Cardinal Welfare, Individualistic Ethics, And Interpersonal Comparisons of Utility

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Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of UtilityAuthor(s): John C. HarsanyiSource: Journal of Political Economy, Vol. 63, No. 4 (Aug., 1955), pp. 309-321Published by: The University of Chicago Press

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CARDINAL WELFARE, INDIVIDUALISTIC ETHICS, AND

INTERPERSONAL COMPARISONS OF UTILITY'

JOHN C. HARSANY1

University fQueensland

I

T HE naiveconcept fsocialwelfareas a sumof ntuitivelymeasurableand comparable individual cardi-

nal utilitieshas been found unable to

withstand the methodologicalcriticismofthePareto school. ProfessorBergson2has therefore ecommended ts replace-mentby the moregeneralconcept of asocial welfarefunction, efined s an ar-bitrarymathematical functionof eco-nomic (and othersocial) variables, of aform reely hosen ccording o one'sper-sonal ethical (or political) value judg-ments. Of course, in this terminology

everybodywill have a social welfarefunction f his own,differentrom hatofeverybody lse,exceptto theextent owhich differentndividuals' value judg-mentshappen to coincidewith one an-other.Actually,owingto theprevalenceof ndividualistic alue judgments n oursociety, thas beengenerally greedthata socialwelfare unction houldbe an in-creasingfunction f the utilitiesof indi-viduals: ifa certainsituation,X, is pre-ferred y an individualto another itua-tion,Y, and if noneof theother ndivid-

I I am in(lebted o rmyolleagues at theUniver-sity of Queensland,Messrs. R. W. Lane and G.Price,forhelpful omments. fcourse, heresponsi-b)ility orshortcomings f this paper and fortheopinionsexpressed n it is entirelymine.

2 A. B3ergson Burk), A ReformulationofCertainAspectsof WelfareEconomics, Quarterly

Journal fEconomics, II (Fehruary, 938),310-34,and Socialist Economics, in A Surveyof Con-temporaryconomics, d. H. S. Ellis (Philadelphia,1949), esp. lplp 12-20.

uals prefersY toX, thenX shouldbe re-garded as sociallypreferableo Y. But nootherrestrictions to be imposedon themathematical formof a social welfarefunction.

Recently,however, rofessor leming3has shownthat fone acceptsonefurtherfairlyweak and plausible ethicalpostu-late, one findsone's social welfarefunc-tion to be at once restricted o a rathernarrowclass of mathematicalfunctionsso as to be expressible after ppropriatemonotone transformation f the socialwelfare nd individualutility ndexes ifnecessary) s theweighted umof the n-

dividuals' utilities.This does not mean,of course, a return o the doctrine thattheexistence fan additivecardinalutili-ty functionis intuitively elf-evident.The existence of such a function be-comes, rather,the consequence of theethicalpostulatesadopted and is whollydependent on these postulates. Still,Fleming's resultsdo ina sense nvolveanunexpected revival of someviews of the

pre-Paretoperiod.In thispaper I propose,first fall, to

examine the precise ethical meaningofFleming'scrucialpostulate and to showthat it expresses n individualistic aluejudgment going definitelybeyond thegenerally dopted individualisticpostu-

I M. Fleming, A CardinalConceptofWelfare,Quarterly ournal of Economics,LXVI (August,1952),366-84. For a differentpproachto thesame

problem ee L. GoodmanandH. Markovitz, SocialWelfareFunctionsBased on IndividualRankings,AmericanJournal fSociology, ol. LVIII (Novenm-ber,1952).

309

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310 JOHN C. HARSANYI

late mentionedearlier, though t repre-sents, s I shall argue, a value judgmentperfectly cceptable according to com-

mon ethicalstandards (Sec. II). I shall

also attemptto show that, f both socialand individualpreferencesre assumedto satisfy the von Neumann-Morgen-stern-Marschakxioms about choicesbe-tweenuncertainprospects, ven a muchweaker ethicalpostulate than Fleming'ssuffices o establish an additive cardinalsocial welfarefunction Sec. III). In ef-fect, it will be submittedthat a mere

logical analysis of what we mean byvalue judgmentsconcerning ocial wel-fare and by social welfare functionsleads, without any additional ethicalpostulates, o a social welfare unction fthis mathematical orm Sec. IV). Final-ly, I shall turnto the problemof inter-personal comparisonsof utility,whichgains new interestby the revival of anadditive cardinal welfareconcept, and

shall examinewhat logical basis, ifany,there s for uch comparisons Sec. V).

II

Fleming expresseshis ethical postu-lates in terms f two alternative oncep-tual frameworks:one in terms of anideal utilitarianism of G. E. Moore's

type,the otherin terms of a preferenceterminologymorefamiliar oeconomists.

Thoughheevidently etsgreater torebythe first pproach, shall adopt the sec-ond,whichseemsto be freer funneces-sary metaphysical ommitments. havealso taken the libertyof rephrasinghispostulatesto some extent.

PostulateA (asymmetryfsocial pref-erence).-If from a social standpoint 4situationX is preferred o situation Y,thenY is not preferredo X.

PostulateB (transitivityfsocial pref-erence). If from social standpointX ispreferred o Y, and Y to Z, thenX ispreferredo Z.

PostulateC transitivityyf social indif-ference)- -If from a social standpointneither of X and 1 is preferred o theother, and again neitherof Y and Z ispreferred o the other, hen ikewisenei-therofX and Z is preferred o theother.

These three postulates are meant toinsure that social preference estab-lishes a complete rdering mong the pos-sible social situations, from which theexistenceof a social welfarefunction atleast of an ordinal type) at once follows.(Actually, two postulates would have

sufficed f, in the postulates, weakpreference,which does not exclude thepossibility f ndifference,ad been usedinstead of strong preference.)

Postulate D (positiverelationof socialpreferenceso individualpreferences).-Ifa given ndividual prefersituationX tosituationY, and none of the other ndi-viduals prefersY to X, thenX is pre-ferred o Y from social standpoint.

As already mentioned ostulate 1) ex-presses generally ccepted individualis-tic value judgment.

Finally, Fleming's Postulate E statesessentially that on issues on which twoindividuals' interests preferences) on-flict, ll other ndividuals' nterests eingunaffected, ocial preferenceshould de-pend exclusively n comparing he rela-tive social importance fthe interests t

stake ofeach ofthetwo individualscon-cerned.In otherwords, t requiresthat

4Of course,when I speak ofpreferencesfroma social standpoint, often bbreviatedto socialpreferencesnd the ike, alwaysmeanpreferencesbased on a given ndividual's value judgments on-cerning social welfare. The foregoing ostulatesare meant toimpose restrictions n any n(lividual'svalue judgemnentsf this kind, and thusrepresent,as it were,value judgmentsof the second order,that is, value judgments concerningvalue juldg-

ments.Later I shall discuss theconceptof l)refer-ences from a social standpoint at some lengthand introduce he distinctive erm ethical prefer-ences to describe them (in Sec. IV). But at thisstage I do not want to prejudgethe issue by usingthis terminology.








WELFARE, ETHICS, AND UTILITY 311

thedistribution f utilitiesbetween eachpairof ndividuals houldbe judgedsepa-ratelyon its own merits, ndependentlyof howutilities or income) are distribut-ed among the other members of thecommunity.

PostulateE (independentvaluationoftheutility istribution5etween ach pairof individuals). (1) There are at leastthree ndividuals. 2) Suppose that indi-vidual i is indifferentetweensituationsX and X' and also between situationsYand Y', but prefers ituationsX and X'

to situationsY and Y'. Suppose,further,that individual is also indifferente-tweenX and X' and betweenY and Y',but (unlike individual i) prefersY andY' to X and X'. Suppose also that allother ndividuals re indifferentetweenX and Y, and likewise betweenX' andyV.6 Then social preferences hould al-ways go in thesameway betweenX andY as theydo betweenX' and Y' (that is,

iffrom social standpointX is preferredto Y. thenX' should also be preferredo1'; if from social standpointX and Yare regarded as indifferent,he sameshould be trueof X' and Y'; and if froma social standpointY is preferredo X,then Y' shouldalso be preferredo X').

Postulate E is a natural extension ofthe individualisticvalue judgment ex-pressed by Postulate D. Postulate D al-

ready mplies that ifthe choice betweentwo situationsX and Y happensto affectthe interestsof the individuals i and j

5The more general term utility distributionis used insteadof the term income distribution,sincetheutility njoyed by each individualwill, ngeneral, depend not only on his own income butalso, owingto external conomies nd diseconomiesofconsumption, n otherpeople's incomes.

6 It is notassumed,however, hat the other ndi-

vidualsare (like i and ) indifferentetweenX andX' and between Y and Y'. In effect, erethis re-strictive ssumptionnserted ntoPostulateE, thislatterwouldcompletelyose the status ofan inde-pendentpostulateand would becomea mere corol-laryofPostulateD.

only,without affecting he interestsofanybodyelse, social choicemustdependexclusively n i's and j's interests pro-

vided that i's and j's interests gree inthis matter.Postulate E now adds thatin the assumed case social choice mustdependexclusively n i's andj's interests(and onweighing hesetwo interests neagainsttheother n terms fa consistentethical standard), even if i's and j's in-terests are in conflict. hus both postu-lates make social choicedependent olelyon the individual interestsdirectlyaf-

fected.7 hey leaveno roomfor hesepa-rate interests f a superindividual tateor ofimpersonal ulturalvalues8 (exceptforthe ideals of equity incorporated nthe ethicalpostulatesthemselves).

At first ight, ostulate E may ook in-consistentwith the widespreadhabit ofjudgingthe fairness or unfairness fthe distribution f incomebetween twoindividuals,notonlyon thebasis ofthese

two people's personal conditions andneeds,but also on thebasis ofcomparing

I n view ofconsumers' otorious irrationality,somepeople may feelthat thesepostulatesgo toofar in accepting the consumers'sovereignty oc-trine.These people mayreinterprethe terms n thepostulates referring o individual preferences sdenoting, ot certainndividuals' ctualpreferences,but rather their true preferences,hat is, thepreferenceshey would manifest nder ideal con-ditions, n possessionofperfect nformation,ndactingwithperfectogicand care. With some nge-nuity tshouldnotbe toodifficultogiveevensomesortof operational meaningto these ideal con-ditions, r to someapproximation fthem, ccepta-ble forpracticalpurposes. Or, alternatively,hesetermsmaybe reinterpreteds referringven to thepreferenceshat these individualsought o exhibitin terms f given thical tandard.The latter nter-pretationwould,ofcourse, eprive hepostulatesofmostof theirndividualisticmeaning.)

8 These postulatesdo not exclude,however, hepossibilitythat such considerationmay influencethe relativeweightsgiven to differentndividuals'

utilitieswithintheadditive social welfare unction.Even by meansofadditionalpostulates, hiscouldbe excludedonly o theextent o which hecompari-sonof ndividualutilities an be puton an objectivebasis independent of individual value judgments(see Sec. V).









their incomeswith the incomes of theothermembersof theirrespective ocialgroups.Thus people's judgmentson the

income distributionbetween a given

worker nd his employerwill also dependon the current arningsof othersimilarworkers nd employers.But the conflictwithPostulate E is more apparentthanreal. n a societywith mportant xternaleconomies nd diseconomies fconsump-tion,where theutilityof a given ncomedependsnot onlyon its absolutesize butalso on its relationto other people's in-

comes, t is not inconsistentwithPostu-late E that, in judging the incomedis-tribution etweentwo individuals, therpeople's incomes should also be takeninto account.An incomedistribution e-tween a givenworkerand a given em-ployer,which in the original situationseemed perfectly fair in terms of agiven ethical standard, may requiread-justment in the worker's favor, once

wages have generallygone up, since theworsening f this worker'spositionrela-tive to that ofhis fellowsmusthave re-duced himto a lower evel ofutility.

PostulateE requires hatthe distribu-tion of utilitybetween two individuals(once the utility evels of the two indi-viduals are given) should always bejudged independently f howutility ndincome are distributed among other

membersof the society. n the absenceof external economiesand diseconomiesof consumption, his would necessarilyalso mean udgingthe distribution f n-come between two individuals ndepend-ently of the incomes of others. In thepresence of such economies and dis-economies, however,when the utilitylevel of any persondependsnot onlyonhisown ncomebut also on otherpersons'incomes, t is not inconsistentwithPos-tulate E thatourvalue judgmenton thedistribution f income between two in-dividualsshouldbe influenced y the n-

comedistributionnthe restof the socie-ty in so far as the incomedistributionin the restofthesociety ffects heutili-ty levels of these two individualsthem-selves and consequently hedistributionof utilitybetweenthem.Postulate E de-mandsonlythat,once theseeffects avebeen allowed for,the distribution f in-come in the restof the societymustnothave any furthernfluence n our valuejudgment.

III

In accordancewith prevalentusage in

welfareeconomics,1leming's postulatesrefer o social or individualpreferencesbetween ureprospects nly.However, tseems desirable to have both sorts ofpreferences efinedforchoices betweenuncertainprospects s well. More oftenthan not, we have to choose in practicebetween social policies that promisegivendefinite esultsonlywith argerorsmallerprobabilities.On theotherhand,

ifwe subscribeto somesortof individu-alisticethics,we shouldlike to m-akeso-cial attitude toward uncertainty ome-how dependenton individual attitudestoward it (at least if the latter do notmanifest oo patentand too greatan in-consistency nd irrationality).

Sincewe admit thepossibility fexter-nal economiesand diseconomiesof con-

sumption, both socialand individual

prospects will, in general, specify theamounts of differentommoditiescon-sumed an(l the stocksof differentoodsheldby all individuals t differentuturedates (up to the tim-e orizon dopte(I)together with their respective proba-bilities.

As the von Neumann-Morgensternaxioms9 or the Marschak postulates1?

9See J. von Neumann and 0. MAorgenstern,Theoryof Games and EconomicBehavior 2d e.;Princeton,1947), pp. 641 ff.

10J. Marschak, Rational Behavior, UncertainProspects,and Measurable Utility, ' conome/rica,









equivalent to them(which atter shalladopt) are essentialrequirements orra-tional behavior, t is natural enough todemand that both social and individualpreferences 1hould satisfythem. Thisgives us:

Postulate -Socialpreferencesatis-fyNMarschak'sostulates 1, II, III', andIV.

Postulate b. Individual preferencessatisfy hesame fourpostulates.

in addition,we need a postulate tosecure the dependence of social prefer-

enceson individualpreferences:Postulate . If twoprospectsP and Qare indifferentromthe standpoint ofevery ndividual, hey realso indifferentfrom social standpoint.

Postulate c once more represents, fcourse, n individualistic alue judgment

thougha veryweak one, comparable

XVIII (1950), 111-41, esp. 116-21. Marschak's

postulatesan

besummarized s follows.

ostulate(comnpleherdering): he relation fpreferencestab-lishes a complete orderingamong all prospects.Postulate I (continuity): If prospect P is pre-ferredo prospectR, whileprospectQ has an inter-mediateposition betweenthem beingpreferred oR but less preferredhan P), then there exists amixture fP and R, withappropriate robabilities,suchas to be exactly ndifferentoQ. PostulateII'(sotf/icientumber fnonindifferentrospects): hereare at least fourmutuallynonindifferentrospects.Postolote V (equivalenceof mixture f equivalentprospects): f prospectsQ and Q' are indifferent,then, or nyprospect , a givenmixture fP andQis ni(lifferenttosimilarmixturefP andQ', (that s,to a mixture fP and Q' whichhas thesameproba-bilities or hecorrespondingonstituentrospects).

Postulate is neededtoestablish heexistence feven an ordinalutility or welfare)function,whiletheotherthreepostulatesare required o establishtheexistence fa cardinalutility orwelfare)func-tion.But, as Postulates I and III are almost rivial,Postulate V may be regarded s beingdecisiveforcardinalitys againstmereordinality.

11 hereare reasons o believe that, n actuality,individualpreferences etweenuncertainprospects

do not always satisfy hese postulatesof rationalbehavior (for example, owing to a certain loveof (langer ; see Marschak,op. cit., pp. 137-41). Inthis case we may fallback again upon the prefer-ences each individualwouldmanifest nder idealconditions see n. 5).

to Fleming's Postulate D rather han tohis Postulate E.

I proposeto showthatPostulatec suf-ficesto establishthat the cardinalsocialwelfarefunctiondefinedby Postulate acan be obtainedas a weighted umof thecardinal individual utilityfunctionsde-finedby Postulate b (on the understand-ing that the zero pointof the social wel-fare functions appropriately hosen).

Theorem .---There xists a social wel-farefunctionuchthat ts actuarialvalueis maximized by choicesconformable o

the social preferences iven. This socialwelfarefunction s unique up to lineartransformation.

Theorem II.-For each individualthere existsa utilityfunction uch thatits actuarial value is maximized bychoices conformable o the individual'spreferences. This utility function isunique up to linear transformation.

Both theorems ollow romMarschak's

argument.Let W denote a socialwelfare unction

satisfyingTheorem I and Uj denote autility function of the i'th individual,satisfying heoremII. Moreover, et Wbe chosen so that W = 0 if forall thenindividuals U1 = U2 = ... = Un = 0.

Theorem II. W is a single-valuedfunction of U1, U2, . . . , Un. This fol-lows, nview of Theorems and II, from

Postulate c.Theorem V.-W is a homogeneous

function f the first rder f U1, U2, ...

Un.

Proof.-We want to show that,if theindividual utilities U1 = u1; U2 = u2;

... .; U = ut correspondto the socialwelfareW = w,thenthe ndividualutili-ties U1 = k-ul; U2 = k-u2;. . . ; Un =

k-n

correspondto the social welfareW = k-w.

This will be shownfirstforthe casewhere0 ? k < 1. Suppose that prospect0 representsU1 = U2 = . * . ( n= 0









for the differentndividuals and conse-quently representsW = 0 for society,while prospect P representsU1 = ul;

U2= H12; .

*.

; Un=

unfor the former

and W = wforthe atter.Moreover, etQ be the mixed prospect of obtainingeitherprospect0 (with the probability1 - p) or prospectP (with the proba-bilityp). Then, obviously,Q will repre-sentU1 P ul; U2 = . .. ; Un =

p u, for the individuals and W= p-wforsociety. Now, if we write k= p, acomparisonbetween the values of the

variables belongingto prospect P andthose belongingto prospect Q will, inview of Theorem III, establish the de-siredresult or he case where0 < k ? 1(p, being a probability,cannot be <0or > 1).

Next let us considerthe case wherek < 0. Let us chooseprospectR so thatprospect 0 becomes equivalent to themixedprospectofobtainingeitherpros-

pect R (withtheprobabilityp) or pros-pect P (with the probability1 - p). Alittle calculationwill show that in thiscase prospect R will represent U1 =

(1- 1P)-u1; U2 = (1 - 1P)-112; ... ;Un = (1 - I/p)-un for the differentn-dividuals and W = (1 - 1 p) -w forso-ciety. If we now write k = 1 - 11p, acomparison between the variables be-longingto R and those belongingto P

will establish the desired result for thecase k < 0 (by an appropriatechoice oftheprobability ,we can makekequal toany negativenumber).

Finally, the case wherek > 1 can betaken care of by finding prospect SsuchthatprospectP becomesequivalentto themixedprospect fobtaining itherS (with a probabilityp) or 0 (with aprobability - p). Then this prospectwill be connectedwith the values U1 =l/p*Ul; U2 = lp8U2; ... ; U,. = l/p.

it. and W- 1p-w. Ifwenowwritek =

11pwe obtain the desired resultforthecase where k > 1 (by an appropriatechoiceofp we can make k equal to anynumber>1).

TheoremV. W is a weighted um ofthe individual utilities, f the form

W'=la. U,

where ai stands for the value that Wtakes when Ui = 1 and Uj = 0 for allj 5 i.

Proof.--Let Si be a prospect repre-senting heutilityUi to the th individu-

al and the utility ero to all other ndi-viduals.Then, according oTheorem V,forSi we have W = ai-Us.

Let T be themixedprospectofobtain-ing eitherS or S2 or . . . Sn, each withprobability11n. Then T will representtheindividual utilitiesU11n, U2/n, .

U/is and the social welfare

1W=-*wNa -Us

1'1

In viewofTheorem V, thisdirectlym-plies that if the individualutilityfunc-tions take the values U,, U2, . . ,Un

respectively, he social welfarefunctionhas thevalue

W= la* U.,

as desired.'2

IVIn the pre-Pareto conceptual frame-work, hedistinction etween ocial wel-fare and individual utilities was free ofambiguity. ndividual utilities were as-sumedto be directly iven by introspec-tion,and social welfarewas simplytheirsum. In themodernapproach, however,the distinction s far less clear. On theone hand,our social welfare oncepthas

12 If we want a formalguarantythat no indi-vidual's utility can be given a negativeweight nthe social welfare unction,we mustadd one morepostulate for nstance,PostulateD ofSec. II).









come logically nearer to an individualutility oncept. Social welfare s no long-er regarded s an objective quantity, hesame for all, by necessity.Rather, eachindividual is supposed to have a socialwelfarefunctionof his own, expressinghis own individualvalues in the sameway as each individualhas a utility unc-tionofhis own,expressinghis own indi-vidual taste. On the other hand, our in-dividual utilityconcept has come logi-cally nearer to a social welfareconcept.Owingto a greater wareness of the im-

portance of externaleconomies and dis-economies f consumptionnoursociety,each individual's utilityfunction s nowregarded s dependentnot only on thisparticular individual's economic (andnoneconomic) onditionsbut also on theeconomic (and other) conditionsof allother ndividuals n the community-inthe sameway as a socialwelfare unctionis dependenton the personal conditions

ofall individuals.At the same time,we cannot allow the

distinctionbetween an individual's so-cialwelfare unctionnd hisutility unc-tionto be blurred f we want (as most ofus do, I think) to uphold the principlethat a social welfare unction ughtto bebased not on theutility unctionsubjec-tive preferences) f one particular ndi-vidual only (namely, the individual

whosevalue judgmentsare expressed nthis welfarefunction), ut ratheron theutility unctionssubjective preferences)ofall individuals,representing kindoffair compromise mong them.'3Even

if both an individual's social welfarefunction and his utility function n asense expresshis own individualprefer-ences, theymust express preferences fdifferentorts: the formermust express

13 This principle s essentiallydenticalwithPro-fessorArrow's nondictatorship postulate in hisSocial Choice and Individual Values (New York,1951), p. 30 (see also n. 12).

what this individual prefers or, rather,would prefer) n the basis of impersonalsocial considerations lone, and the lat-termust expresswhat he actually prefers,whetheron the basis of his personal in-terests ron any otherbasis. The formermay be called his ethical preferences,the latter his subjective preferences.Onlyhis subjective preferenceswhichdefine his utility function) will expresshis preferences n the full sense of theword as they actually are, showinganegoistic attitude n the case of an egoist

and an altruistic ttitude in the case ofan altruist. His ethical preferences(whichdefinehissocial welfare unction)will, on the otherhand, expresswhatcanin only a qualified sense be called hispreferences :they will, by definition,

expresswhatheprefers nly n thosepos-sibly raremomentswhen he forces spe-cial impartial and impersonal attitudeupon himself.'4

In effect, he ethical postulates pro-14 Mr. Little's objection to Arrow'snondictator-

ship postulate (see Little's review article in theJournalof PoliticalEconomy, X [October,1952],esp. 426-31) loses its force,once the distinctionbetween ethical and subjective preferencessnoted.It does, then,make sensethat an individualshouldmorally isapprovein terms f his ethicalpreferences)f anunequal ncomedistribution hichbenefitshim financially, nd should still prefer t(in terms f his subjective preferences)o a moreegalitarian ne orshouldeven fight or t-behavior

morallyregrettable ut certainlynot logically n-conceivable.Arrow's distinction between an individual's

tastes (whichorder ocial situations nlyaccord-ing to their effects n his own consumption)andhis values (which take account also of externaleconomies nd diseconomies f consumptionnd ofethicalconsiderations,n ordering ocial situations)does not meetthe difficulty,ince t doesnot explainhow an individualcan without nconsistencyccepta social welfarefunction onflicting ith his ownvalues. This can be understood nly f his social

welfarefunctions epresents referencesf another

sortthan his values do. (Of course, n mytermi-nologyArrow's values fall in the class of sub-jective preferencesnd not n the classof ethicalpreferences,s is easilyseen from heway in whichhe defines hem.)









posed in Sections II and 111-namely,Postulates D, E, and c can be regardedas simply n implicitdefinition fwhatsort of impartial or impersonal atti-tude srequired ounderlie ethical pref-erences: hesepostulatesessentially erveto exclude nonethicalsubjective prefer-ences from ocial welfarefunctions.Butthis immayalso be securedmoredirect-ly by explicitlydefining he impartialand impersonal ttitudedemanded.

I have argued elsewhere' that an in-dividual's preferencessatisfy this re-

quirement f impersonality fthey ndi-cate what social situation he wouldchoose ifhe did not know what his per-sonal positionwould be in the newsitua-tion choosen (and in any of its alterna-tives) but ratherhad an equal chanceofobtaining any of the social positions'6existing n thissituation,from hehigh-est down to the lowest. Of course,it isimmaterialwhether his individualdoes

not in factknow how his choice wouldaffect his personal interests or merelydisregards hisknowledgefora momentwhenhe is makinghis choice.As I havetriedto show 7 in eithercase an imper-sonal choice preference) fthiskindcanin a technical sense be regarded as achoicebetween uncertain prospects.

This implies, however,without anyadditional ethicalpostulatesthat an in-

dividual's mpersonal references,ftheyare rational, must satisfyMarschak's

I See my CardinalUtilitynWelfare conomicsand in the Theory of Risk-taking, Journal ofPoliticalEconomy, XI (October,1953),434-35.

16Or, rather,f he had an equal chance ofbeingput in theplace of any individualmember fthe

society,withregardnotonlytohis objectivesocial(and economic)conditions,but also to his subjec-tiveattitudes nd tastes. n otherwords,he oughtto judge theutility fanother ndividual'sposition

not in termsof his own attitudes and tastes butrather n termsof the attitudes and tastes of theindividualactuallyholdingthisposition.

17 p. cit.

axioms and consequentlymust definecardinal social welfarefunction qual tothe arithmeticalmean18 fthe utilities fall individuals in the society (since thearithmeticalmean of all individualutili-ties gives the actuarial value of his un-certain prospect, definedby an equalprobabilityof being put in the place ofany individual in the situationchosen).

More exactly, f the formerndividualhas any objective criterion or omparinghis fellows'utilitieswithoneanother ndwith his own (see Sec. V), his social wel-

fare function will represent the un-weightedmean of these utilities,while ntheabsence of such an objectivecriterionit will, n general,represent heirweight-ed mean, with arbitraryweightsdepend-ing only on his personalvalue judgments.In the former ase social welfarewill ina sensebe an objective quantity,whereasin the attercase it will contain n impor-tant subjective element;but even in this

latter case it will be something erydif-ferent rom he utility unction fthe n-dividual concerned.19

V

There is no doubt about the fact thatpeople do make, or at least attempt tomake, interpersonal omparisons futili-ty,both in thesenseofcomparingdiffer-entpersons'total satisfaction nd in the

18 Obviously, he unweighted r weighted)meanof the individual utilities definesthe same socialwelfare unction s their um weighted y the samerelative weights), except for an irrelevant ropor-tionality onstant.

19The concept of ethical preferences sed in thissection mplies, fcourse, n ethical theory ifferentfrom he now prevalent ubjective attitude theory,since it makes a person's ethical judgmentstheexpression,not of his subjective attitudes n gen-eral, but ratherof certain special unbiased imper-sonal attitudesonly. shall set out thephilosophiccase for hisethical theoryna forthcomingublica-tion. (For a similar view, see J. N. Findlay, TheJustification f Attitudes, Mind, N.S., LXIII[April, 9541, 45-61.)









sense of comparing ncrements r decre-ments n differentersons' satisfaction.20The problem s only what logical basis,if any, there s for uch comparisons.

In general,we have two indicatorsoftheutility hatother eople attachto dif-ferent ituations:theirpreferencess re-vealed by their ctual choices,and their(verbal or nonverbal)expressions fsat-isfaction r dissatisfactionn each situa-tion. But while the use of these indica-tors for comparingthe utilitiesthat agivenperson ascribes to differentitua-

tions s relatively reeofdifficulty,heiruse for comparingthe utilitythat dif-ferent ersons ascribe to each situationentails a special problem. n actual fact,thisproblemhas two ratherdifferents-pects, one purelymetaphysical nd onepsychological,whichhave not,however,always been sufficientlyept apart.

The metaphysicalproblem would bepresenteven ifwe triedto comparethe

utilities njoyedby differentersonswithidenticalpreferencesnd with identicalexpressive reactions to any situation.E1'venn this case, it wouldnot be incon-ceivable that such persons should havedifferentusceptibilitiesto satisfactionand should attach different tilities toidentical situations, for, in principle,identical preferencesmay well corre-spondto differentbsolute evels of utili-

ty as longas theordinalproperties fallpersons'utility unctionsre thesame21),and identical expressivereactionsmaywell ndicatedifferent entalstates with

2' See I. AM.D. Little, A Critique of WelfareEIconomicsOxford, 950), chap. iv. I have nothingto add to Little's conclusionon the possibility finterpersonal omparisons futility. onlywant tosupplementhis argumentby an analysis of thelogicalbasis of such comparisons. shall deal withthe

problemf comparisions etween otal utilities

only,neglecting heproblem f omparisons etweendifferencesn utility, ince the social welfarefunc-tions discussed in the previous sections containonly total utilities f ndividuals.

differenteople. At thesame time,undertheseconditions his ogicalpossibility fdifferentusceptibilitiesto satisfactionwould hardly be more than a meta-physicalcuriosity. f two objects or hu-man beingsshow similarbehaviorin alltheirrelevantaspects open to observa-tion,the assumptionof some unobserv-able hidden differencebetween themmustbe regarded s a completely ratui-tous hypothesis and one contrary tosound scientificmethod.22This principlemay be called the principleof unwar-

ranteddifferentiation.n the ast analy-sis, t is on the basis of thisprinciple hatwe ascribemental states to otherhumanbeings at all: the denial of this principlewouldat once ead us to solipsism.23husin thecase ofpersonswith similarprefer-ences and expressive reactionswe arefully ntitledto assume thattheyderivethe same utilities rom imilar ituations.

In the real world,of course,different

people's preferencesnd their xpressivereactions to similar situations may beratherdifferent,nd this does representveryrealdifficultyncomparing heutili-ties enjoyedby differenteople--a diffi-culty n additionto themetaphysical if-ficultyust discussedand independent fit. I shall refer o it as the psychologicaldifficulty,ince t is essentially questionofhowpsychologicaldifferencesetween

people in thewidest sense (forexample,

21Even identical preferencesmong uncertainprospects (satisfyingthe Marschak axioms) arecompatiblewith differentbsolute levelsofutility,since theydo not uniquelydetermine hezeropointsand the scales of the correspondingardinalutilityfunctions.

22 By makinga somewhatfreeuse of ProfessorCarnap's distinction,we may say that theassump-tion of different usceptibilities f satisfaction nthis case, even though t would not be against the

canons ofdeductiveogic,would mostdefinitely eagainst the canonsofinductiveogic.

23See Little, A Critiqueof WelfareEconomics,pp. 56-57.









differencesn consumptionhabits, cul-tural background, ocial status, and sexand otherbiologicalconditions, s well aspurelypsychologicaldifferences,nbornor acquired) affect he satisfaction hatpeople derive fromeach situation. Theproblemin general takes the followingform. f one individual prefers ituationX to situationY, whileanotherprefersYto X, is thisso because the formerndi-vidual attaches a higher tilityto situa-tion X, or because he attaches a lowerutility o situationY, than does thelat-

ter-or is thisperhaps the resultofboththese factors at the same time? And,again, if n a givensituationone individ-ual givesmoreforcible igns of satisfac-tion or dissatisfaction han another, isthisso because the former eelsmore n-tense satisfactionor dissatisfaction, ronly becausehe is inclined o givestrong-er expression o his feelings?

This psychologicaldifficultys acces-

sible to directempirical solutionto theextent to whichthesepsychologicaldif-ferencesbetweenpeople are capable ofchange, and it is therefore ossible forsome individuals to make direct com-parisonsbetween the satisfactions pento one human type and those open toanother.24 fcourse,manypsychologicalvariables arenotcapable ofchangeorarecapable ofchangeonly nsomedirections

butnot nothers.For instance, numberof nbornmentalor biologicalcharacter-istics cannot be changed at all, and,though the cultural patterns and atti-tudes of an individualbornand educatedin one social group can be considerablychanged by transplantinghim to an-other,usually they cannot be completely

24 On thereliability fcomparisons etweentheutilityof differentituations before a change inone's taste (taken n thebroadest ense) andafterit, see the first wo sections ofmy Welfare Eco-nomics of Variable Tastes, Revjcw of EconomicStudies,XXI, (1953-54), 204-8.

assimilatedto the culturalpatternsandattitudes of the second group. Thus itmay easily happen that, if we want to

comparethesatisfactions ftwodifferent

classes of humanbeings,we cannotfindany individual whose personal experi-ences would cover the satisfactionsofboth these classes.

Interpersonal comparisons of utilitymade in everyday ifeseem,however, obe based on a different rinciple whichis, of course, eldomformulated xplicit-ly). If two individuals have opposite

preferences etween two situations,weusually tryto findout thepsychologicaldifferencesesponsiblefor this disagree-ment and, on the basis of our generalknowledgeofhumanpsychology, rytojudge to what extentthese psychologi-cal differencesre likely to increase ordecrease theirsatisfactionderived fromeach situation.For example, f one indi-vidual is readyat a givenwage rate to

supplymore aborthan another,we tendin generalto explain this mainly by hishavinga lowerdisutility or abor if hisphysiqueismuchmore robustthanthatof theother ndividualand ifthere s noascertainabledifferenceetween the twoindividuals' economicneeds; we tend toexplainit mainly by his havinga higherutilityforincome (consumptiongoods)if the two individuals' physiques are

similarand if the former videntlyhasmuch greater economic needs (for ex-ample, a largerfamily o support).

Undoubtedly,both these methodsoftacklingwhat we have called the psy-chologicaldifficulty re subject to rath-er argemargins f error.25n general,thegreater hepsychological, iological,cul-tural,and social differencesetweentwo

25 Thoughperhaps it would not be too difficultto reduce these marginsquite considerably (forexample, by using appropriate statistical tech-niques), should therebe a need for more preciseresults.









people, the greater the margin of errorattached to comparisons between theirutility.

Particular uncertainty is connectedwith the second method, ince t dependson our general knowledgeof psychologi-cal laws, which s still n a largelyunsat-isfactory tate.26What is more, all ourknowledge bout the psychological awsofsatisfaction s ultimately erivedfromobservinghowchanges n differentpsy-chological nd other) variables affect hesatisfactions n individualobtains from

various situations.We therefore ave nodirect mpirical videnceon how people'ssatisfactions re affected y the variablesthat, for any particular ndividual, arenot capable of change. Thus we can, ingeneral, udge the nfluence f these un-changeable variables only on the basisof the correlations ound between theseand the changeable variables, whoseinfluencewe can observe directly.For

instance, et us take sex as an exampleofunchangeable variables (disregarding

the few nstancesofsex change) and ab-stractive ability as an example ofchangeable variables. We tend to as-

sume that the averageman findsgreatersatisfaction than the average womandoes in solvingmathematicalpuzzles be-cause, allegedly, men in general havegreater bstractiveabilitythan women.

But this reasoning depends on the im-plicitassumptionthat differencesn theunchangeable variables, if unaccom-

p)anlied y differences n the change-able variables, are in themselves m-

26 Goingback to our example,for nstance,thedisutility f abor and theutility f ncome re un-likely, o be actually independentvariables (as Ihave tacitly ssumed), thoughtmaynotalwaysbeclearin whichfway heirmutualinfluencectually

goes. In any case, income s enjoyed n a differentway, depending n the ease with which t has beenearned, nd labor s put upwith na differentpirit,dependingon the strength f one's need for addi-tional ncome.

material.For example,we must assumethat men and women equal in abstrac-tive ability and the otherrelevant har-acteristics)would tend to find the samesatisfactionn working n mathematicalproblems.

Of course, the assumption that theunchangeable variables in themselves

have no influences exhypothesiot opento direct empiricalcheck. It can be jus-tified nly by the a prioriprinciple hat,when one variable is alleged to have acertain nfluence n another,theburden

ofproof ieson thosewhoclaimthe exist-ence of suchan influence.27hus the sec-ondmethodof nterpersonal tility om-parison rests in an important ense onempiricalevidencemore indirect28hanthat underlyinghe firstmethod.On theotherhand, the second methodhas theadvantage of also being applicable inthose cases where no one individual canpossiblyhave wide enough personal ex-

perienceto make directutility ompari-sons in termsof thefirstmethod.

In any case, it should now be suffi-ciently lear that interpersonal ompari-

27 This principlemaybe called the principleofunwarranted orrelation nd is again a principleof nductive ogic, closelyrelated to the principle funwarranted ifferentiationeferredo earlier.

28 There is also another reason forwhich con-clusionsdependent n theprinciple funwarranted

correlationhave somewhat ess cogencythan con-clusions dependent only on the principleof un-warranted differentiation. he former principlerefers o thecase wheretwo individualsdiffern acertainvariableX (inourexample,nsex) butwherethere s no specialevidencethattheydifferlso in acertainother variable Y (in susceptibility o satis-faction). The latterprinciple,on the otherhand,refers o the case where there s no ascertainabledifferencet all between the two individuals inany observable variable whatever,not even in X(in sex). Now, thoughthe assumption that thesetwo individuals differ n Y (in susceptibility o

satisfaction)would be a gratuitoushypothesis neithercase, obviously t would be a less unnaturalhypothesisn the first ase (wherethere s some ob-served difference etween the two individuals)than n thesecondcase (where here s none).









sons of utilityare not value judgmentsbased on some ethicalorpoliticalpostu-lates but rather re factualpropositionsbTased n certainprinciplesof inductivelogic.

At thesame time,ProfessorRobbins29is clearlyrightwhen he maintainsthatpropositionswhichpurportto be inter-personal omparisons futility ften on-tain a purelyconventionallementbasedon ethical or political value judgments.For instance, heassumption hat differ-ent individuals have the same suscepti-

bility o satisfaction ften xpresses nlythe egalitarianvalue judgmentthat allindividuals should be treated equallyrather han a belief n a factualpsycho-logicalequalitybetweenthem.Or,again,different eople's total satisfaction isoften omparedon thetacit understand-ing that the gratification f wants re-garded as immoral in terms of a cer-tainethical tandard hall notcount. But

in orderto avoid confusion, uchpropo-sitions based on ethical or political re-strictivepostulatesmust be clearlydis-tinguishedfrominterpersonal ompari-sons of utilitywithout a conventionalelementof thiskind.

It must also be admittedthat theuseofconventional ostulatesbased on per-sonalvalue judgmentsmaysometimes edue not to our freechoice but ratherto

ourlack ofthefactual nformation eed-ed to give our interpersonal tility om-parisons moreobjectivebasis. In effect,ifwe do not know anythingabout therelative urgency of different ersons'economicneeds and stillhave to make adecision,we can hardlyavoid acting on

29See L. Robbins, Robertson on UtilityandScope, Economica,,N.S.,XX(1953),99-ill,esp. 109;see also hisAnwssay onl heNature and

Signific(anceofEconomic Science (2d ed.; London, 1948), chap.vi; and his Interpersonal omparisons fUtility,Economic Journal, XlIII (December, 1938)635-41.

the basis of personalguessesmoreor lessdependenton our ownvalue judgments.

On the other hand, if the informationneededis available, individualistic thicsconsistently equiresthe use, in the so-cial welfarefunction, f individualutili-ties not subjected to restrictivepostu-lates. The imposition f restrictive thi-cal or political conventionson the indi-vidual utilityfunctionswould necessari-ly qualify our individualism,since itwould decrease the dependence of oursocial welfare function on the actual

preferencesnd actual susceptibilities osatisfaction, f the individualmembersofthe society,putting n its place a de-pendenceon our own ethicalor politicalvalue judgments see nn. 5 and 6).

To sumup, the morecompleteour fac-tual informationnd themorecomplete-ly individualistic urethics, he more thedifferentndividuals'socialwelfare unc-tionswill converge owardthe same ob-

jectivequantity,namely, he unweightedsum (or ratherthe unweighted rithme-ticmean) ofall individualutilities.Thisfollowsbothfrom eitherof twoalterna-tive sets of) ethicalpostulatesbased oncommonly ccepted individualistic thi-cal value judgmentsand from he merelogicalanalysisof theconceptof a socialwelfare function.The latter interpreta-tion also removes ertaindil-'culties on-

nectedwiththe concept of a social wel-farefunction,whichhave been broughtout by Little's criticismof certain ofArrow's conclusions.

Ofcourse, hepracticalneedfor each-ingdecisions npublicpolicywillrequireus to formulate ocial welfare unctions-explicitly r implicitly even ifwe lackthe factualinformation eeded forplac-ing interpersonal omparisonsof utilityon an objective basis. But even in thiscase, granting he proposed ethicalpos-tulates ortheproposed nterpretationf









the concept of a social welfare unction),our social welfare unctionmust take theform f a weighted um (weightedmean)of all individual utility functions,withmore or less arbitraryweights hosen ac-cording o our own value judgments.

There is here an interesting nalogywith the theory of statistical decisions(and, in general,the theoryof choosingamong alternative hypotheses). In thesame way as in the latter, it has beenshown30that a rational man (whosechoices satisfy ertainsimple postulates

ofrationality)must act as ifhe ascribednumerical ubjective probabilitiesto all

30See Marschak's discussion of what he callsRamsey's norm, n his paper on Probability n

the Social Sciences, in Alathematical hinkingntlhe ocial Sciences,ed. P. F. Lazarsfeld (Glencoe,Ill., 1954), Sec. I, esp. pp. 179-87; also reprintedsNo. 82 of Cowles CommissionPapers (N.S.).

Fora survey f earlier iteratureeeK. J. Arrow,AlternativeApproaches o theTheoryofChoice inRisk-taking ituations, Econometrica, IX (Octo-ber,1951), 404-37, esp. 431-32, and the referencesthere uoted.

alternativehypotheses, ven if his factu-al informations insufficiento do this onan objective basis---so in welfare eco-nomicswehave also found hat a rationalman (whose choices satisfy certainsimplepostulates of rationality nd im-partiality) must likewise act as if hemade quantitative interpersonalcom-parisonsofutility, ven ifhis factual n-formation s insufficiento do thison anobjectivebasis.

Thus if we accept individualisticethicsand set public policy the task of

satisfyinghepreferences f the individ-ual members fthe society decidingbe-tween conflictingreferencesfdifferentindividuals according to certain stand-ards of mpartialequity), our social wel-farefunctionwillalwaystend to take theformof a sum (or mean) of individualutilities; but whethertheweightsgivento these individual utilitieshave an ob-jectivebasis or not willdependwholly n

the extentof our factual (psychological)information.

Cardinal Welfare, Individualistic Ethics, And Interpersonal Comparisons of Utility

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