in ways

corresponding to the variation in how valuable it is to benefit the badly off, given the

size of benefit that a transfer would realise. The second element of indifference can be

identified with a limit on the extent to which the value of benefitting the badly-off may

vary in accordance with how badly off they are. As I have explained, such variation

can occur only insofar as some benefits will take recipients to levels above the

threshold. Such benefits are of less value than same-sized benefits whose effect is

exhausted in ways that do not move the recipient beyond the level of the threshold.

Analogous claims apply to lowering the welfare of the well-off, given that

some persons must inevitably incur the burden of supporting redistributive transfers.

Recall that, given the structure of the piecewise-linear function, transfers will be

favoured only up until a point at which a distribution contains either no persons living

at levels below the threshold, or no persons above it. This is what will happen in the

likely event that the total deviation of shares to one side of the threshold is perfectly

equal to that on the other side. In such a case, either some among the badly-off may be

denied the benefits that redistributive transfers confer on other members of that group,

or some among the well-off will avoid having to provide for such transfers. The

second way in which the function is indifferent is with respect to who is ‘left out’ of

the relevant transfers. The piecewise-linear function does not imply, for example, that

those who are least badly off must be the ones left unassisted if there are insufficient

114 Analogous claims apply to lowering the welfare of the well-off.

63

members of the well-off to sustain enough transfers to raise everyone to the level of

the threshold. Similarly, the function does not state that those who are most well-off

must be the first to give up their shares for the purposes of transferring to those who

are much worse-off.

The general point is that it is possible for the function to favour that some sub-

set of transfers occur within some larger set, and yet to some degree remain indifferent

as to which sub-set this is. All the function advocates is that transfers proceed so long

as some people live above a certain threshold whilst other live below. It says nothing

about who among these two groups is to participate in such transfers, until the point at

which some members of one group are left out. Because of these elements of

indifference, the same material distribution could be modified in very different ways,

such that no way is more favourable than any other. A wide range of permissible

inequalities are available given regulation by the piecewise-linear function. This

reflects the fact that the piecewise-linear function does not really have a target in any

strong sense. The ‘ideal’ distribution is one that exhibits the minimal amount of sub-

threshold deprivation that is possible, given the facts about the distribution in question

(roughly, how deviation below the threshold compares with that above). But, as I have

explained, there exist various possibilities as to how close a distribution may be made

to conform to this ideal and, for that matter, many permutations compatible with any

given degree of conformity. This is partly because there is no baseline specifying

exactly how much a given person’s shares depart from where they ought to be.

Crudely speaking, Nozick’s question suggests that a commitment to redistribution

requires a sort of tunnel-vision. Less metaphorically, the point is that such a

commitment is compatible with the absence of any strong commitment to an abstract

ideal state of shares, but rather an ideal property of distributions whose realisation is

compatible with a range of different permissible inequalities, large or small.

As an afterthought, it is worth noting that its elements of indifference may

contribute to the intuitionistic appeal of the piecewise linear function. Critics of

Prioritarianism have often accused it of attaching too much significance to variations

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in the absolute levels of persons in a distribution. If a strictly concave function is

adopted, then it can seem that too many distinctions will be drawn. As Roger Crisp has

said, “there is something absurd about claiming that equality or justice requires that

the rich be benefitted instead of the super rich”115. As I have said, the defence of the

piecewise-linear function is not dependent on these sort of intuitions. However, it is

worth pointing out that the appeal of giving some sort of priority to the worst-off may

survive in the face of criticisms that gain their force more from the strong implications

of strictly concave functions than the general Prioritarian idea, which we have seen

may be formulated more weakly.

3.3 History versus pattern

The argument of the previous section enables further observations to be made

about how the piecewise-linear function allows a commitment to redistribution to be

reconciled with apparently competing political ideals. In this section, we may finally

begin to look more closely at the importance of factors that shape material shares, but

which operate separately from (if not in total isolation from) the influence of

endowments.

Certain authors, notably Libertarian theorists, have emphasised the way in

which entitlements ought to be regarded as sensitive to voluntary choices. These

authors believe that there is an important political value in being free to choose how

much to produce, how to exchange it with others, and how much of it to simply give

away to others. The exercise of such freedoms will inevitably have an impact on the

material distribution, and most likely bring about substantial inequalities116. But we

should be hesitant about regarding these effects as relevant to what person’s

entitlements are. According to Libertarians, persons are entitled to their shares so long

as these shares occur as part of a distribution formed through free choices and

exchanges. Naturally a distribution could fail to be shaped in this way, if the relevant

115 (2003b: 120). Virtually the same criticism is made by Hausman and McPherson: “When inequality obtains among people who are all very fortunate...why should one place less moral weight on the interests of those who are better-off?” (2006: 180). 116 As famously illustrated by Nozick’s ‘Wilt Chamberlain’ example (1974: 160-64).

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exchanges were governed by coercive or deceptive activities. Libertarians may also be

prepared to acknowledge certain principles governing the legitimate initial acquisition

of resources, whose violation may render a distribution unjust even if these

acquisitions are followed by exclusively voluntary exchanges117. None of these

constraints on entitlements is connected in any interesting way, however, with the

extent to which material shares might end up unequally distributed.

It has been argued that the importance of factors like freedom is incompatible

with the use of any sort of redistributive principle of distribution. Nozick relates this

argument to an abstract distinction he draws between two types of theory, or

theoretical consideration. In Nozick’s terminology, ‘historical’ considerations are

those pertaining to how it is that a certain distribution came about, irrespective of what

this distribution happens to look like. This contrasts with ‘end state’ or ‘patterned’

principles, which say that justice may require the conversion of one arrangement of

shares into some other one arrangement118. According to Nozick, these two categories

are incompatible with each other. The basic idea is that the history of any set of

material shares is contingent, in ways that prevent it from being ‘read-off’ the way in

which these shares happen to be distributed. As such, end-state principles are bound to

be insensitive to the force of such considerations. Conversely, as I have said, a

historical entitlement to some set of shares may obtain regardless of what the facts are

about the shares of other people. Because of this, upholding historical principles of

justice will disrupt any simultaneous attempt to regulate distribution in accordance

with the terms of an end-state principle.

Now, it is worth pointing out that the class of historical theories is, in

principle, larger than the sub-class of historical theories that emphasise the value of

117 Much could be said about how to understand the political significance of concepts of coercion and acquisition. For a good general response to Nozick’s use of these concepts, see G.A.Cohen (1995b). The study of acquisition has a long history prior to the treatment it receives from Nozick. On this see Waldron (2005). 118 As a matter of fact, Nozick also distinguishes between ‘end state’ and ‘patterned’ views (1974: 153-55). However, the way in which he does this is not relevant to the matters being discussed here, and in any case I am not convinced that Nozick stuck to this distinction after having made it. For more on these exegetical points see Bader (2010) and Schmidtz (2005: 159).

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choice or freedom in particular. Broadly speaking, the history of any material

distribution is just the causal account of how that distribution came to be what it now

is. This means that the conflict between history and pattern is not equivalent to any

conflict between freedom and pattern. And although Nozick argues at length for the

latter conflict, he doesn’t really offer an argument for anything more general.

Although the distinction between history and pattern clearly has a certain generality,

the supposed conflict might not. This point will turn out to be significant.

Nozick’s conception of the relation between history and pattern has

considerably influenced subsequent theorising. The fact that such theorising is carried

out by those strongly opposed to Nozick’s Libertarianism does not eliminate such

influence, even if it hides it. Luck Egalitarianism has been the dominant alternative to

Libertarianism during the decades since Nozick, even if it is now losing popularity.

The Luck Egalitarian strategy can be viewed as a response to Nozick’s dichotomous

view about history and pattern. For example, when writing about Ronald Dworkin’s

version of Luck Egalitarianism, G.A.Cohen remarks that Dworkin has “performed for

Egalitarianism the considerable service of incorporating within [his view] the most

powerful idea in the arsenal of the anti-Egalitarian right: the idea of choice and

responsibility”119. This assessment is correct given that Luck Egalitarian does offer a

genuine sensitivity to free choice, whilst embedding an aversion to material inequality.

However, this is achieved only in a way that is rather concessive to Nozick’s outlook.

Generally speaking, Luck Egalitarianism is subject to a methodological focus

on the basis of interpersonal comparisons. The distinctiveness of the various Luck

Egalitarian proposals is that they emphasise they equality of some particular good,

such as resources, opportunity for welfare, or something else. This recalls the ‘metric

question’ first noted in chapter two. The sensitivity to choice and responsibility is

meant to be embedded within the selection of a basis for interpersonal comparisons

that is not purely welfarist. Also relevant here is the distinction between brute and

option luck described earlier. These ideas come together in something like the

119 (1989: 933).

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following way: Equality of resources is meant to provide one way in which the victims

of bad brute luck may be construed as worse off than others, but the victims of option

luck not. Proposals that focus on some other basis of comparisons tend to approximate

to slightly different ways of distinguishing when a person is affected by brute luck

rather than option luck. The relevant point here, given the focus on Nozick, is that

Luck Egalitarians have abandoned the possibility of achieving sensitivity to such

considerations by way of fixing the form of a distributive principle. This is precisely

what shifting attention to the basis of interpersonal comparison amounts to. It is a shift

from focusing on how to regulate distribution, to a preoccupation with what

distribution to regulate120.

The question of finding an appropriate basis for interpersonal comparisons is

an important one. And its importance is not exhausted by the fact that it offers one

way of making entitlements sensitive to persons’ free choices. However, the sort of

strong sensitivity that is gained arguably turns out to be a principal weakness of Luck

Egalitarianism, not one of its strengths. This matter will receive some more attention

later in the chapter. My main concern now is to explain why the form of a distributive

principle can, after all, be compatible with certain sensitivity to choice and other

historical considerations.

The force of Nozick’s dichotomy relies on the idea, already mentioned, that an

end-state principle is committed to treating any pair of materially identical

distributions in exactly the same way, ignoring the histories behind these distributions.

This is not in fact the case. A principle of distribution only satisfies this description

when it satisfies the more general description of being subject to a precise baseline, or

aiming to promote a very narrowly construed ideal distributive trend. I have already

explained, at some length, why the piecewise-linear function is an exception to this

description. The elements of indifference that I described in the last section are notable

in that they provide a substantial amount of room in which the relevance of historical

considerations may operate. As I explained, the function will typically be indifferent

120 I borrow this turn of phrase from Hurley (2003: 4).

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between a wide range of different material distributions, many exhibiting some

material inequality, within the scope of its more general preference for decreasing the

overall deviation below a certain threshold. In other words, the function exhibits a

certain redistributive character whilst allowing entitlements to be distinguished by

appealing to historical factors. More precisely, the history of a person’s shares may be

what is decisive in whether they are prioritised as beneficiaries of redistributive

transfers, or may be what determines the share of the burden that they must incur so

that such transfers may happen. In this way, a somewhat badly-off person may have

much stronger entitlements to larger shares than one who is much worse-off. This

gives considerable force to whatever historical considerations entail this, even though

the overall system of transfers is one that is in some sense guided by a concern about

end-states.

Now, based on what I have said, it may be objected that there is no real

reconciliation here. The piecewise-linear function merely allows history to break ties.

In other words, history only has influence with respect to where the function is

indifferent. Faced with two distributions that the function actually orders, historical

factors will have no impact. In this way, history remains subordinated to pattern, even

if the conflict is not as stark as Nozick’s account of it suggests. There are two lines of

response available to this objection. The first is that a consideration’s having a tie-

breaking role does not mean that its role is as small as the description often suggests.

Importantly, the component of a theory that breaks ties may turn out to have a very

substantial role, if the other components of the theory are designed to generate a

particularly high frequency of ties. This is a fairly accurate description of what the

piecewise-linear function is like, even if the ‘design’ to break ties is not really literal

(given that the selection of the function is guided by its satisfaction of chapter one’s

hypothetical condition). This point has some force, but does not assuage the worry that

historical factors remain dominated, or rendered subordinate. The second line of

response addresses this concern. The argument here recalls the fact that the history

behind any distribution is broader than the free choices that led to that distribution.

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Facts about endowments, and how they are distributed, are included as well.

Remember that the crucial characteristic of historical factors is their causal aspect.

Construed in this appropriately general way, history is not rendered

subordinate to pattern on the piecewise-linear function. This can be highlighted if we

recall the method in which the function’s threshold is located. Recall that the level at

which this threshold rests is determined by what the expectations of persons are, given

their endowments alone (the threshold is located at the average expectation). Now,

notice that this qualifies as a perfectly historical factor. Crucially, the value of this

average is contingent in relation to the facts about the way a material distribution is

actually arranged. As I conceded in chapter two, we might expect some relation

between actual welfare levels and a major component of what determines expected

welfare levels. Nevertheless, the threshold’s location can quite easily vary even if the

state of a material distribution does not vary at all. This is enough for it to be regarded

as a historical factor. Recall, in addition, that the threshold can be regarded as deciding

the conditions under which the function is indifferent between different distributions

that might be reached. Fixing the threshold’s location is what decides the extensions of

the two ranges of welfare levels, and thus the ranges within which it is indifferent to

transfers. Variations in its location similarly dictate how else it is indifferent. There is

no subordination of history to pattern. A more accurate description is that certain

elements of history are subordinate to a certain patterned concern, which it is itself

subordinate to (indeed defined by) sensitivity to historical considerations of a different

sort.

Now, this is a reconciliation of sorts. But nothing said above shows that the

piecewise-linear function reconciles an egalitarian concern with Nozick’s

thoroughgoing Libertarianism. This is because the sort of reconciliation that has been

reached is one that ultimately extends only between the general categories of historical

and end-state theory. Ultimately, then, a Libertarian theory of justice must be ruled out

by the framework I have proposed. This was, in effect, acknowledged in chapter one

when it was announced that an intermediate theory would be pursued. At this point, it

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is perhaps worth emphasising that there may be independently motivated objections to

the Libertarian emphasis on freedom. One objection arises when we observe that

exchanges between persons, even if voluntary, may restrict the choices available to

others (what economists call externalities). Large material inequalities tend to reduce

the options available to those whose shares are much worse than the shares of others.

Now, if free choice is regarded as valuable, then reducing a person’s choice set might

be viewed as disrespectful to this person’s capacity to choose. Indeed, it is perhaps

strange to assert that the importance of being free to choose is preserved just so long

as a person can make some choices, the range of choices not otherwise mattering.

Thus it may be claimed that externalities are sometimes unjust, and that certain ways

of regulating material shares count as an appropriate response. Whether it is possible

to defend this sketch of an argument, or any other argument with a similar conclusion,

is not an issue that will be further investigated. This dissertation is not going to include

a sustained critique of Libertarianism. However, what has been provided is an account

of how an intermediate approach might incorporate some elements more familiar from

the Libertarian tradition, whilst falling short of being a member of that tradition. As I

indicated earlier, Luck Egalitarian theories have been presented as able to achieve

something similar. I shall close the chapter with some further discussions of these

theories.

3.4 Brute and option luck

In chapter one, I explained how Luck Egalitarianism rests on the idea that

persons ought not to be worse-off through no fault of their own. What I left relatively

undiscussed was the typical way in which this idea is refined, namely, the way in

which entitlements are linked to the operations of brute and option luck (the former

generating entitlements and the latter not). This distinction has been subject to a

considerable amount of attention and it is worth registering some of the objections

raised against it. I have already discussed the claim that it is impossible to specify the

degree to which brute luck affects a person badly. Doubts about the metaphysical

separability of a person’s own self from their set of endowments mean that we lack a

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baseline against which to measure the badness of any brute luck. Accordingly, we

cannot say how much compensation the victims of brute luck are entitled to. I have

argued that this objection can be avoided if we adopt rather different views about the

way in which endowment inequality guides distributive justice. I mention it again now

as a reminder that it may retain its force against the Luck Egalitarian position.

Further doubts exist. In one way, the Dworkinian distinction is parallel to

whether a person is in some sense the author of their own social position. That is to

say, holding individuals responsible for the effects of option luck involves treating

them as responsible for outcomes that are at least partly the results of their actions.

One objection to the distinction is that this simply captures the wrong sense of

responsibility that is appropriate within a theory of distributive justice. We might, for

example, agree with T.M.Scanlon that there is an important distinction between

attributive responsibility and substantive responsibility121. The latter sense is the

authorial version of being responsible just mentioned. The substantive sense relates to

the narrower idea that whether a person ought to be held responsible for their choices

depends on whether they have any complaint against those holding them responsible,

for not providing what might have been owed. In particular, substantive responsibility

may be withheld given a failure to be provided with the sort of information that might

have led the subject to choose differently. There are probably different ways of filling

this idea out, and it is an open question how often its implications would differ from a

view guided by the attributive version of the distinction.

A more aggressive objection to Luck Egalitarianism asserts that its

implications are so harsh as to be surely unjust. This objection emphasises the fact that

withholding compensation from the victims of option luck often seems incredibly

harsh. Very often, imprudent choices have such bad effects that regarding the victim

as entitled to no assistance at all means condemning them to an extremely miserable

situation, or worse. Elizabeth Anderson has written one of the better-known attacks on

Luck Egalitarianism, which includes a number of examples of option luck victims who

121 (1998: Ch.6).

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make intuitive candidates for redistributive compensation, but are apparently denied

assistance by the Luck Egalitarian theory122. The objection has greatest force when we

note that exposing oneself to the risk of bad option luck is often highly rational, and

the degree of exposure small123. Adapting one of the cases from Anderson, we may

imagine a car driver who takes a journey based on the expectation that her life will be

made much better than if she does not take this journey. As with car journeys in

general, there is a small risk of incurring a very serious injury in an accident. This is

precisely what happens in the imagined case, but due to the fact that the driver took an

avoidable, ‘calculated gamble’, she lacks any entitlement to assistance,

notwithstanding the severity of her injuries. Its main point seems to be that Luck

Egalitarianism makes entitlements wholly insensitive to the urgency of someone’s

actual situation. Most of us would agree that our society would be less just if it were

like this124. As Samuel Scheffler has said, it is implausible that choice can have this

kind of one-dimensional, “make or break” significance125.

Options for the Luck Egalitarian are limited, given the commitment to brute

luck as a sole generator of entitlements. Of course, this ‘harshness’ objection only

remains so long as the Luck Egalitarian retains the view that entitlements only accrue

if a person’s situation can be blamed on brute luck. It is perfectly coherent to regard

bad brute luck as a sufficient rather than necessary condition of having certain

122 See Anderson (1999). The point is also made more briefly by Arneson (2001). 123

The objection has less force against the possibility of ‘abandoning’ persons who repeatedly take serious risks and frequently require costly rescue. Zofia Stemplowska argues that we can make a principled case for not compensating such individuals on grounds that their conduct “unreasonably privileges their own interests over those of others” (2009: 251-54). 124

Seana Shiffrin (2004) illustrates the wide range of real-world practices of ‘cost absorption’, which can be treated as instances of society’s unwillingness to adopt the implications of Luck Egalitarianism that Anderson highlights. (Shiffrin’s diagnosis of why we have cost absorption practices is similar to Anderson’s, but she stops short of explicitly denying the importance of “choice sensitivity” in the way Anderson does.) 125 (2003: 19). Elsewhere, Scheffler adds “few people hold the general view that inequalities resulting from choice are always legitimate but that it is always unfair if people are better or worse off as a result of their differing talents and abilities” (2005: 10). Part of the point of the positive view in this dissertation is that both points can be accommodated: Poor choices may sometimes be compensated, and some inequalities deriving from endowment differences may be permissible.

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entitlements126. The Scanlonian suggestion offers some encouragement as to how to

take this idea further, but it takes the fundamental focus away from luck (and, by

extension, away from the endowment distribution), and places it on ideas about

interpersonal relations and what we owe to each other. A plausible response to the

worries about Luck Egalitarianism is one that merely makes the commitment to the

Dworkinian distinction less inflexible. Such a strategy is what is offered by the

framework that has been provided: The piecewise-linear function has implications

that, at most, approximate those that follow from distinguishing more sharply between

brute and option luck. Roughly speaking, there is a tendency that those with bad starts

in life will be most well-represented among those who are entitled to redistributive

compensation. A necessary condition of having such entitlements is that one be worse

off than the level identified with the function’s threshold. Since this threshold is fixed

at the level of expected welfare associated with an average set of endowments, the

idea of having a bad start in life is strongly connected with whether one is entitled to

assistance from the state. Moreover, the paradigm examples of those falling victim to

bad option luck are of persons who have been born into unfavourable situations.

Clearly, this connection between entitlements and expectations is defeasible.

As I have said, one might have a bad start in life but end up doing well, or one’s level

may fall below the threshold in spite of having begun life with favourable

expectations. Such defeasibility, however, is exactly what should be desired if the

problems with the Luck Egalitarian distinction are taken seriously. The function leaves

it open whether those badly off as a result of their own recklessness are to have

weaker entitlements, or indeed denied entitlements altogether. Of course, this is

something that might depend on how badly off such victims of option luck actually 126 Ronald Dworkin claims that his use of the insurance model for determining entitlements does not abandon the victims of option luck ((2002), (2003)). Dworkin points out that an entitlement accrues whenever someone falls victim to the effects of luck that they would have insured against if “acting prudently” when offered the opportunity to buy insurance in the hypothetical setting of resource equality (2002: 114). The reference to prudence is problematic. Part of what gives Anderson’s point its force is the fact that prudence may often require the acceptance of a risk, given the balance between the cost of purchasing insurance (whether in a hypothetical situation or not) and the expectation of incurring a cost if exposed to the relevant risk. So long as it can be prudent to take uninsured gambles, then the Dworkinian insurance model may generate the same sort of implications as the cruder form of Luck Egalitarianism.

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are, in addition to how we evaluate how criticisable their choices have been. Overall,

however, such an approximate position might give the distinction the degree of

recognition it deserves. The framework on offer preserves the idea that there is

something particularly objectionable about persons being left the victims of bad brute

luck, but it offers sufficient scope for any departures we might want to take from the

view that personal choice makes the ‘all or nothing’ contribution to persons’

entitlements.

3.5 Summary remarks on Luck and Egalitarianism

My earlier discussion of the bare self problem included some description of

how a concern about endowment inequality could provide fundamental guidance for a

theory of justice. It is worth elaborating on how these represent a departure from the

Luck Egalitarian view, whilst remaining fundamentally concerned about the effects of

luck in ways guided by some sort of Egalitarian commitment.

Critics of Luck Egalitarianism, like Anderson and Scheffler, have

supplemented their more focused objections with a more general opposition to the

underlying focus on luck. Specifically, it has been said that the aim of Egalitarian

justice does not lie with the “elimination” of luck’s effects as such127. It may often be

true that victims of bad brute luck are entitled to compensation. But this, it is said, is

not simply because this is a politically important description, which they happen to

satisfy. Instead, Egalitarian justice is more fundamentally concerned with equality of

status. This idea is yet to be spelled out in very great detail, or at least hasn’t been

identified with very precise claims about how to regulate the material distribution

(given that the Luck Egalitarian method is being rejected). Of course, authors

emphasising the importance of status-equality can plausibly claim that regulation of

material shares would be required to make sure that some do not undergo the decline

127 Anderson (1999: 288-89). Scheffler argues that appeals to choice and responsibility play at most a “defensive” role in Egalitarian theorising, by having a use in resisting conservative complaints about redistributive policies that “reward the lazy”. These complaints portray the badly off as responsible for their situation, and Egalitarians may plausibly deny that this is so by advancing a better account of when persons are responsible (2005: 7-8). But according to Scheffler, however, Egalitarianism as a positive view does not assign a substantial role to responsibility.

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in status that such views regard as fundamentally unjust. It bears emphasis, however,

that it is unclear what all of this comes to, and certainly unclear why this view couldn’t

simply converge in some way with principles that make more nuanced, but still

essential, reference to the effects of luck.

Luck Egalitarianism is, after all, merely one possible development of the view

that luck and justice are intimately related. The critique of Luck Egalitarianism does

indicate good reasons for not relying too heavily on the distinction between brute and

option luck. But in rejecting the Luck Egalitarian view, we do not need to make ideas

about luck and endowments non-fundamental. We might instead seek a more nuanced

way of being guided by such ideas. For all that has been said about the importance of

status, no clear argument has been given for the claim that a focus on luck must be

excluded. Anderson has argued that identifying people as “victims” of brute luck risks

humiliating those that the theory aims to help, by presenting them to the rest of society

as talentless, ugly, or otherwise less valuable individuals. She points out that persons

with disabilities exhibit a clear dissatisfaction with state assistance when it comes in

the form of “condescending benevolence”. However, this may only reveal the fact that

we ought not to allow the recognition of entitlements to be accompanied with such

condescension. It is certainly possible to do the same on a theory where entitlements

are generated by facts other than those about luck: There might not be anything less

condescending about helping certain members of society only having highlighted them

as ‘vulnerable to being dominated by others’, or ‘incapable of looking after their own

status’. At the very least, avoiding humiliating someone by identifying them as

entitled to more than they in fact have is something that ought to be possible on any

view128.

The critics of luck-based views have emphasised the idea that a theory of

justice should treat people as equals. To say that persons ought to be equally regarded

is a moral platitude that is, in some sense, impossible to deny without saying

128

Dworkin claims that Anderson’s aversion to highlighting who is badly off could be as much of “a shield for the indifference of the rich not the dignity of the poor” (2002: 116-17).

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something gravely offensive. On the other hand, there is a sense in which people are

not equals at all. People are not equally disposed to taking risks, or equally willing to

work hard. What we might seek is a theory of justice that reflects both the moral sense

in which people are equally important, and the morally relevant ways in which they

are nevertheless different from each other, and how peoples’ differences might affect

their material entitlements. In effect, the framework that has been offered is one whose

appeal lies in the attempt made to be sensitive to both sets of considerations at once.

The piecewise-linear function specifies the terms for regulating the material

distribution in a hypothetical situation in which persons are perfectly equal in all the

relevant senses. A situation in which endowments are uniquely decisive in causing

material inequality can be regarded as one in which there do not exist the various ways

in which we are unequal with respect to many of the other morally relevant differences

between us. The view proposed is one on which these important factors are then able

to add their own contribution to a larger theory of justice. In this way, the piecewise-

linear function reflects a connection between justice and luck that is less objectionable

than the one provided by the Luck Egalitarian view.

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Chapter Four: Holistic Approaches to

Aggregation

I now intend to study more carefully the distinction between separable and

non-separable methods of aggregation. As I remarked in chapter two, this distinction

relates to a more abstract one between value holism and value atomism. The strategy

in this chapter is one that aims to establish conditions under which an item is valuable

in ways described by holistic views. The account developed may then be applied to the

more focused question of how to evaluate distributions of welfare. Whether

distributive principles are plausible when non-separable will depend on whether

distributions can be regarded as satisfying the conditions derived from the reflections

on value holism. In this chapter, I will argue that they do not. This counts in favour of

strongly separable principles of distribution, in general.

4.1 Ways of being concerned about inequality

Recall that a method of aggregation is strongly separable when the contributive

value of a life is determined in ways that are sensitive to the welfare, or personal

value, of that life, but independent of the welfare of other lives. I argued in chapter

two that the piecewise-linear function satisfies this definition. Generally speaking,

functions are non-separable when relations between the welfare of different lives are

allowed to matter. One question we might first ask is whether an Egalitarian approach

to distributive justice must be of the sort where an aversion to inequality is built into

the method of aggregation itself. By answering this question, we can get a sense of

how strong the motivation is for avoiding strongly separable functions129.

129

As I remarked in chapter two, Egalitarian functions are not the only non-separable ones. It is possible to motivate the rejection of strong separability, for example, by attaching some concern to average welfare. I regard this as a less interesting way of motivating a holistic approach to distribution, and in any case I have already expressed certain views about average levels in chapter three. As I have announced, the argument eventually given in this chapter is one that counts against the plausibility of all non-separable functions, including ones embedding references to average welfare.

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The chief motivation for a non-separable, strongly Egalitarian function has to

be some commitment to the view that inequality is bad in itself. Any other concern for

inequality will be instrumental, or intrinsic in ways less directly connected with the

distribution as such. If a concern for equality has this more indirect character, then a

strictly Egalitarian method of aggregation will not be among the commitments of the

overall view. This is because a range of distributive principles will favour certain ways

of reducing inequality so long as they are appropriately non-linear. This is all that is

needed for a principle to recommend the sort of redistributive transfers that reduce

inequality – that a principle be non-separable is not a necessary condition of it having

this sort of implication. Thus, for any view on which the badness of inequality falls

short of its being bad in itself, some sort of Prioritarian function might be adopted. If,

however, material inequality is regarded as intrinsically bad, then there is considerable

pressure to adopt Egalitarian kinds of non-separable function, such as the one sketched

in chapter two. It is only these functions that can always attach value to reductions in

material inequality. Prioritarian functions only advocate the reduction of inequality by

way of transfers. By definition, this means that inequality’s reduction is only valuable

when it involves some person being made better off. However, inequality can also be

reduced in ways that benefit no one, as occurs simply when the better-off are made

worse-off. Some have argued that this sort of ‘levelling down’ is hardly the sort of

thing favoured by any plausible distributive principle. The fact that it is endorsed by

strictly Egalitarian principles is often seen to count heavily against such principles.

Although much has been made of the distinction between Egalitarian and

Prioritarian views, authors who are particularly concerned with distributive justice

have often sought to deflate it. This is partly because these sorts of theorists tend to

have little time for the idea that material inequality is bad in itself130. It is also because

they tend to distinguish the political motivations for a principle of distribution (which

may be purportedly Egalitarian) from the form of the principle itself (which may not

be Egalitarian in the strict sense). Writing about “politically engaged” Egalitarians,

G.A.Cohen writes that: 130

See for example O’Neill (2008).

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What they find wrong is that there is, so they think, unnecessary hardship at the lower end

of the scale. There are people who are badly off and who, they believe, would be better

off under an equalising redistribution...For these Egalitarians, equality would be a good

thing because it would make the badly-off better-off. They do not think that it is a good

thing about equality that it would make the well-off worse-off.131

Cohen expresses a view whose possibility confirms what I have just suggested,

namely, that not all elements of what motivates a distributive principle need to be

replicated in the principle’s extensional structure itself132. It is enough that a principle

delivers results that happen to respect the values that generated the need for a

distributive principle in the first place. Part of what is suggested is that the ‘equality

versus priority’ question is merely a question about extensional content, which doesn’t

have any deeper political significance133.

Cohen may be right that an Egalitarian concern remains just as worthy of the

name even if it excludes the idea that inequality is bad in itself. If so, then there is no

decisive link between favouring the value of equality as part of regulating the material

distribution, and being committed to a non-separable principle for the purposes of

directing such regulation. However, non-separable principles may remain motivated

even if it is only a rather narrow sort of Egalitarianism that would motivate them.

Unlike others, I find it difficult to simply rule out the view that certain distributions, or

distributive trends, may be bad in themselves. Or, at least, I am open to the idea that

distributions may have ‘bad making’ properties. This means that our evaluation of

distributions may be partly sensitive to the intrinsic badness of certain patterns, even if

such evaluation is more substantially governed by other concerns.

The idea that it would be unjust for endowment inequality to have an

unconstrained impact on material shares does not entail the view that certain material

131

(2008: 31). 132

In a publication that was released just prior to completing this dissertation, Cohen makes a very similar point (2011: 69-72). 133

This is not to say that the extensional question lacks interest. Apart from differences relating to levelling-down, Prioritarian and Egalitarian principles have rather different implications with respect to the evaluation of risk, which indicate further substance to the distinction. On this, see the exchange between Fleurbaey (forthcoming) and Broome (forthcoming)

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distributions are bad in themselves. However, as I remarked during chapter one’s

discussion of Rawls, it is hard to completely abandon the view that there might be

something intrinsically bad about certain distributive consequences, even if other

factors make a larger contribution to the regulation of these consequences134. Now,

none of this entails that any intrinsic badness of distributions is attached to any

material inequalities that they might exhibit. But still, the intrinsic badness of

inequality remains a possible position just so long as the intrinsic badness of anything

about the material distribution remains a possible position. Given this, there remains

something to be said for gaining a more thorough understanding of non-separability

and the value holism that lies behind it.

4.2 G.E.Moore on parts and wholes

In 1903, G.E.Moore claimed, “The value of a whole must not be assumed to be

the same as the sum of the values of its parts”135. This is commonly known as his

Principle of Organic Unity. It is easy to think of examples that confirm its truth. A

mosaic gets its value not merely from the respective values of its stones, but from the

value of their being arranged in a certain way. Jumble up the stones a bit, and you

might spoil the mosaic. But you won’t have made any of the stones worse. Similarly,

the same set of musical notes could be arranged into an irritating noise, or a pleasant

piece of music. But the set of actual notes, and their respective values, may be the

same in either case. In Moore’s terms, mosaics and symphonies are examples of

‘organic wholes’. How we understand the nature of such wholes forces us to think

carefully about the metaphysics of value.

On its own, Moore’s principle is a purely negative view. We will need a more

substantial metaphysics of value if we are to explain what makes his principle true,

and to identify any less obvious (and more interesting) cases of organic wholes. Now,

Moore did hold views that count towards a fuller metaphysics of value, and his readers

134

Recall (1.3), above. 135

(1903: 28)

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have extracted positive principles from these views. Here is a formulation from

Thomas Hurka:

The intrinsic value in a whole composed of two or more parts standing in certain

relations need not equal the sum of the intrinsic values those parts would have if they

existed alone, or apart from those relations.136

We may call this view ‘Moorean Holism’. It goes beyond the Principle of Organic

Unity by explaining why summing the values of parts may not yield the value of the

whole. Moore’s explanation is that relations between these parts also matter. Moorean

Holism recalls the need to distinguish an item’s contributive value from other senses

in which it has value. When talking about distributions, I have contrasted the

contributive value of a life with its personal value. This terminology works for

distributions construed as sets of lives, but it doesn’t fit with more general claims

about parts and wholes. Following Hurka, we may simply replace ‘personal value’

with ‘intrinsic value’. After all, personal value was understood as how good a life is to

live. Bearing in mind that this is distinct from the value of the person living this life,

there seems nothing wrong with regarding personal value as intrinsic value. Clearly,

Moorean Holism retains the idea that a part’s contributive value may be greater or less

than its intrinsic value137. Moorean Holism implies that a part’s contributive value may

vary according to which relations obtain between that part and other parts. Changes in

these relations may affect a part’s contributive value even if its intrinsic value is held

fixed.

At this point, it is worth adding a qualification that wasn’t made during any

discussion of the way in which lives contribute to the value of distributions. This is

that ‘contributive’ value is meant to have a purely inferential sense. This is to say, the

value of a whole may merely be deduced from the contributive values of its parts. This

inferential claim should not to be confused with the more metaphysically committed

view that the parts (and the relations between them) contribute a value to the whole in

136

(1998: 300, emphasis added). 137

Intrinsic value may be here regarded as a more general term than ‘personal value’, which allows the same contrast with contributive value in the narrower context of distributions of welfare.

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the sense of conferring value on the whole. This metaphysical claim asserts that parts

of a whole have a sort of evaluative priority over the whole itself. As I shall suggest

later on, such priority may sometimes obtain, but may sometimes run in the opposite

direction. Treating contributive value as an inferential idea permits neutrality with

respect to the direction of evaluative priority, and about other metaphysical matters.

I shall now make a small digression. Hurka’s formulation of Moorean Holism

is attractive, but I propose we amend it in one way. Specifically, we should seek to

replace the notion of summing the values of a whole’s parts. This idea is actually too

narrow. It is possible for the value of a whole to be insensitive to any relations

between its parts, and to be distinct from the sum of the values of its parts. To see this

we need only recall some of the details laid out in chapter two. For example, the value

of a whole may be equal to the sum of the square roots of the value of its parts. Other

suitable examples could be provided by any strongly separable function that also

happens to be non-linear. If Moorean Holism is to be presupposed only by non-

separable functions, then it needs to exclude more than the idea that a whole’s value

can be deduced from the sum of its parts’ values. As a matter of fact, Moore seemed to

realise this. In one of his formulations he claimed that, “the value of a whole bears no

regular proportion to the sum of the values of its parts”. The relation ‘bears no regular

proportion to’ is wider than ‘is equal to the sum of’. If the value of a whole is gained

by (say) summing the squares of the values of its parts, then there is still a strong sense

in which the whole’s value varies in proportion with the parts’ values. Really, Moore’s

principle is not just a denial of the view that we can always derive a whole’s value by

summing its parts’ values.

The purpose of this digression is to highlight one particular fact. What Moore

really wants to deny is value atomism. Roughly speaking, atomism is the view that, for

any whole, each of its parts makes an independent contribution to the value of that

whole, i.e., contributes the same regardless of what other parts may be present. The

question of whether atomism is true is what underlies the question of whether it is ever

plausible to avoid non-separable functions.

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4.3 How the value of a whole might depend on relations among its parts

As I have said, Moore did not develop his metaphysics of value to so great an

extent that we have a complete account of his holism. If we had a fuller account of

organicity, then we might be in a better position to assess views that posit organic

wholes in particular contexts, such as certain principles of distribution. Unfortunately

(for our purposes), most work on Moore has focused on defending his view against

alternatives, rather than filling it out and further applying it. The chief contention here

has been over whether Moore had the right alternative to value-atomism. Some

authors think that Moore was right to assert the Principle of Organic Unity, but got his

holism wrong. These authors agree that certain wholes are valuable in ways

incompatible with value atomism. But they deny Moore’s positive claim that the value

of these wholes can be inferred from facts about the relations between their parts. Such

authors maintain that organic wholes occur in virtue of the fact that a whole’s parts

may change their contributive value as they move from whole to whole138. Most of the

recent literature has been concerned with the question of whether this ‘Dynamic

Holism’ is more plausible than the Moorean view. An effect of this focus is that there

has been very little work done within the terms of Moorean Holism itself. I do not

have anything to add to the more popular debate here. So, I shall have to assume that

Moorean Holism is at least as plausible as Dynamic Holism139. In any case, it has been

said that the disagreement between Moorean and Dynamic views will not make any

difference to which wholes are organic, but merely to the explanation of why they are

organic140. But Moorean Holism strikes me as a sufficiently interesting view to

motivate some further development, even if not everyone accepts it.

I want to first focus on the question of which kinds of relation among a whole’s

parts are those that affect the contributive value of those parts. We might begin with a

comment made by Jonathan Dancy:

138

See Dancy (2003), Korsgaard (1983) 139

Authors that defend Moore against the Dynamic Holists include Hurka (1998) and Brown (2007). 140

Hurka argues for this point.

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When some part contributes to the whole more value than it has in that whole, part of

the value of the value of the whole is to be explained by appeal to the presence of that

part, but not by appeal to the value of the part.141

Dancy is claiming that a part can contribute to a whole’s value not just by having a

certain intrinsic value, but by being a certain sort of part. This observation invites the

following distinction: On the one hand, the value of a whole may depend on the

relation between the intrinsic values of its parts. On the other hand, the important

relation might be one that extends between some other properties of the parts, besides

their values. Dancy seems to be affirming this second possibility at the expense of the

first. For the sake of convenience, I propose that we call the first possibility, de dicto

organicity, and the second, de re organicity.

We can determine whether an organic whole is of the de re or de dicto variety

by examining what could happen if certain parts were removed, and replaced with

different parts that have the same intrinsic value. The effectiveness of this method can

be demonstrated by recalling one of the earlier examples of an uncontroversial organic

whole. Suppose that one stone is removed from a mosaic and replaced by another.

This might improve the mosaic. But the improvement may take place in spite of the

fact that the new stone isn’t any more attractive, when viewed in isolation, than the

stone it has replaced. Plausibly, this is because the greater contributive value of the

new stone is owed to the way in which it better complements the stones elsewhere in

the mosaic. Another equally attractive stone may fail to do this as well. The point is

that complementary relations between colours are not relations that obtain between the

intrinsic values of stones. Therefore, the organicity of mosaics is de re rather than de

dicto.

Now, Egalitarian methods of aggregation imply that distributions of welfare

are de dicto organic. This is because they place importance on relations between the

welfare levels of different lives, not a relation between any other properties of lives.

And the welfare of a life (construed as something that can be lived) is just its intrinsic

141

(2003: 630, emphasis added).

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value. Substituting lives in a distribution is, therefore, not like substituting stones in a

mosaic. Removing one life from a distribution, and replacing it with a very different

life lived at the same level of welfare will never effect the value of a distribution142. So

far, it is hard to know why this would count against Egalitarian principles. However,

the significance of the distinction between de dicto and de re organicity becomes clear

only once we observe a second distinction.

4.4 Evaluative priority and explanatory priority

As I have said, ‘contributive value’ can be read in either a strongly

metaphysical or a merely inferential sense. The metaphysical sense pertains to the

direction of evaluative priority: When wondering about the relation between a whole

and its parts we may ask which of these has, so to speak, fundamental status with

respect to the other. Roughly speaking, evaluative priority runs from one item to

another when the second item bears value of a sort that is derivative of the first item’s

value. As is familiar, the fact that one item’s value can be derivative of another’s is

something that can obtain in more than one way. An item may confer value on some

other item in virtue of being an intrinsically valuable effect of the second item. In this

case, the value conferred is instrumental. Or, it may confer value non-causally, as

when some item is valuable for the way in which it represents some other, intrinsically

valuable item. I shall come back to this distinction in due course. First I just want to

focus on the fact that, at least in principle, evaluative priority can run in one of two

directions. On the one hand, the value of some set of parts may be at least partly

derivative of the value of the whole they are in. I will call this inward organicity. This

alludes to the idea that value is conferred, as it were, by the whole onto its ‘interior’

parts. On the other hand, we may conceive of outward organicity. This occurs when a

whole’s parts confer value onto the whole itself.

142

Note that by ‘substitution’, the life is removed from a distribution not in the sense that the person who lives it is killed, but the more conceptual point that the distribution is imagined to have not included that life in the first place.

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It should be observed, although it is somewhat incidental, that a case of

outward organicity is one in which the parts of the relevant whole remain intrinsically

valuable. This can seem odd. As I have said, it is customary to regard derivative value

as instrumental (having valuable effects), or extrinsic (gaining value from another

source)143. However, neither of these descriptions fit with the possibility that

evaluative priority can obtain within an organic whole. Clearly, wholes need not make

their parts instrumentally valuable, or vice versa. The concept of extrinsic value may

seem more appropriate, but the problem is that this is normally understood as value

gained from a metaphysically external source, such as when a wedding ring gains its

value from the marriage it represents144. The fact that evaluative priority within

organic wholes cannot run from intrinsic to extrinsic value is, crudely speaking, owed

to the definitional truth that parts cannot be external to the whole they’re in. Value

conferred by parts onto a whole will still be intrinsic value just because, on the

standard definition of intrinsicness, the whole would still have this value if it were the

only thing existing in the universe, given that the whole’s own existence still requires

the existence of its parts. If, on the other hand, a whole confers value on its parts, then

it might be appropriate to regard this value as extrinsic, since any such part wouldn’t

have this value if it existed alone, without the other parts necessary for the whole to

exist.

What these points suggest is that evaluative priority comes apart in some way

from the intrinsic/extrinsic value distinction. The facts here are evidently quite

complicated, and they make it difficult to get a fully satisfactory account of exactly

how evaluative priority is related to this distinction. Nevertheless, I think the idea that

organicity may be inward or outward remains coherent. That is to say, there is nothing

obviously wrong with the idea that sometimes a whole’s value is conferred on it by the

value of its parts, whilst it is equally conceivable that things might be the other way

round. The question I wish to now ask is how these two distinctions fit together.

143

This categorisation comes from Langton (2008). 144

This example is also from Langton.

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I have said that, within an organic whole, evaluative priority may run in either

of two directions. I will now expand a little on what evaluative priority amounts to. To

use Langton’s example again, to say that a marriage confers value on a ring is not to

exhaust what might be said about the relation between the two. It is plausible, in

addition, that the explanation of the ring’s value can be identified with the intrinsic

value of the marriage. I am going to depend on this claim in some arguments that I am

about to make. Because it plays an important role in these arguments, I will highlight

it, and give it a name:

The Parallel Priorities Principle

For all instances of derivative value, part of what explains this value is

identical to what confers it.

In short, the principle above expresses the view that evaluative priority

includes, or at least entails, some sort of explanatory priority as well. I do not have

time to properly defend this principle. But it seems to me to be true, and in any case it

appears to be confirmed by uncontroversial cases of organic wholes. We care about

the notes in a symphony because we care about the symphony itself. It is not as if

symphonies are good things just because they ‘contain’ something that we care about

prior to their being assembled as the symphony itself, namely single musical notes.

Similar remarks could be made about mosaics. We don’t admire mosaics because we

admire stones as such (even if valuing stones as such happens to be something we

independently do). We admire a plurality of stones when (and because) it has been

arranged into a mosaic. Thus the contributive value of a mosaic stone is dependent not

just on the intrinsic value of that stone, but also on the extrinsic value conferred onto it

by the whole.

Four metaphysical combinations have now been identified. Organicity may be

de re inward, de re outward, de dicto inward, or de dicto outward. When organicity is

affirmed in particular contexts, it may be that a particular combination is thereby

affirmed as well. And this combination, in that context, may be implausible. If I am

right in what follows, we can use PPP as a means of helping to decide this.

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4.5 Why the material distribution is not an organic whole

I shall first ask which combination fits with the uncontroversial cases of

organic wholes. Recall that mosaics and symphonies exhibit de re organicity. It is also

plausible to regard them as organic in the inward sense, for reasons that I have

explained. As I have said, Egalitarian methods of aggregation treat material

distributions as de dicto organic. The next question is what to say about evaluative

priority.

To answer this question, we can plausibly claim that the distribution of welfare has

importance just because people have importance. This view is often affirmed by

political philosophers145. I find it hard to deny, and it is rarely, if ever, contested by

others. Elizabeth Anderson has provided a fuller statement of this idea:

To pile up people so that more ‘welfare’ can exist, or to get rid of them so that a

higher average level of welfare can exists, is to regard people as merely the

extrinsically valuable containers for what is supposedly intrinsically valuable – states

of affairs in which welfare exists. The mistake is…to lose sight of the fact that what

gives the pursuit of or desire for welfare its only point is that we ought to care about

the people who enjoy it.146

Anderson makes these remarks as part of an argument against Utilitarian theories, but

she might have presented it as a worry about aggregation in general. Anderson’s

complaint is really with the idea of betterness orderings of distributions of welfare

(Utilitarian or otherwise), as if distributions can be construed as value-bearers in their

own right. It is worth pausing to gain an understanding of exactly what objection is

being made here, and what its implications are.

Anderson’s objection can be interpreted as connecting aggregation with value-

fetishism. Roughly speaking, value-fetishism is what occurs when an item is valued in

ways that are inappropriate, given the sort of value (if indeed any) that this item

actually has. We can improve on this definition if we make further reference Rae

145

For example, Anderson (1993: 27). 146

(1993: 28).

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Langton’s work on categories of value. Langton has explained, recall, that there are

three types of value, namely intrinsic, instrumental, and extrinsic. This taxonomy

allows us to better define value-fetishism as the act of miscategorising an item’s value.

That is to say, one fetishises an item’s value when one responds to this item as if it

falls into a category other than the one into which it really falls147. That is to say,

value-fetishism consists in treating what is instrumentally valuable as if it were

intrinsically valuable, or treating what is intrinsically valuable as if it were

extrinsically valuable, and so on. Anderson claims that a concern with the distribution

of welfare only makes sense if it is guided by a more fundamental concern with

persons, given that it is persons who constitute distributions of welfare, and who are

affected by changes in a distribution’s shape. For Anderson, the problem with methods

of aggregation, or at least with Utilitarian methods, is that they treat the distribution of

welfare as bearing intrinsic value when it only bears extrinsic value. As such,

Utilitarian methods of aggregation require us to fetishise the value of welfare.

The idea that caring about distributions depends on caring about persons

implies that distributions of welfare are outwardly organic. Because of this, and

because of the commitment to regarding a distribution as de dicto organic, Egalitarian

methods of aggregation entail the denial of the earlier principle that evaluative and

explanatory priority run parallel. Here is why: The intrinsic value of persons is what

explains the value of distributions of welfare. But, if a commitment to non-separable

principles is plausible, then what confers value on distributions is surely something

else. This recalls the essential motivating idea that inequality is bad in itself.

Egalitarian principles accommodate this idea by making the value of a distribution

depend, in part, on differences between the welfare levels of persons. In this way, the

relation between welfare levels is included in what confers value on a distribution, but

is excluded by what explains this value (the fact that the distribution contains lives

147

This definition is, I think, adequate for our purposes. But it will need to be made more complex if it is to be generally plausible. As Langton observes, items often don’t fall into one category exclusively. Rather, something may be intrinsically valuable and yet instrumentally valuable in some other respects. Thus, items tend to fall into the various categories in some sort of combination. Thus, value-fetishism may consist in getting this combination wrong (the cruder definition just given counts as an instance of this).

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lived by intrinsically valuable persons). This is contrary to the principle state above.

The only way in which this principle could be satisfied is with the help of a view on

which the intrinsic value of persons somehow includes their capacity to be better or

worse off than each other. But even if this view turned out to be coherent, it hardly

seems plausible. To accept this view, we would need to accept that part of what makes

persons matter is something that would disappear if it turned out that all persons could

only live at the same level of welfare. Even thought it might be regrettable if this were

true of persons, it hardly seems to imply that persons would matter less.

Now, one might think that theories of justice don’t really fit Anderson’s

positive view of why should care about distribution either. At least, theories of justice

are designed for use in bringing material shares into conformity with what persons’

entitlements are. One can talk about this project as being motivated by values such as

fairness, freedom, or (depending on one’s theory) perhaps other values as well. But

it’s less often that one encounters anyone claiming that their theory of justice is

ultimately about valuing persons themselves148. One might apply these general

observations to the use of a piecewise-linear function, and point out that the value of

persons was not once mentioned when the case was assembled for this function in

earlier chapters. In response to this line of thought, one might point out that the ‘value

of persons’ is, in any case, something of a slogan that means different things to

different philosophers, and has been appealed to in the defence of rather different

views. This is why it is perhaps advantageous to take Anderson’s point mainly in its

negative guise just described, which is just that any principle of distribution,

Utilitarian or otherwise, should not be adopted as a result of fetishising trends in the

distribution as such. This, I think, is right. And as I am about to suggest, it is arguable

that this sort of fetishism is present in non-separable methods of aggregation. Since the

use of the piecewise-linear function is motivated by a fundamental concern about not

148

Robert Nozick claims that “political philosophy is concerned only with certain ways that persons may not use others”, and also claims that his Libertarian theory has a Kantian dimension in virtue of the importance it places on persons not being treated merely as a means so that others may be made better off (1974: 32). This is close to a position that grounds justice in views strongly associated with the value of persons. I leave it open whether Nozick’s brief allusion to Kantian foundations is one that is genuinely Kantian, or whether it increases the plausibility of his views on justice.

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allowing endowment inequality to have unfettered influence on the material

distribution, this sort of value-fetishism is avoided. Or, at any rate, there is enough in

the view I have defended to resist the conception of distributions as organic wholes in

the first place, and thus the direction of their organicity does not arise. I shall leave it

open as to whether there is any room to be made for the value of persons in all of this,

although I shall return to Anderson’s view again in the final chapter.

The right conclusion, I think, is to conclude that non-separable principles

require us to make a mistake about how the value of a distribution is conferred on it.

In particular, they are mistaken in believing that inequality is bad in itself. It is worth

noting, moreover, that the argument just made may have no further revisionary

implications about organic wholes. This is because I don’t believe any other wholes

exist that are de dicto organic. A commitment to de dicto organicity seems to be an

important part of what generates a violation of the parallel between evaluative and

explanatory priority. Roughly, the apparent safety of de re organicity is perhaps

attributable to the importance being placed on relations between intrinsic properties of

the parts. Very often, it is the intrinsic properties of something that explain both why it

is intrinsically valuable, and why it confers intrinsic value on anything else. In

contrast, de dicto organicity requires that certain quantitative relations (those

extending between the values of parts) are what affect the contributive values of those

parts. But, offhand, it’s hard to imagine why the good-making properties of some set

of items would include these numerical relations.

4.6 Summary comments on non-separable aggregation

This concludes my treatment of non-separable methods of aggregation and

how their assessment may be related to matters about the metaphysics of value. I have

blamed the failure of Egalitarian principles on the motivating idea that inequality is

bad in itself. This may seem to also threaten my earlier expression of sympathy

towards the more general idea that one or another distributive trend might be bad in

itself. I didn’t say which trend this had to be, and it needn’t be material inequality.

Given the resemblance of the piecewise-linear function to the Prioritarian function, the

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more natural suggestion is that there is something intrinsically bad about some persons

being badly off in an absolute sense, not in their being worse off than others.

I should stress that I am rejecting non-separable theories as a consequence of

the arguments in this chapter. Certain others, however, have rejected the idea of non-

separable aggregation more swiftly than I have. Recall that non-separable principles

tend to judge the contributive value of a life according to facts about other lives. Some

critics find this feature to be independently implausible. One thing that has been

pointed out is that a non-separable method of aggregation is committed to taking into

account even lives that are quite remote in time or space from a given life whose

contributive value is to be determined. If a sufficient number of remote lives have a

very high quality, then the addition of a new life that is also of high quality may turn

out to be a bad thing. As Derek Parfit remarks, “research in Egyptology cannot be

relevant to our decision whether to have children”149. This is a touch rhetorical and

perhaps Parfit overstates the point. However, a non-separable function avoids

whatever difficulty is present. I share the intuition that the difficulty here is a genuine

one. But I have not used this common complaint about separability in the arguments of

this chapter. In large part, the arguments of the latter half of this chapter can be viewed

as an attempt to articulate such doubts about separability with more thoroughness,

involving an argument from more independent premises. (Parfit’s remark also raises

the challenging matter of how to evaluate variations in population size, which is the

subject of the next chapter.)

The distinction between separable and non-separable methods of aggregation

has been long regarded as related to the matter of whether views about the regulation

of distribution are genuinely Egalitarian. I discussed some elements of this debate in

the opening section of this chapter. Here, it was suggested that the distinction between

Egalitarian and Prioritarian principles is really confined to the extensional content of

149

(1984: 420). For a similar point, see Broome (2004: 194-95). It has also been pointed out that separability makes a theory much easier to implement in practical contexts, since it allows a theory to be put to use even if information about the welfare of certain people cannot be acquired; see Blackorby et al (2005: 86).

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these principles, in ways that may not do enough to justify the claim that Prioritarians

are (necessarily) not concerned about material equality. Although it is sometimes said

that the Prioritarian function is non-comparative, it may be that it rests on motivations

that are comparative, just not in ways best captured by functions that have an explicit

measure of inequality built into their structure. If the arguments of this chapter are

correct, then strongly separable functions, such as Prioritarian ones, may offer the only

way of giving precise content to certain Egalitarian ideals.

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Chapter Five: Population Size

This chapter returns to a focus on the piecewise-linear function discussed at

some length in chapters two and three. I shall close this dissertation by relating this

function to a long-standing problem about distributions, albeit one that has not

featured very prominently in recent debates about distributive justice. This is the

problem of how to evaluate variations in population size. More specifically, the focus

here will be on how to compare such variations with other ways in which a

distribution may undergo change (specifically, ways in which the welfare of existing

people may change). The argument of this chapter will be that the piecewise-linear

function provides the most balanced way of accommodating the various competing

considerations. In articulating this argument, I shall be relying more heavily than

before on some of the more technical features of distributive principles that were

introduced in chapter two.

5.1 Adding lives versus improving lives

Common sense suggests a moral distinction between the value of adding

human lives to the world, and the value of affecting the quality of human lives that

already exist. The fact that common sense is so inclined is easy to see. First, suppose

that one fails to improve the well-being of an existing person. Very often, a failure to

improve the well-being of someone else seems like a failure to do something good, or

a failure to act on a moral reason that one has, even if that reason is not very strong.

Suppose, on the other hand, that one fails to bring into existence a new, ‘extra’ person.

Setting aside the effects that the creation of a new life may have had on the quality of

existing lives, this sort of failure does not seem as if it should be evaluated in the same

way. In particular, it doesn’t seem that the world is less good just because some

possible person does not get added to it. Also, it seems like the failure to bring people

into existence is not a failure to act on a moral reason. At any rate, adding well-being

to the world by way of adding it to a human life seems to be rather different, morally

speaking, than adding well-being by way of increasing the number of human lives. As

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Jan Narveson once said, “we are in favour of making people happy, but neutral about

making happy people”150. Not only is this view in tune with common sense, it also

shows up in health policy as well151.

Narveson’s claim is just a slogan. And the claims I made in the opening

paragraph do not go very far beyond it. One thing that will become clearer as I go on

is that giving a proper formulation of the common sense view is not altogether

straightforward. Defending it is even harder. This chapter tries to do something about

this. In what follows, I shall treat the problem posed by the common sense view as one

that falls within the ethics of distribution. That is to say, the common sense view

should be analysed by way of investigating whether it can be accommodated by some

principle of distribution, such as those familiar from various debates in moral and

political philosophy. Regarding the common sense view as some sort of claim about

how we evaluate distribution is not the only way of understanding it152. But it is a very

natural one.

Any attempt to accommodate a given view within a larger theoretical

framework requires the assumption that the view one wants to accommodate is

plausible to begin with. We might therefore pause to ask why we should take the

common sense view seriously. In response to this, I am not going to provide any

original argument for why the common sense view expresses some deep truth. But I

will pause to consider, all the same, some abstract statements about the value of

human life, which appear to count in favour of some distinction between adding

human lives and improving human lives. T.M. Scanlon provides a readable example:

150 (1973: 73). 151 In its current (2004) guidelines on fertility treatment, the UK’s National Institute for Clinical Excellence recommends that the creation of new life be not included among the beneficial effects of assisted reproduction treatments. According to NICE’s guidelines, the benefits of such treatments are restricted to effects on existing people, such as the parents of babies born as a result of such treatment. 152 One might try to flesh out the common sense view in terms of something other than a principle of distribution, for example by appealing to familiar distinctions between harming and benefiting. Various strategies of this sort are examined by McMahan (2009). As McMahan shows, the common sense view is no easier to defend on any of these strategies than it is on the one adopted here.

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Appreciating the value of human life involves seeing that we have strong reason not to

destroy it and reason to protect it when we can…Those reasons themselves do not flow

from the thought that it is a good thing for there to be more human life rather than less.

This is shown by the fact that while we have strong reasons to protect human life and not

to destroy it, we do not have the very same reasons to create more human life when we

can. Insofar as we have reasons to create new life, these are different from, and weaker

than, our reasons not to destroy it.153

In addition to Scanlon’s, various similar claims may be found scattered around the

literature on moral and political philosophy154. The quotation from Elizabeth

Anderson, used in the last chapter, is one such example. If authors like Scanlon and

Anderson are right, then the fact that something is valuable does not call for any

increase in the number of instances of that thing. Instead, the value of something

appears to require that whatever instances there are of that thing need to be preserved,

respected, or otherwise taken care of155. The value of persons, according to Scanlon, is

a case in point. Simply having more persons around is not, in itself, particularly

important, even though persons are valuable things. But promoting the well-being of

whatever persons there are does seem to be important, and its importance is explained

by the fact that persons are valuable. Scanlon’s abstract view about the nature of value

seems plausible enough to me. At least, it seems to provide a foundation for the

common sense view that is sufficiently strong to show that common sense might be

taken seriously here. Hence, we should do what we can to preserve the common sense

view in our attempts to develop a proper account of how to compare distributions

containing different numbers of lives.

5.2 Refining the common sense view

Efforts at refining the common sense view have been made by other

philosophers, and these give us a good place to start. One formulation has been

provided by John Broome, by way of what he calls the Principle of Equal Existence:

153 (1998: 104). 154 Very similar remarks are to be found in Adams (1999: 119-20) and Dworkin (1993: 73-74). 155 Readers familiar with Scanlon’s work will recognise that this claim is an important element of his wider theory of value, which is laid out throughout his (1998).

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Suppose two distributions have the same number of people, except that an extra person

exists in one who does not exist in the other. Suppose each person who exists in both

distributions is equally as well off in one as she is in the other. Then there is some range

of wellbeings such that, if the extra person’s wellbeing is within this range, the two

distributions are equally good156.

Broome adds that it is natural to think that the neutral range has a lower bound,

beyond which there is a ‘negative range’ of well-being levels. This means that adding

a life can count as a bad thing, when the life in question is of a low enough quality.

Something close to Broome’s refinement of the common sense view is proposed by

Jeff McMahan, which he calls The Asymmetry:

The fact that a person's life would be worse than no life at all (or "worth not living")

constitutes a strong moral reason for not bringing him into existence, the fact that a

person's life would be worth living provides no (or only a relatively weak) moral reason

for bringing him into existence.157

Structurally speaking, Broome and McMahan’s formulations do not differ very much.

McMahan’s Asymmetry is one respect stronger than Broome’s Principle of Equal

existence. It is explicit about where the boundary might lie between what I have

described as the neutral and negative ranges. According to McMahan, the addition of a

life is neutral so long as it would be lived at a level high enough to be worth living.

Broome’s formulation of the common sense view leaves it open where the boundary

might lie, and ventures no more than that both of the ranges exist. As we shall see later

on, it is advantageous to allow ourselves some flexibility as to where to locate this

‘neutral level’. Because of this, I shall proceed with Broome’s formulation over

McMahan’s. 158

156 (2004: 146). 157 (1981: 100). 158 Another more obvious difference is that McMahan uses the vocabulary of moral reasons, whilst Broome makes reference to the ‘betterness’ of states of affairs. I have so far switched between these terms myself. However, these differences in vocabulary are normally thought to correspond to substantive issues. The substance of these issues is genuine, but I do not wish to take any stance on these matters here. Part of the reason for thinking that Broome and McMahan are interested in an idea about distribution that is independent of these differences of vocabulary is the fact that both make explicit reference to Narveson’s claim, stated at the outset, as the view that they are attempting to

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Now that we have gained a more precise formulation of what the common

sense view actually says, we may begin to ask whether there exists any principle of

distribution that can do justice to it. As anyone familiar with work done on population

size will know, the results are going to be disappointing. That is to say, the common

sense view does not, after all, represent a coherent view of the sort that can be fit into

any principle that can properly compare different possible distributions of well-being,

at least given some fairly uncontroversial assumptions about the nature of these sorts

of comparisons. I shall review the arguments that establish this in the next section. In

later sections, I will be concerned with explaining why the disappointment we ought to

feel might be less severe than it might first seem.

5.3 Trouble with the common sense view

John Broome has shown that his own formulation of the common sense view

leads to problems that warrant its rejection. Broome’s argument is persuasive, and I

am more interested with understanding its lesson than in querying it. So I shall

rehearse Broome’s argument with fairly minimal detail.

Recall that Broome formulates the common sense view in terms of a ‘neutral

range’ of wellbeing levels. It is this idea of a range of such levels that generates

trouble. To see this, imagine two different welfare levels, m and n, where both lie

within the neutral range and where m < n. According to Broome’s Principle of Equal

Existence, a distribution containing one life at m is equally as good as a larger

distribution containing two lives at level m. For short, we might say that the vector

<m> is equally as good as the vector <m, m>. It should be obvious why the common

sense view regards these different distributions as equally good: The only way in

which they differ is that one of them contains an extra life, whose well-being lies in

refine. At any rate, I think that whatever the vocabulary with which one chooses to refine the common sense view, one will still have an interest in the question of which principles of distribution come closest to satisfying that refinement. As I shall show, what is of most interest is the form of different distributive principles, which is independent the meta-ethical commitments that might accompany them. For this reason, I shall be somewhat liberal in continuing to switch between the two forms of vocabulary later on.

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the neutral range. So if the common sense view is right, this addition has neutral value.

Similarly, <m> is equally as good as another alternative distribution, <m, n>. Once

again, n lies in the neutral range. Now, based on what has just been said, one might

conclude that <m, m> and <m, n> are equally good. What warrants this conclusion is

the fact that both are equally as good as the smaller distribution <m>. On the

assumption that ‘equally as good as’ is a transitive relation, any two items that are

equally as good as some third item must also be equally as good as each other.

However, it is very natural to believe that these two larger distributions are not equally

good. Rather, it is plausible that <m, m> is better than <m, n>, just because one person

is better off in the latter than the former, and no person is worse off in the latter than in

the former. In other words, we now seem faced with a dilemma: Either take the drastic

step of denying the transitivity of ‘equally as good as’, or else give up the common

sense view159.

Broome’s argument shows the impossibility of a principle of distribution that

accommodates the intuition of neutrality, given continued assumptions about

transitivity and other plausible conditions160. We haven’t needed to even look at any

particular principles of distribution in order to see this. Yet this does not mean that

there is nothing else to say about adding lives compared with improving lives.

Although we must reject the common sense view, it remains open as to how much

might salvaged from it. It will turn out that different principles of distribution manage

to preserve different elements of the common sense view, and that some do rather

better, overall, than others. Before going ahead with any investigation of actual

principles, however, it is worth pausing to get a sense of where we are, now that the

full common sense view has been rejected.

Broome himself gives a succinct diagnosis of what the falsity of the common

sense view entails. As he puts it, the addition of new lives may “cancel out” the

159 Although I lack the space to properly explain this, Broome’s argument would quite easily carry over to McMahan’s formulation as well, given that McMahan’s is in one sense merely logically stronger. 160 Of course, it is possible to resist Broome’s argument by denying properties such as transitivity and completeness, as highlighted in chapter two. Broome provides some reasons against taking these routes in (2004: Ch11). For a reaction to Broome’s views on these matters, see Bradley (2007),

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badness of other effects on the distribution of well-being. Among the real examples of

such ‘badness’ are the predictable effects of climate change. Although it is hard to

know the effects of climate change in full, Broome points out that we can reliably

predict that variation in the global temperature will increase the range of tropical

diseases, and lead to an increase in the severity and frequency of famines. Both of

these effects will have a negative effect on the future distribution of well-being: some

future people will be worse off than if disease and famine were not to become as

widespread as climate change will cause them to become. But, Broome explains,

climate change might also cause the global population to increase. Given that the

common sense view is false, an increase in global population might turn out to be a

good thing. It might then outweigh the badness of suffering caused by famine and

drought. This is hard to believe – how could it be that adding lives to a population

could be a way of making up for the suffering inherent in existing lives, as opposed to

just preventing such suffering from occurring in the first place? But there is not much

we can do about this: the common sense view cannot be accommodated by any

principle of distribution, without making even more radical revisions to how we think

about comparability. What remains open is the degree of canceling-out to which we

might have to commit. Certain properties of distributive principles will do something

to ensure that this degree is low. The further we can get in constructing a principle in

which these features are prominent, the further we may come to preserving something

close to the common sense view.

5.4 Lines of response

I said that there are two properties of a principle of distribution that bear on its

ability to preserve a distinction between adding lives and improving lives. Both of

these were introduced in chapter two. The first is the ‘shape’ of that principle’s

function. Recall that a function’s shape may be understood, roughly, in terms of the

value of a benefit is made to vary with the well-being of its recipient. This variation

decreases with the extent to which a function approaches a strictly linear shape (in

which case there is no variation at all). The second significant feature is the location of

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the function’s ‘neutral level’ for existence. This was first discussed when Critical

Level Utilitarianism was introduced in chapter two. Recall, the neutral level is the

quantity of well-being at which the addition of an extra life fails to make the

population better or worse than it otherwise was. We have seen that it is impossible to

have a neutral range of well-being levels, but it remains perfectly possible to have a

single level that is neutral. Where we locate this level will make a difference to how

we evaluate the addition of extra lives. A higher neutral level tends to make a principle

of distribution less prone to value the addition of lives. As I shall argue, however, the

key to salvaging something from the common sense view depends on the relation

between a function’s shape and its neutral level. It does not depend, as one may think,

on raising the neutral level alone.

It is now time to begin examining actual principles of distribution. Here I will

repeat some of the descriptions from chapter two, albeit in ways that relate the relevant

functions to the problem of population size in particular. One view that certain

principles aim to avoid is the ‘Repugnant Conclusion’, as named by Derek Parfit in

one of the earlier philosophical treatments of variable population size161. Roughly, this

states that certain relatively large distributions may be better than much smaller

distributions, even though every life in the small distribution is much better than every

life in the larger distribution. Friends of Utilitarianism (including Broome himself)

have been led to propose Critical Level Utilitarianism so as to avoid this sort of

implication.

CLU departs from the classical theory by way of adjusting the location of the

neutral level for existence. On Classical Utilitarianism, the neutral level is equal to the

zero-level for well-being: Adding a life makes a distribution better if and only if the

well-being of that life is positive, worse if and only if the well-being of that life is

negative (less than worth living). The idea of Critical-Level Utilitarianism is that the

neutral level be located somewhere higher than zero welfare. This means that the

value of a distribution is equal to the sum of each person’s welfare, minus the value of

161 Part four of Parfit (1984).

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the critical level. For example, if the critical level is identified at some well-being

level ‘L’, then the value of any distribution of welfare levels, presented as a vector

<w1, w2,.. wn>, is equal to the sum of (w1-L) + (w2-L)…+ (wn-L). Partly to facilitate

easy comparison with non-Utilitarian principles of distribution that I shall later

discuss, it is worth looking at the graph of this theory. This gives us a way of

appreciating the shape of the function, which is independent of where the neutral level

is located. Recall what the graph for Critical Level Utilitarianism looks like:

The horizontal axis represents the well-being of any given individual, increasing from

left to right. The vertical axis represents ‘moral value’ or, to be more precise, the

contribution the presence of an individual makes to the value of a distribution

(sometimes called ‘contributive value’). The graph’s line plots the relation between

these two variables. The line keeps going upwards (the function is ‘strictly

increasing’). This means that the higher someone’s welfare is, the greater the

contribution they make to the distribution’s overall value. Now notice two things on

this about this graph. First, the zero points on the two axes do not occur at the

intersection of these axes. The zero for well-being lies to the left of the intersection,

which is where the zero for moral value occurs. The intersection of the axes is located

such that the zero for moral value coincides with the location of the critical level, L,

instead. This feature is what distinguishes Critical-Level Utiltiarianism from Classical

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Utilitarianism, on which zero moral value coincides with zero well-being. Otherwise,

the two views have the same function: The fact that the graph has a perfectly straight

line means that benefiting a person has exactly the same value, no matter how well-off

this person is, nor whether their being benefitted increases or decreases overall

inequality, and so on. The value of improving a life is equal to the degree to which a

life is improved, nothing else.

Critical-Level Utilitarianism is somewhat less favourable to the addition of

lives than its classical counterpart is. Accordingly, the Critical-Level view avoids the

repugnant conclusion. How exactly does it do this? Roughly, the answer is that, when

total well-being is increased by adding a life, an extra subtraction of the critical level L

must occur. If total well-being is increased by way of improving existing lives, then no

such subtraction need take place. In other words, improving a life is worth L more than

adding a life, assuming that the effects on total well-being are the same. Of course, it

is still possible for additions to substantially improve the value of a distribution. But

the higher the value of L, the harder it will be for additions to cancel-out the badness

of lowering the welfare of existing lives. One might think that it is possible to secure a

strong bias towards improving lives over adding lives, just by setting L very high.

Nevertheless, raising the neutral level is something leads to questionable implications,

which become more questionable the higher the level is raised. As soon as the neutral

level for existence is above zero well-being, it follows that it can be a bad thing to add

a life to a distribution, even if that life is worth living. This may seem a welcome

implication at first – perhaps it is bad if we create extra people whose lives are barely

worth living, even these lives are not strictly ‘bad’ for the people who live them. Once

the neutral level gets higher, though, this sort of implication becomes harder to defend.

Indeed, one result is that a distribution containing a few lives that are horrendously

bad may be better than a distribution in which all lives are certainly worth living, but

lived at a level just below the inflated level of L. Thus, one of the popular objections to

Critical-Level Utilitarianism is that it prefers the creation of a small number of the

worst lives imaginable, than some larger number of ‘mediocre’ lives. This is what

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Gustaf Arrhenius has called the ‘Sadistic Conlcusion’162. This isn’t just a problem for

Critical-Level Utilitarianism, but rather for any attempt to reduce the value of adding

lives by raising the neutral level.

Now recall the Prioritarian function. The typical formal analogue of this claim

assigns a value to a distribution by summing a strictly increasing concave

transformation of the welfare of each person in a distribution. Now, a transformation is

just a further device for turning some input value into an output value. For our

purposes, an increasing transformation is strictly concave when its output value

increases at a gradually decreasing rate, given a steady increase in the rate of its input

value163. That is to say, some transformation V is concave when, for some arbitrary

positive level of welfare, w, ((Vw+e)-(Vw)) > ((Vw+2e)-(Vw+e)), where e is any real

number. In other words, for any three levels of welfare separated by gaps of a constant

size, a concave transformation of these levels is such that the transformed values of

the upper two levels are not as far apart as the transformed values of the lower two

levels. This idea can be made clearer if we look at an actual example of V. The square

root is a familiar example of a concave transformation, and is often used to formulate

the standard Prioritarian method of aggregation (its familiarity for illustrative purposes

should be noted alongside the fact that it may not be the most plausible transformation

to use).

What do Prioritarian functions say about adding lives versus improving lives?

Here there are two implications worth commenting on. The first is quite startling164.

What Prioritarianism says is that if some fixed total of well-being is to be added by

way of new lives, then it is better for it to be added via as many additions as possible.

This is easy to see. For any fixed amount of well-being, n, the value of (√n) < 2(√½n).

This means that adding lives may cancel out badness more quickly if the standard

162 Arrhenius (2010). A similar, but less severe, implication is identified by Mulgan (2002). 163 I have used this definition because it excludes concave functions that are not strictly increasing. In effect, this is to ensure that the output rate does not stop increasing, even if the rate of increase gets less. This restriction is plausible just because a Prioritarian is likely to say that benefiting a person always counts for something, even if it counts for less, the higher this person’s welfare. 164 A version of the following point is developed in Arrhenius (2009).

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Prioritarian approach is taken, than if a Utilitarian one is. Roughly speaking, the value

of adding well-being in the form of new lives can be inflated just by spreading out the

added well-being among as many individual new lives as possible. Utilitarian

functions do not imply this. Because certain sorts of additions can have even higher

value on the Prioritarian function than on a Utilitarian one, it appears to preserve even

less of the common sense view.

In an attempt to get around this problem, friends of Prioritarianism might

follow Critical-Level Utilitarians by raising the neutral level165. They will get a similar

result: For some value L, it will be false that (√n-L) < 2(√½n-L). As with the

Utilitarian deployment of this strategy, the explanation for its effectiveness is that the

value of L enters twice into the addition of two lives, so that more is subtracted from

the total amount of well-being added to the population. Still, though, the problem has

not entirely gone away. The reason has to do with the second implication I want to

discuss. Crudely speaking, the Prioritarian function has certain discounting tendencies

inherent in the shape of its function. Really, this is just evident from the Prioritarian

slogan, which can also be written as the claim that benefits count for less, the better

off the recipient. Whilst Prioritarianism is normally presented as a view about the

variable value of benefits, it also allows the value of harms, or lowerings of well-

being, to vary in a corresponding way. This means that lowering the well-being of an

existing life often has relatively little affect on the value of the distribution of which

this life is a member. If lowering the quality of a life is sometimes less bad on a

Prioritarian function than on a Utilitarian one, then its badness could be more easily

cancelled by the addition of a life, even if the neutral level is the same on both

functions. It does not strictly follow that Prioritarianism makes it easier for additions

to cancel-out badness. But this does not matter. What we can see is that there is a

second feature of functions that needs to be addressed if we are to learn how to

165 In fact, it is arguable that Priroritarians have a better reason for doing this than Utilitarians do. In some sense, Prioritarianism expresses an aversion to lives being lived at low levels of well-being. Raising the neutral level says, in effect, that it would be better if people’s lives were not absolutely low. Utilitarianism, on the other hand, contains no such aversion to lives lived at low levels of well-being, so long as such lives are lived at a positive level. We might wonder, although I shall not push this point, whether Critical-Level Utilitarianism is rather ad hoc.

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preserve more of the common sense view. And this feature remains present, regardless

of what is done about a function’s neutral level, since it concerns a function’s shape.

As I shall explain, however, the solution is not to remove any discounting tendency

altogether. Rather, the best thing to do is to retain some element of discounting, but to

thereby realize a particular relation between the function’s shape and the location of

the neutral level. This will require us to propose a rather different function, distinct

from both the Utilitarian and Prioritarian ones already presented.

5.5 Piecewise-linear functions again.

What we want to do is make a function preserve as much of the common sense

view as we can, whilst remaining otherwise plausible. We have just seen that we

cannot rely purely on raising the neutral level. What I propose, then, is that we think

more carefully about the shape of the function as well. In particular, we need to do

something about the way the Prioritarian function discounts well-being. Recall now

the piecewise-linear function:

In earlier chapters, I argued that this function forms part of a view that is intermediate

between Luck Egalitarian and Libertarian views about justice. For the purposes of this

chapter, it may also be regarded as an intermediate between Utilitarian and Prioritarian

functions. The intermediacy attaches to the limited tendency of the piecewise-linear

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function to discount the value of benefits in the manner of the standard strictly

concave function. This is brought about by the retention of some linearity in the

function’s shape.

So far, I have not commented on any way in which the function’s threshold is

relevant. What I propose is that the two ranges of well-being are separated by a

threshold that also serves as the location of the neutral level L. In earlier chapters, I

explained how this threshold might be fixed with reference to a certain average level

of expectations. The argument of this chapter requires a slightly stronger view than

this. In particular, it requires that the location of this threshold is above zero welfare.

Since most people in fact have lives that are worth living, the average level of

expectation might be regarded as lying well above zero welfare (even if restricted to

what is expected given endowments alone). Otherwise, the idea of a neutral level

means exactly the same thing here as what it meant when discussed in connection with

Utilitarian and Prioritarian functions. Identifying the neutral level with the boundary

between the two linear segments has significant features. As I shall explain, it means

that the stronger parameter only ever weighs changes in the well-being of existing

lives. It never weighs the value of additions, except when these additions have

disvalue (in which case they can never cancel out the badness of lowering the well-

being of existing lives).

It will help things if we also recall the function in written form. On a

piecewise-linear function such as the one graphed above, the value of a distribution is

equal to:

{ }{ }∑ ∑< ≥

−+−Lww Lww

ii wLBLwA )()( where A > B > 0, and L >

0

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In other words, greater weight is given to lives lived below the critical level L than to

those above. The function also gives negative value to lives lived below L166. Part of

what is distinctive about this approach is that the weight does not vary in accordance

with how far above or below the threshold a life is (as I shall explain below, this is not

tantamount to the claim that the value of improving a life located a long way below L

is less than the value of improving a life marginally below it). What I shall do now is

explain why this function preserves more of the common sense view than the

Utilitarian and Prioritarian functions already discussed.

If the neutral level is equal to L, then it follows (as I have said) that the

stronger parameter A, will never come into play for any addition that has a positive

contributive value. It will only fix the contributive value of improvements or additions

of lives below the neutral level. This is important. If we add the claim that the neutral

level is greater than zero welfare, then some further claims follow. For any increase in

total welfare n, which consists in the improvement of a life (or lives), then this

improvement will always count for more than if it were an addition of a life (or lives).

The reason is as follows: For an increase in total welfare, n, that is brought about by an

addition of an extra life, the value of this addition will always be B(n-L)167. For an

improvement, the value will always be either B(n), A(n), or some combination of these

two parameters. Now, any of these latter transformations produces an output greater

than B(n-L). Hence, a piecewise-linear function is ‘improvement biased’ when its

neutral level is positive. So far, this is only to repeat the earlier claims about how

improvement-bias is affected by the location of the neutral level. However, a greater

degree of improvement-bias is gained due to the different strengths of the linear

weightings A and B. This is because only improvements stand any chance of being

weighted by A. This adds to the tendency to treat improvements as more valuable than

166 It’s important not to confuse this claim with the more objectionable claim that the existence of these people is undesirable. To say that a set of circumstances is worse due to some person living a bad life in those circumstances is not to say that this person’s life is regrettable, but just that the badness of this life is regrettable (we wish that the person in question lived a better life, not that they hadn’t existed). For more on this point see McMahan (1998). 167 It will be even less if n is added by way of more lives, for the familiar reason that more subtractions of L will be made on the divided parts of n.

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additions. The independence of this contribution is guaranteed by the fact that a

piecewise linear function will still exhibit some improvement-bias if the neutral level

L is located at zero welfare. If L = zero, then there will still be a tendency to prefer

improvements to additions. An addition of n welfare by way of an addition will be less

valuable than an improvement of n units that accrues to a person located below the

threshold, prior to accruing the n units of increased well-being. This remains true

whatever the absolute location of the neutral level identified with L. Raising this level

higher, in absolute terms, increases the number of improvements that fall within the

scope of the stronger parameter A. Thus, a raised neutral level still contributes to

improvement-bias. But it contributes alongside, and in ways independent of, the shape

of the function.

The above point about the way in which a function’s shape matters can be

made in another way, by returning to the idea of discounting discussed in connection

with the Prioritarian function. As I explained earlier, making use of a function that

gets less steep is a way of discounting benefits at higher absolute levels of welfare.

Concave functions and piecewise linear functions both discount benefits, but in

different ways. The most familiar concave functions, as it were, never stop

discounting, and they discount within the range of well-being levels that extends

beyond the neutral level. Piecewise-linear functions do not have this feature. To the

extent that they discount benefits at higher welfare levels, this only occurs due to one

discrete change in the function’s shape, rather than as some continual change. And the

change occurs at the neutral level, not beyond it. This is what prevents additions from

being weighted with the stronger parameter, which only weights changes to the well-

being of existing lives.

The above is perhaps the key point in all of this. What a piecewise-linear

function does is provide us with a certain way of discounting the value of benefits,

such that we can limit the positive value of additions, without limiting too much the

negative value of lowering the well-being of existing lives. This is what enables us to

do the most to limit the tendency of the latter to be canceled-out by the former. It

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remains open exactly how strong this limit is. Ultimately, this will depend partly on

the ratio between the two parameters (that is, the degree to which the graph’s lower

segment is more steep than its upper segment). The greater this ratio, the greater

resistance the function will exhibit to the sort of canceling-out with which we have

been concerned. However, it should be remembered that a larger ratio will also have

implications to how the function evaluates distributions of fixed size. A large ratio, for

example, will attach greater value to transfers from lives above the threshold to lives

below. We should think carefully about what sort of value we should want this to

have. Nevertheless, what we now have is a framework in which we may salvage more

from the common sense view than other functions can get us. Further questions,

internal to the idea that we might adopt a piecewise-linear function, are questions that

I shall leave for now.

5.6 Concluding remarks

Some further remarks might be made about the relation between the piecewise-

linear function, and both strictly concave functions and CLU. This will bring things to

a close.

First, it should be said that CLU does not represent a very large philosophical

departure from Classical Utilitarianism. Not much has been said in favour of CLU

apart from the fact that the critical level helps avoid certain unintuitive consequences.

The basic idea of CLU is that the neutral level for existence may be above the zero for

well-being, or the personal value of a life. But what rationale is there for this, within

the Utilitarian idea? It might be said that the critical level gains its support from the

idea that we should be especially concerned about the possibility of lives that are lived

below some absolute level of well-being. However, there is nothing in the Utilitarian

tradition that really recommends this. Rather, it would appear to be the sort of thing

that Prioritarians might say. If a concern for low absolute levels of well-being is what

motivates CLU, then why not express such concern by adjusting the shape of the

function as well? Left with this motivation for raising the neutral level, CLU might

appear to embody a certain type of concern in an artificially restricted way.

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The reason that CLU works less well than a piecewise linear function is that it

does not imply an especially strong distinction between adding lives and improving

lives. In particular, it is committed to a particularly strong form of what Broome called

Canceling-Out. Because CLU is still identified with a strictly linear function, the

disvalue of any lowering in total welfare caused by worsening existing lives will be

canceled out by any addition that increases total welfare to a degree equal to the

lowering plus the value of the critical level. As Broome has said, it is hard to believe

that additions can cancel out the badness of worsenings in this way. But it is harder to

believe that an addition can cancel out a relatively large lowering of an existing

person’s welfare than it is to believe that it will cancel out only the badness of a

relatively smaller lowering. That is to say, how hard it is to accept Canceling-Out

depends on how strong a version of it we must accept. Because a piecewise-linear

function discounts the value of increasing welfare above the threshold L, it need not

imply as strong a view about Canceling-Out as CL-Utilitarianism implies. This is a

strong reason for preferring a view of this sort to CL-Utilitarianism.

I have said that concave functions never stop discounting the value of benefits.

However, the fact that all concave functions satisfy this description is not to say

anything about the rate of discount that they must exhibit. This rate varies across

different concave functions. Roughly speaking, a concave function’s rate of discount

corresponds to the degree of curvature exhibited by that function’s graph. Now, on

some functions, benefits become discounted quite substantially so that, the count for

very little once a certain range of welfare levels has been entered. This is implied by

the concave function depicted earlier on, whose graph curves quite substantially.

However, it is possible to select different degrees of curvature. In particular, it is

possible to identify concave functions on which a benefit’s contributive value is

discounted at an increasingly slower rate. The curve of a function like this will not

flatten out. Instead, it will tend towards being linear at higher welfare levels. Such a

function will be rather similar to a piecewise-linear function. In particular, it will

exhibit a considerable amount of improvement-bias, albeit marginally less than the

degree exhibited by whatever piecewise-linear function it tends towards.

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These facts may seem to show that the standard Prioritarian method of

aggregation can satisfy all of the claims about improvement-bias that I have made in

this section. This is true, in the sense that the argument of this section does not show

any blatant failing of concave functions in general (at most it creates a problem for

those on which the contributive value of benefits is steadily discounted). However,

there is a sense in which the only argument available for using a strictly-concave

function is one that appeals to the desirability of a piece-wise linear function. The

point is, roughly, that a concave function comes to exhibit improvement-bias only to

the extent that it is made to resemble a piecewise-linear function: It is the tendency

towards linearity that accounts for the constrained discounting of benefits’

contributive values. In other words, the case for this sort of concave function falls foul

of a plausible methodological principle, roughly, that if a member of some type of

theory becomes more plausible the closer it comes to resemble members of some other

type, then this little more than an argument for adopting a theory like one that is a

member of the second type. At any rate, although it is possible to select concave

functions that perform relatively plausibly under variable population conditions, this

fact can be traced not to an interesting feature of those theories, but their resemblance

to another theory.

There remain unanswered questions. We still do not know, for example, to

what extent the addition of lives may ‘cancel out’ the badness of other lives lived at

low welfare. As I have said, we are going to be committed to the possibility of such

Canceling-Out. Depending on what the ratio is between the parameters that transform

sub- and super-threshold deviation, the form of Canceling-Out to which the theory

commits us could be made stronger or weaker. Leaving this question unanswered for

now may render incomplete the work of this chapter, but it does not undermine the

main conclusion: A piecewise-linear function is still the best way of accommodating a

strong improvement-bias.

The moral of this chapter’s story is perhaps something like the following:

Securing improvement-bias is not just a matter of configuring the level of welfare at

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which an addition is at least as good as a non-addition. It has to do with the shape of a

function as well. In particular, the most desirable shape of a function that discounts the

value of a benefit, but not continually. A piecewise-linear function is precisely this

sort of function. Thus, we have arrived at the theory I proposed in earlier chapters via

an altogether different route. The relation between population size and distributive

justice is a complicated one, and I haven’t done any real work to examine it. As such,

it is difficult to say whether the argument of this chapter counts as an interesting

development of the framework laid out in earlier chapters, or just its application to a

rather different set of issues. Suffice it to say that more work on the piecewise-linear

function could yet be carried out.

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Appendix A: Speaker Relativity, 9ormativity,

and Incentives

G.A.Cohen has claimed that the “persuasive value” of a normative argument

may be “speaker-audience relative”168. This appendix explores the way in which he

supports these claims.

The argument for incentives is meant to be a case in point:

(i) Some people are endowed with productive capacities. Their enacting such

capacities will serve the common advantage.

(ii) Those endowed with productive capacities will only enact these capacities if

given incentives.

(iii) Therefore, those with productive capacities ought to be given incentives.

Cohen’s basic idea is that certain normative arguments may be assessed in ways that

depend on who is presenting them to whom, and how the identity of the presenter is

related to the truth of one or more of the argument’s premises. Roughly speaking, an

argument fails the “interpersonal test” when its presenter “cannot fulfil a demand for

justification that does not arise when the argument is presented by and/or to others”.

I will begin with some complaints about Cohen’s diagnostic technique: He

never properly explains what is actually wrong with arguments that fail the

interpersonal test. He offers little more than opaque remarks such as “a normative

argument will often wear a particular aspect because of who is offering it and/or to

whom it is being addressed”169, and that an argument “does not sound so good” in

certain contexts of presentation. This makes it unclear whether what is being tested is

an argument itself. The opaque terminology reflects the fact that Cohen does not wish

to claim that an argument is rendered invalid, or unsound, when it satisfies the

168 (2008: 42). The quotations used in this paragraph appear on this same page of Cohen’s text. 169 (2008: 36).

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conditions he is interested in. We have not been told why (i) or (ii) are false, or why

(iii) does not follow from them.

Really, for an argument to fail Cohen’s interpersonal test is for it to fail to

establish the right sort of conclusion, given its dialectical setting. Any ‘devaluation’ in

persuasive value is best understood in terms like these. Revising the diagnostic

language in the way I propose accords with the idea, mentioned in chapter one, that

what is at stake with the incentives argument is whether the ‘ought’ of its conclusion

takes a strictly moral sense. But this revision should not invite the claim that

arguments for moral ‘oughts’ are in any interesting sense better arguments than those

for prudential ‘oughts’.

Cohen says, “the incentives argument does not serve as a justification of

inequality on the lips of the talented rich, because they cannot answer a demand for

justification that naturally arises when they present the argument, namely, why would

you work less hard [in the absence of incentives]?”170. Part of the reason why this

demand arises is the fact that premise (ii) of the incentives argument has been made

true by the choices of those who, in presenting that argument, make an incentive

demand.

Now, Cohen’s handling of the ‘makes true’ relation is rather under-argued. The

idea is supposed to be that when one makes true a premise in a normative argument,

then one may be asked to justify that fact. Cohen claims that this justification cannot

be supplied when the incentives argument is presented “on the lips of the talented

rich”. But, as I said when discussing the idea of an incentive in isolation from the idea

of incentive inequality, it is perfectly possible for a poor person to be able to produce

in ways that promote the common advantage, and to ask for an incentive for doing so.

One could certainly present a version of the incentives argument, having made true its

second premise, yet without being one of the “talented rich”. So long as a person asks

for a reward that goes beyond compensation, then they ask for an incentive. Cohen

170 (2008: 42).

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presumably believes that a poor person, when making an incentive demand for the

sake of becoming less badly off, does not face an insurmountable burden of justifying

the ‘making true’ of the incentive’s argument second premise. At any rate, if Cohen

doesn’t think this, then it would be puzzling as to why he focuses on the incentives

argument as presented by “the talented rich”. It would seem, then, that making true the

premise of the incentives argument is hard to justify only if the incentive one is asking

for is one that will increase inequality. But this distinction, between poor and rich

incentive-demanders, is not argued for.

Thus, Cohen’s opposition to incentives is not fundamentally grounded in this

idea of making true an argument’s premise, but rather just in an aversion to inequality

itself. If the idea of making true the premise were sufficient to make incentive

demanding behaviour unjust (as opposed to being sufficient merely for exposing one

to a request to justify that demand), then Cohen would be voicing a general opposition

to incentive demanding behaviour. But to attach such significance to the ‘makes true’

relation all on its own is implausible, at least because it implies the condemnation of

just about any sort of demand for a reward for productive activity: Recall that a person

can be worse-off than others and yet still demand an incentive for whatever modest

levels of production they can achieve. Giving such a person this incentive will not

increase inequality; it will probably decrease it. But such an individual still makes true

the proposition that they will not produce absent that incentive. Cohen must either say

that incentive demands by the worse-off are unjust, which is not very plausible, or

claim that such demands satisfy the burden of justification. But all that distinguishes

incentive-demanding behaviour among the worse-off is the fact that granting the

relevant incentives won’t increase overall inequality. But to fall back on this criterion

is, in accordance with what I have already said, tantamount to making one’s aversion

to inequality do the real work.

Thus, Cohen’s view may turn out to be an application of egalitarian justice to

incentives, not a free-standing account of what is independently interesting about

incentives. Given this, there may be nothing in Cohen’s critique on incentives that

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really threatens the idea of permissible inequality, absent some antecedent desire for

material inequality, or some other substantive commitment that may distinguish

incentive demands made by the poor from those made by the rich171.

171 Such as the Rawlsian ideas that Cohen targets (reciprocity, fraternity, etc). This appendix has sought to examine Cohen’s critique as a free-standing objection to incentive inequality, not an objection to the Rawlsian endorsement of such inequality. I have suggested why the critique might fail in the former guise. It may well retain its force against Rawls.

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Appendix B: Scepticism about the Betterness of

Outcomes

I have, in various places, suggested that a theory of distributive justice can

include some sensitivity to the intrinsic value of outcomes. This is not something I

heavily rely on, and a similar case could be made for my main proposals without it.

Nevertheless, there is some motivation for engaging with arguments that have been

given against the idea that one outcome may be better than another.

One philosopher representative of scepticism about betterness is J.J.Thomson.

Among other things, Thomson has claimed:

People do say the words ‘This is better than that’, but what they mean is always that

the first thing is better to eat, or better for use in making cheesecake, or better for

Alfred, and so on. (1997: 276)172

These remarks acknowledge that, given the surface grammar of everyday utterances,

we might be led to think that the two-place ‘better than’ relation is deeply entrenched

in our thinking about the world. But, as is well-known, a sentence’s surface grammar

can fail to include certain elements of the proposition a speaker may communicate

when uttering that sentence. Thomson’s view of our linguistic practice is that,

whenever we utter claims containing the relation ‘better than’, we are actually using

this relation as shorthand for some three-place version of the relation, with some

preposition attached to it (as per the examples she provides). Thomson takes this as

evidence that there is “no such property” as betterness. When philosophers talk of the

betterness of states of affairs, then, they (and their theories) fail to make any sense. For

it is certainly true that moral theories of this sort rely on the two-place version of the

relation being robust. It is one thing to say that saving the greater number is morally

required because it brings about a better outcome. It hardly sounds plausible to say,

172 See also her (2001: 17-18). For a similar view, with some differences from Thomson’s, see Kraut (2007: 66-81). To say that Thomson is representative of the sceptical view is not to say that all holding this view rely on those of her arguments that I am going to discuss. On the other hand, Thomson’s writings are the most well-known, and perhaps the most well-developed, on this topic.

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alternatively, that such a requirement exists because saving the greater number is better

for those saved, or better in any of the other ways that saving the greater might be.

Assuming the truth of Thomson’s claim that ‘better than’ only ever acts as

proxy for one of its three-place analogues in everyday speech, we may yet ask why she

takes this claim to be evidence against the robustness of the two place relation. After

all, the fact that a relation is not commonly referred to in everyday speech does not

entail that this does not exist. The answer is often thought to lie with an older argument

given by Peter Geach, to which Thomson makes explicit appeal. This argument

concerns the positive adjective ‘good’. The relation ‘better than’ is its comparative.

Geach’s treatment of ‘good’ begins from a distinction between two kinds of adjectives,

attributive ones and predicative ones. According to Geach, an adjective is predicative if

and only if it can be split from its adjunct noun. That is to say, for any adjective A, and

any noun B, A is predicative when the inference from ‘x is an A B’ to ‘x is A’ is valid.

Any adjective failing to meet this condition is attributive. Thus, adjectives like ‘red’

are predicative: From ‘all Ferraris are red cars’ we may validly infer ‘all Ferraris are

red’. Adjectives like ‘big’ are attributive: From ‘Harry is a big flea’ we cannot infer

‘Harry is big’. As Geach pointed out, ‘good’ is rather like ‘big’. From ‘Biggs was a

good thief’ we cannot infer ‘Biggs was good’. Geach’s conclusion was, roughly, that

attributive adjectives are meaningless when they occur in isolation. At any rate, his

view about ‘good’ was similar to Thomson’s view about ‘better than’. As he put it;

“There is no such thing as being just good or bad, there is only such thing as being a

good or bad so-and-so” (1956: 34)173. And this goes for states of affairs, not just

burglars.

Thomson takes Geach’s treatment of goodness to count in favour of what she

says about betterness (1997:275-76). Now, suppose it is conceded that Geach’s

argument rules out the intelligibility of any talk about the goodness of states of affairs.

What does Geach’s argument tell us about the ‘better than’ relation? Actually, nothing

at all. It is tempting to think that the facts about comparatives are intimately related to 173 I shall follow Thomson (1994:9) in treating ‘is a good so-and-so’ as equivalent to ‘is good for’ or ‘is good with’, or some other appended preposition.

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the facts about their positives. But actually, this can lead to mistakes being made.

Thomson certainly writes as if Geach’s argument extends naturally to the comparatives

of attributive adjectives, and does so without argument. But Geach’s argument clearly

does not go this far. The fact that Geach’s test leaves comparatives untouched can be

easily seen just by examining some other attributive adjective. Granting Geach’s point

against the coherence of ‘Harry is big’, there is nothing problematic about saying that

Harry is bigger than other fleas, or even other non-fleas. More generally, the fact that a

positive adjective makes sense only once it comes with a preposition attached does not

entail that the comparative of that adjective must similarly come with a preposition

attached.

Now, it is not immediately obvious why it might make any difference whether

Geach’s argument doesn’t extend to comparatives. After all, philosophers who like to

talk about one state of affairs being better than another very often also talk about the

‘goodness’ of states of affairs. Indeed, the vocabulary of ‘goodness’ and ‘betterness’ is

often used quite interchangeably. We might think, therefore, that any philosopher who

relies on the betterness of states of affairs must also be committed to the goodness of

states of affairs, and therefore vulnerable to Geach’s argument all the same. However,

it is not clear that talk of goodness is necessary, or useful. Philosophers whose theories

involve claims presented using ‘good’ or ‘better than’ tend to be interested in making

no more than comparative claims. Typically, they want their theories to provide us

with orderings of states of affairs174. At least, in order to be action guiding, a moral

theory need only help us identify which state of affairs is better than all the others that

might be made to obtain instead. If such a theory failed to tell whether any of these

states of affairs are also good, then it would be no less action-guiding for that.

Thomson does not register the possibility that there might be some respects in

which the facts about comparatives don’t follow from the facts about their positives.

Her claims against the intelligibility of betterness are generally mixed in with claims

against goodness in ways that suggest she thinks that analogous claims apply to each.

174 The remarks in this paragraph are guided by Broome (1993).

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However, if it is correct that talk about betterness does not presuppose talk about

goodness, then it is possible to continue talking about the betterness of states of affairs,

for anything that Geach has said. And, after all, it is perhaps worth noting that Geach

did not extend his discussion to comparatives in the first place; it is his readers who

have taken it upon themselves to do so. The point, then, is that even if utterances of

‘better than’ are often shorthand for three-place versions of that relation, this is not

grounds for scepticism about the two-place relation. Such grounds would only exist if

there were some independent reason for doubting the robustness of the two-place

relation. Such reason is not established by infrequency of use in everyday speech.

Nevertheless, there remains something to Thomson’s point. Specifically, even

if one is well-disposed towards the sorts of moral theories that involve claims about the

betterness of affairs, Thomson gives some cases whose puzzling character is hard to

deny. For example Thomson asks us to reflect on the question of whether Russell’s

theory of descriptions is better than chocolate. As she says, the question here is not

which of the two is better in some way or another, but which of them is “pure,

unadulterated better” than the other175. It’s hard to make sense of a question like this.

But if it is asked which is better, say, as a treat for bored children, it’s not so hard to

answer. This is in effect a second argument, independent of anything to do with Geach.

Specifically, the problem seems to be that there exist certain mysterious instances of

the ‘better than’ relation, which can be ‘demystified’ only once a preposition is added.

This counts in favour of the claim that there is something amiss about the two-place

relation.

I would like to approach this argument by accepting that attaching a preposition

to a two-place relation often is a way of making that relation non-mysterious. But I

should then like to ask whether preposition attachment is the only way in which to

achieve this. As I shall argue, there are instances of two-place relations that cannot

have a preposition attached to them, and yet are puzzling if the two-place relation is

understood such that anyone wanting to use it is committed to some obscure property.

175

(1994: 12).

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The reasons for why this is so will suggest that friends of betterness in moral

philosophy may be in a position to respond to the sorts of cases Thomson provides.

Let me first note a comparative relation that undoubtedly needs to take a

preposition, even though it very often takes a two-place form in the surface grammar

of everyday utterances. Here I have in mind the relation ‘nearer than’: Suppose I claim

that London is nearer than Tokyo. Here I might mean that London is nearer to some

other location than Tokyo is, or nearer to hosting the Olympic Games, or something

like that. What I can’t do is deny that I mean any of these things and insist that I mean

to communicate, as Thomson would say, that London is just ‘pure, plain nearer than

Tokyo’. There is no such property as nearness, only nearness-to.

The case of nearness has, I take it, precisely the features that Thomson thinks

hold of betterness. The case of nearness might therefore be thought to count in favour

of her position. However, things are not so straightforward. Consider now another

comparative, ‘longer than’. I may claim that the Great Wall of China is longer than the

wall in my garden, and I may also claim that the Bronze age was longer than last week.

It is clear that, in each case, I am not referring to the same kind of relation. We all

know that there exist at least two types of length, these being spatial length and

temporal length. If I were to claim that I didn’t mean to refer to either of these kinds of

length, and insisted on the existence of some property of length simpliciter, then I

wouldn’t be making any more sense than if I had insisted on referring to the property

of nearness simpliciter. However, what is notable about this case is that we do not

avoid referring to a mysterious ‘pure, plain longer than’ by relying on prepositions,

present in surface grammar or not. To the contrary, it is rather hard to attach a

preposition to ‘longer than’ and still have a claim that makes sense, much less a claim

that represents what one really wants to communicate. There is, I submit, a reason for

this. For certain comparative relations, of the sort that refer to one of multiple

properties, it is possible to identify which property is referred to by examining what the

relation is said to extend between. In other words, whether ‘longer than’ refers to

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spatial length or temporal length is something that can be ‘read off’ the identities of the

relata.

What makes this point significant is the fact that we can construct puzzling

cases for relations like ‘longer than’, without these counting against the coherence of

that relation. I may ask, for example, whether the Bronze Age was longer than the

Great Wall of China. This question doesn’t make sense, but not in ways that warrant

any sort of scepticism about the two-place relation ‘longer than’. All the case

demonstrates is that there exist certain pairs of relata that between which the relation

‘longer than’ cannot obtain. The point, then, is that the possibility of constructing

puzzling cases does not show that a comparative relation is itself worthy of suspicion

when in two-place form. All such cases show is that this relation cannot extend

between any old pair of relata. That is to say, friends of betterness in moral philosophy

may say of betterness more or less what has just been said about length: The relation

cannot extend between such things as chocolate and Russell’s theory, but it may yet

extend between other things, such as states of affairs.

Of course, it may still be pointed out that ‘better than’ is not like ‘longer than’

at all. For one thing, there is nothing metaphysically suspect about properties of spatial

and temporal length. And unless betterness can be similarly associated with some

metaphysically robust property, then use of the two-place ‘better than’ relation will

remain objectionable. If this is what is claimed, however, then the argument has

become question-begging. That is to say, if some argument is to be found for why we

should be sceptical about betterness, then this argument cannot appeal to what it is

supposed to establish, namely, that the two-place ‘better than’ relation commits its user

to a mysterious metaphysical view. A non question-begging argument would be one

that began from observations about ‘better than’ that do not also hold for comparatives

about which we have no reason to be sceptical about. If I am right, then at least two

candidates for such an argument (the extension of Geach’s argument about good, and

Thomson’s argument from puzzling cases), turn out not to lack their advertised power.

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I will end on a concessionary note. I have merely suggested how some attempts

to argue for a sceptical view about the relation ‘better than’ may be less powerful than

otherwise thought. This is not to say that there is not still a burden on theorists to

explain exactly what is meant by the betterness of states of affairs, or similar locutions.

Indeed, I leave open the question of whether there is yet something mysterious or

otherwise objectionable about the property of betterness. This includes my leaving it

open whether usage of the ‘better than’ relation really does commit its users to the

existence of a property of betterness simpliciter, should such a property turn out to be a

mysterious one after all176.

176 As suggested by one reviewer of Thomson (1997) – see Tannsjo (2004: 788-89).

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Appendix C: The Inequality Relation

In chapter two I mentioned that Egalitarian functions presuppose some way of

measuring material inequality. There are different ways in which such measurement

can be done. One approach to inequality’s measurement, proposed by Wlodek

Rabinowicz177, reduces a situation of inequality to a set of instances of the relation ‘is

worse off than’. We may call this the ‘Inequality Relation’. On the approach I am

speaking of, inequality is measured by aggregating the various instances of the

inequality relation. The simplest case would be to simply add up the sizes of each

instance of inequality. Thus, if the relation may be expanded to ‘is worse off by n

than’ (where n is some amount of welfare or goods). A distribution’s inequality may

then be calculated by simply adding up all the values of n, spread around each instance

of the inequality relation.

Work on inequality measurement traditionally distinguishes inequality of

individuals from inequality of groups178. This is sometimes labelled as the distinction

between ‘univariate’ and ‘bivariate’ types of inequality. What has not been explored is

the possibility that the inequality relation might hold between an individual and a

group. We might call this conception, ‘isovariate’ inequality. We can make this idea

more precise in the following way. For each instance of the relation ‘is worse off by n

than’, the left hand side of this relation is occupied by an individual, and the right hand

side occupied by a group. This sense of inequality is neither univariate (individuals

occupying both sides) or bivariate (groups occupying both sides). It is, to coin a phrase

‘isovariate’. It might also be said that the inequality relation is being construed as

asymmetric.

Many conceptions of groups are possible (races, genders, and so on). It is

possible to identify groups simply as sets of individuals living at the same welfare

level, or within the same welfare range. On this approach, the inequality relation

177 See his (2008). 178 Temkin (1993: 101-102).

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obtains whenever there is an individual who is worse off than the set of individuals at

some higher welfare level. On this sense of ‘group’, a novel way of measuring

inequality can be conceived. To see this, consider the following three vectors of well-

being:

(a) <10, 20>

(b) <10, 20, 20>

On an isovariate measure, the might be no difference between (a) and (b) with respect

to inequality. This is because both only contain one instance of the inequality relation.

In (a), inequality obtains between the individual at level 10 and however many

individuals are at level 20. In (b), all that is different is that there are more people at

20. But the extra person at 20 merely increases the number of people standing in one

single instance of the inequality relation. It does not increase the number of times that

relation obtains. On a univariate measure, however, the inequality relation obtains

when at least one individual is worse off than at least one other individual. This means

that there is an extra instance of the inequality relation in (b). Therefore, (b) contains

more inequality than (a).

If the inequality relation is asymmetric, then we will need to revise some of our

beliefs about inequality. This includes the way in which we understand the idea of

‘levelling down’. It is normally believed that, where there is inequality, it can be

reduced by making the better-off worse-off. On an isovariate measure, this is false.

Compare (b) with a third distribution, (c):

(b) <10, 20, 20>

(c) <10, 10, 20>

The move from (b) to (c) is what would normally be offered as an example of

levelling-down. But on an isovariate measure, there are actually more instances of the

inequality relation in (c) than in (b). This indicates that levelling-down can increase

inequality, not reduce it. Of course, one could construct cases in which inequality

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could be reduced by levelling down, even on an isovariate measure. All that is needed

is that all members of the best-off group be made worse-off. However, the point is that

an isovariate measure does not regard levelling-down as, in general, a good thing.

There are various different ways in which levelling-down can occur, which are

differences more or less ignored by univariate measures of inequality. But because an

isovariate measure would be sensitive to these differences, there may be no fact of the

matter as to whether anything general is implied about levelling-down.

I haven’t said what reasons there might be for regarding the inequality relation

is asymmetric in a way such as the one described. It is hard to see any reasons, but it is

also hard to see why the burden of proof is such that there ought to be any default

preference for a univariate measure. Much of our talk of inequality, such as the gender

‘pay gap’, adopts an obviously bivariate aspect. It might be said that reference to

bivariate inequality typically occurs when qualitative features of some group are

thought to be of relevant importance. In these cases, the concern is not with ‘pure’

material inequality. Crudely speaking, we have reasons to talk about (e.g.) gender

inequality partly because it is inequality between genders, not just because it is another

instance of inequality. Sometimes our references to inequality refer just to the material

inequality that there is. This is so when it is simply said that some are worse off than

others. Are we to understand ‘others’ separately, or collectively, all at once? How we

answer this question determines whether we would have most reason to use an

isovariate or a univariate measure. It is hard to see what reasons could guide this

choice. But, as I have shown, our answers to certain other pressing questions would be

importantly affected by which answer we choose.

128

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