Cultural traits and conformity to norms

Abstract

Social norms affect individual choice through a pressure to conform. Though it is common to

think about the strength of the pressure to conform as one ordinal measure, we demonstrate in

this paper that it is warranted to apply a separate measure for the way in which the pressure

increases as one moves from small deviations from the norm to larger ones. Furthermore, we

suggest a framework for how to classify societies and their treatment of deviant behavior. By way

of some analytical examples we finally show that such a measure captures phenomena that

cannot be captured using the traditional framework, and highlight some insights that result from

an analysis that takes it into consideration. In particular, we illuminate some hidden connections

between orthodox societies and perfectionist individuals, and between liberal societies and lax

individuals.

1. Introduction

A common approach in research relating to social norms is to let the social pressure to conform

be a binary variable – an individual will suffer a fixed social cost by deviating from the norm and

no social cost if she follows it (Lindbeck et al, 2003; Kuran, 1989; Brock and Durlauf, 2001)1.

While this may be a sufficiently accurate description of reality in some cases, in many contexts

1 In some of these models the decision of the individual is binary which of course means that the punishment must be binary too.

there are “degrees in hell”. Just like judicial systems distinguish between different illegal activities,

a large deviation from a norm can be sanctioned differently than a small one.

Yet another simplification used is to analyze societies using a measure of how harshly deviations

are punished, where a tolerant society punishes deviations generally less than an intolerant one. A

recent empirical quest in this direction is presented by Gelfand et al. (2011). They construct a

measure of the tightness of societies that is described as the “overall strength of social norms and

tolerance of deviance”. To measure norms using one measure may be a simplification without

consequence in some instances, while in other settings it will be important to also distinguish

between how a society sanctions small deviations in comparison to larger ones. While one society

may impose harder social pressure for small deviations from the norms compared to a second

society, the second may punish large deviations harder than the first one.

This paper suggests a structure for how to enrich the analysis of social norms and their differing

effects across societies by relaxing the two simplifications mentioned above. It is structured so

that section 2 argues that the convexity or concavity of the social pressure depicts a common

characteristic in how societies sanction norm deviations, section 3 suggests a cultural labeling for

these terms, and finally section 4 shows that this addition matters and extends the analysis of how

norms affect societies. Section 5 concludes. The analytical results in section 4 are expressed

verbally with an ambition to provide intuition for the claims. These results are mainly drawn from

using the analytical framework in Michaeli and Spiro (2012).

2. Observing social pressure

In order to motivate the distinction between how a society sanctions small deviations in

comparison to larger ones, a few practical observations may be in place. An example comes from

experiments using the Public Good Game that have been performed by Herrmann et al. (2008).

They document how participants sanction others who contribute a different amount than

themselves to a public good. By ocular inspection (see figure 1 in Herrmann et al. 2008), their

results suggest that deviations are punished convexly in places such as Copenhagen, Bonn and

Melbourne while being punished concavely in places such as Muscat and Riyadh2. Another detail

to note here is that Melbourne has heavier punishments for large deviations than has either

Riyadh or Muscat, while it has lighter punishments than these two for small deviations. This

means that it is indeed meaningful to separate the general strength of punishment from its

gradual change when going from small to large deviations.

A more anecdotal demonstration of these points is by crudely comparing the punishment

systems in the Israeli Jewish Ultraorthodox community, in the liberal West European institutions

and under the Taliban regime. This is to some extent a comparison of formal and informal

sanctioning. But the purpose here is to highlight that punishment systems can distinguish

between large and small wrongdoings in different ways. Hence, while there are many dimensions

by which they can be compared, for the purpose of this paper we will focus only on two aspects

– the curvature of punishment and its general heaviness.

An important difference between the Taliban and the Ultraorthodox sanctioning systems is that

the Taliban have substantially heavier punishment for any comparable deviation from the norm.

There are numerous accounts of the Taliban using capital punishment for both misdemeanor and

larger offenses, while the Ultraorthodox are characterized by milder punishments, such as

censuring or at most excommunicating norm violators. However, one characteristic that both

these societies have in common is that they advocate “being true to the book”, meaning that they

will sanction relatively harshly (compared to their own scale) any small deviation from the norm,

while large deviations will be sanctioned only slightly more. Among the Taliban this comes from

2 To see this note that in Copenhagen, Bonn and Melbourne, deviations of -20 to -11 are punished less than thrice as much as deviations of -10 to -1. Meanwhile, in Riyadh and in Muscat, the large deviations are punished more than thrice as much as the small deviations. For the cities mentioned here this is also corroborated by Figure S2 in the supplementary material to Herrmann et al (2008), where they show the likelihood (rather than the size) of punishment for various deviations. Mathematically, a convex function y(x) with y(0)=0 is such that a doubling of x implies a more than doubling of y (and vice versa for a concave function). Graphically this means that an increasing convex function bends upwards while an increasing concave function becomes flatter as its argument increases.

the fact that one cannot subject a person to capital punishment more than once. Among the

Ultraorthodox it is the effect of expelling someone from the group whereby further sanctioning

no longer works as the person seizes to be governed by their rules.

Let us now compare the punishment structure of the Ultraorthodox Jewish community in Israel

with that of the liberal West European institutions. Virtually by definition, a liberal democracy

must allow the expressions of (almost) any view. By most democratic constitutions, citizens are

allowed a rather broadly encompassing freedom of expression and are eligible to run for elections

using almost any political platform. But once a party or an individual expresses views that deviate

very far from the consensus, for example a party that wants to abolish democracy or an individual

that incites people to commit crimes, that party may become illegal (like Nazi parties are in

certain countries), and that individual may be fined or arrested (for incitement) or be subject to

surveillance (if she, for example, openly expresses extreme right-wing or extreme left-wing

opinions, or supports Sharia Law). This means that liberal democracies will tend to be convex in

how they constitutionally deal with deviations. Whether this convexity is also present in informal

norm enforcement in Western Europe is harder to say. But the purpose of this illustration is to

show that convex punishment systems do exist. In comparison, the Israeli Ultraorthodox

sanctioning system, as described above, can be considered concave: it is quite strict towards small

deviations, but its sanctioning does not go much beyond this level. For example, a woman may

be censured for wearing a dress that is too short, and a man for publicly supporting the draft of

Ultraorthodox to the Israeli army.3 It should be emphasized here that these examples are minor

3 One example that was extensively covered in the Israeli media is that of Haim Amsalem, an ultraorthodox Sephardi Rabbi who belonged until recently to the elite of the ultraorthodox Sephardi community in Jerusalem and even was one of their representatives in the Israeli parliament. In 2010 Amsalem publicly called for the insertion of core modern studies (like math and English) into the ultraorthodox education system and for the integration of the males of the community in the Israeli workforce and in the Israeli army (currently the vast majority spends all the time in Torah study). In response, the heads of the community published a call for “all those who care for the Torah of Israel” to “stay away from this man”. Consequentially, people stopped attending the synagogue in which Amsalem served as a Rabbi. Later on, another publication in one of the community’s newspaper referred to Amsalem as Amalek (someone who deserves to die according to the Torah), and the Israeli parliament had to appoint armed guards to secure Amsalem against attempts to harm him.

misdemeanors in terms of the Jewish religion. Religious Jews belonging to less extreme factions

treat these behaviors as completely normative behaviors.

[Figure 1]

Figure 1: Social pressure (y-axis) as a function of the deviation from the norm (x-axis). Societies 1 and 2 demonstrate

concave social pressure functions, with society 1 exerting heavier pressure for comparable deviations, while society 3

demonstrates a convex social pressure function.

As incomplete and stylized as these descriptions may be, they do highlight that representing a

punishment system with only one parameter is insufficient. There is on the one hand the issue of

harshness in general, and there is, on the other hand, the issue of curvature of the punishment

system. The latter is most accurately described by the mathematical terms “convex” and

“concave”. A concave system is characterized by hard punishments for small deviations and only

slightly harder punishments for larger ones. A convex system issues small punishments for small

deviations, but once the deviations become large enough the punishment scale increases very

rapidly. This is depicted in figure 1. A system of punishments may be at the same time harsh and

concave (society 1). Alternatively, it may be harsh and convex (society 2). Or, it may be light and

concave (society 3). Finally, it may also be light and convex4 (like the judicial system of some

liberal West European countries). This also means that society 3 may have heavier punishments

than society 2 for small deviations while having lighter punishments towards large deviations, as

is apparent when comparing the punishment rates chosen by subjects in Melbourne and Muscat

in the Public Good Game experiment mentioned earlier. It is also possible to think of a concave

punishment which is always above a convex one. This is arguably the case when comparing the

Taliban with the Western European societies (capital punishment has been abolished in Western

Europe but is widely used among the Taliban.

4 Mathematically there are of course also degrees of convexity and concavity (see Section 4.3 for an implication of the degree of convexity). For a more through treatment see e.g. Palmer (2003).

Just as societies may be characterized by the gradual change in punishments in treating norm

deviations, individuals may be characterized by different sensitivities to the psychological cost

embodied in small misrepresentations and in large misrepresentations when stating biased stances

in public. An individual may have some personal opinions on, for example, the left-right political

scale. While there may be some opinion that society in general or on average accepts the most (or

pressures the least), the true opinions of individuals will often differ from it. In order to relieve

the social pressure, an individual may choose to publicly express an opinion that is closer to the

norm than her true opinion is. Apart from its general strength, the discomfort of the individual

may then rise concavely or convexly the further the expressed opinion is from the true belief5.

3. A system of labels

Can we connect these mathematical terms to more common descriptions relating to societies and

cultures? This section will attempt to do just that. Connecting precise mathematical definitions

into labels useful in social and behavioral sciences always comes with certain subjectivity and we

do not expect there to be a scholar consensus around our suggested labels. Although we find

them useful in connecting mathematical results to societal traits and explaining them on an

intuitive level, the main purpose here is to initiate a discussion of how to describe these

mathematical objects in cultural terms. For a formal analysis such labeling is naturally redundant,

as the mathematical results will hold whatever labels we use.

An important note here is that the same society or group of people may have different traits for

different issues. For example, it is conceivable that a group punishes concavely deviations along a

religious dimension while pressuring convexly deviations along another dimension. Likewise, an

individual may feel a concave displeasure when creating false impressions about certain issues and

5 This list is of course not exhaustive from a theoretical standpoint. One could also, for example, imagine an inner displeasure of lying which rises first convexly and then concavely.

convex when doing so about others. However, such problems arise also when looking at other

measures of social pressure and of misrepresentation.

To represent the general strength of the norm we suggest the term “Tightness” following the

vocabulary of Gelfand et al. (2011). This means that, holding other things equal, a tighter society

will have a harsher social pressure.

Some societies are very meticulous about already minor deviations from the norm but do not

distinguish so much between large and small wrongdoings, i.e., are characterized by a concave

social pressure. We believe that such ambitions to be true to the book represent “Orthodox”

societies. This also seems to be in line with the examples mentioned earlier of Riyadh and Muscat,

societies that we would intuitively label as orthodox. By Herrmann et al’s measure (2008) these

societies indeed exhibit a concave punishment structure in the Public Good Game. Likewise, it

seems sensible to characterize both the Israeli Ultraorthodox community and the Taliban regime

as orthodox. The extreme case of concave social pressure is when exactly following the norm

yields no pressure, while any deviation, large or small, inflicts the same pressure. In models of

binary social pressure this would exactly be the case.

As a counter label, following our descriptions of how liberal democracies formally treat the

freedom of expression and portraying the examples of Melbourne, Bonn and Copenhagen in

Herrmann et al. (2008), we suggest the label “Liberal” to represent societies with convex social

pressure. That is, in these societies small deviations are largely ignored, but for sufficiently large

deviations the pressure is ramped up significantly.

It should be noted that in everyday language (and perhaps even in the scientific one), there is an

overlap of the terms ‘orthodox’ and ‘tight’. Both are often taken to imply the existence of rather

strong social pressure. This is apparent when considering the usage of the measure of tightness in

Gelfand et al. (2011) to capture both the “overall strength of social norms and tolerance of

deviance”. This blend of terms reflects the fact that orthodox societies often use heavier social

pressure compared to liberal ones. To address these concerns we want to emphasize that while

there may in practice be a positive correlation between tightness and orthodoxy (i.e., between a

high average level of pressure and concavity of this pressure), this does not mean that in all cases

orthodox societies exhibit higher pressure for any comparable deviation. Like was noted earlier,

in the experiments of Herrmann et al. (2008) subjects from Muscat used a punishment that was

higher for small deviations and lower for large deviations compared to that used by subjects in

Melbourne. Hence, we believe that tightness is the better term for representing the overall

heaviness of the social pressure, and orthodoxy better describes the concave curvature of that

pressure. As is shown in Michaeli and Spiro (2012) and is roughly described in the next section,

many interesting qualitative insights come out of the distinction between orthodox and liberal

societies rather than as a consequence of the tightness of the norm.

On an individual level, the weight and curvature of the inner displeasure of misrepresentation can

be labeled in a similar fashion. To represent the general measure of displeasure we suggest the

term “Rigid”. Thus, holding all else equal, the more rigid an individual is, the higher is the

displeasure she feels due to misrepresenting her true opinion in public.

An individual may furthermore be very particular about saying exactly what she believes. She may

be very reluctant to exhibit even a slight false impression, but once she does deviate the slightest

from her true opinion, any further deviation makes a little difference for her. That is, she exhibits

a concave displeasure of misrepresentation. We believe that the term “Perfectionist” describes

this individual punctiliousness well. The extreme form of this is when only stating exactly her true

opinion is good enough for her, and any misrepresentation inflicts the same amount of

displeasure. As a counter label we suggest the term “Lax” to represent the individual trait of a

convex displeasure of lying. As long as the misrepresentation is not too extreme it hardly inflicts

any discomfort.

The same observations and objections as with the terms orthodox and tight may be raised here -

in practice the terms perfectionist and rigid are often used synonymously. As before, even if in

reality there is a positive correlation between these two distinct features, they capture two

different aspects of one’s attitude towards misrepresentation. Furthermore, such correlation can

be constructed theoretically by using mathematical forms that imply that perfectionists feel higher

displeasure than lax individuals for comparable misrepresentations. Again, as will be

demonstrated in the next section, for many settings the distinction between perfectionist and lax

individuals has more interesting implications than the level of rigidity has. Note also that the

above labeling is silent about whether a society consists of individuals who are only perfectionists,

only lax individuals or whether these two types coexist. For the purpose of labeling an individual

this is less important, but of course it is central to be clear about such assumptions when

performing the analysis of a model.

4. The effect of concavity and convexity

In this section we describe a variety of results taken from a theoretical model by Michaeli and

Spiro (2012) and apply the method from that paper to a related model by Kandel and Lazear

(1992). The purpose is to demonstrate that the curvatures of social pressure and of individual

preferences lead to new insights regarding decision making in various contexts, and that, from an

empirical perspective, the curvature may be just as important to measure as the tightness of

society if one wants to explain central societal phenomena. Comparable conclusions are also

reached by Clark and Oswald (1998). That the curvature matters for how to represent

preferences has also been pointed out by Eguia (2011). Since they themselves point out this

conclusion, we will not further review it here but rather refer the reader to their original papers.

4.1. A basic trade-off

To begin with, we focus on the case where true opinions (regarding some debatable issue) are

ordered on a one dimensional axis, say from left to right, and the social norm is one opinion on

that axis. Every person in society must take a public stance, where the resultant social pressure

inflicted on her is increasing with the distance between this stance and the social norm. In

addition, declaring a public stance different from one’s true opinion involves an inner displeasure

that is increasing with the distance between the true opinion and the declared stance. Considering

this simple trade-off, what stance would the individual declare?

Generally speaking, an individual whose true opinion differs from the social norm has three

options: the first option is to declare the true opinion in public in order to minimize inner

discomfort, the second option is to declare the social norm as one's stance in order to minimize

the social pressure, and the third option is to declare some stance in the range between the true

opinion and the social norm, thus reducing both the inner displeasure and the social pressure to

some bearable level. As will be shown next, the curvature of the displeasure and that of the social

pressure are key contributors to the choice of the individual.

4.2. The choice of public stances

To realize the effect of the curvature of the social pressure and the curvature of the inner

displeasure on the choices of stances, consider first the social pressure. If social pressure is

convex (a “liberal” society), then a small deviation from the norm in the direction of the true

opinion bears no cost for the individual, while rewarding her with a reduction of the inner

displeasure. This implies that individuals would not fully conform to the norm unless it is

completely aligned with their true opinions. Conversely, if social pressure is concave (an

“orthodox” society), then even a small deviation from the norm in the direction of the true

opinion bears a high cost for the individual, while larger deviations do not add substantial

pressure. This implies that individuals would choose either to fully conform to the social norm in

order to avoid the social pressure altogether, or to move far enough from the norm towards the

true opinion so that the implied reduction in inner displeasure would compensate for the high

social pressure.

The effect of the curvature of the inner displeasure is similar: with a convex inner displeasure (i.e.,

“lax”), one would not stick completely to one’s true opinion, whereas if one has a concave inner

displeasure (i.e., “perfectionism”), one would either choose the true opinion as one’s stance, or

move far enough from the true opinion towards the social norm so that the implied reduction in

social pressure would compensate for the high inner displeasure.

We will not cover here the type of choices that individuals are due to make under every possible

combination of displeasure and social pressure curvatures6. Instead, we will focus on one

qualitative consequence, using two distinctive cases: a lax individual in a liberal society, and a

perfectionist individual in an orthodox society.

When society is liberal and the individual is lax, small deviations either from the norm or from

the true opinion are not costly, hence the individual would look for a compromise solution, i.e.,

would neither fully conform to the norm nor completely stick to her true opinion.

The conclusion that individuals will choose stances somewhere in between their own and the

societal norm may seem intuitive, but this is not always the case. If society is orthodox and the

individual is perfectionist, then the individual either fully conforms to the norm or completely

sticks to the true opinion. So, a compromise solution will not be chosen in this case. To realize

why these two rather extreme solutions are the only possible solutions for the individual, think of

the extreme case in which every deviation from the norm bears the same fixed social cost, and

every misrepresentation on the side of the individual bears the same fixed inner displeasure for

her. In this case, it is clear that any compromise solution, i.e., any stance in-between the true

6 We refer the interested reader to Michaeli and Spiro (2012), where we discuss in addition the implications of each of these combinations for the distribution of declared stances in society.

opinion and the social norm, inflicts the sum of both costs on the individual. Therefore, one

would either fully conform to the norm and bear the inner displeasure that follows it, or

completely stick to the true opinion and put up with the resultant social pressure. The choice

between these two extreme options would be affected by the relative size of these forces, i.e., by

comparing the tightness of the norm and the rigidity of the individual. If the sanctioning of

deviations from the social norm is in the hands of an authority, as is often the case with orthodox

societies, the authority may use the power at its disposal to “help” perfectionist individuals take

the “right” decision. This fact of life is well understood by authoritarian regimes: not only are

they intolerant to small deviations from the authoritarian rule of conduct (concave social

pressure), but they also often tend to use forceful coercion in order to make sure that even

dissidents fully conform.

4.3. Some insights on the distribution of stances in society

When performing the analysis at the level of society rather than at the level of the individual, the

dichotomous distinctions between convex and concave social pressure and between convex and

concave inner displeasure are not enough to reveal the whole picture. For an analysis at the level

of society it is thus important to consider the additional effect of the relative convexity (or relative

concavity) of the two forces, i.e., which of the two is more convex (or more concave) than the

other. It turns out that this relative convexity (or relative concavity) implies some insights about

the relation between the public stances chosen by individuals with different true opinions. This

relation in turn determines the distribution of declared stances in society.

In order to demonstrate the effect of relative convexity on the distribution of declared stances,

assume that all individuals in society are lax to the same degree (this assumption is used here for

brevity but can be motivated by a separate cultural norm for misrepresentation that everyone

follows). Consider first the case where the social pressure is more convex than the inner

displeasure. It is easier then, to think of society as extremely “liberal” (our labels, not the everyday

meaning), i.e., one in which deviating from the norm inflicts no pressure whatsoever, unless the

deviation is extreme enough to inflict a significant pressure. If enough people have true opinions

at the edges of the scale (extreme leftists or extreme rightists), then, remembering that those are

lax people, they will choose a compromise solution that lies at the nearest edge of acceptable

stances. That is, extreme leftists would misrepresent themselves as acceptably leftists, and the

same would hold for rightists. This would result in a bimodal distribution, with the extremists

from each side creating a peak near the edges of the range of acceptable (i.e., not pressured)

stances.

As a different case, if the inner displeasure is more convex than the social pressure, it is helpful to

think of the people as extremely lax, i.e., as long as the misrepresentation is not too extreme it

hardly inflicts any discomfort. Those individuals with true opinions close enough to the norm

would thus choose to almost fully conform to the norm, as almost no inner displeasure is

involved in such a choice. These individuals will form a peak around the social norm in the

distribution of stances. At the same time, individuals whose true opinions are far from the norm

would misrepresent their opinions in public as far as they can do that without feeling high inner

displeasure. Thus, two individuals with different true opinions far from the norm would choose

two different stances, none of which equals their true opinions. The result would be a unimodal

distribution of stances centered at the norm.

The main message here is that bimodal polarization and unimodal concentration, as observed in

many contemporary issues, may be explained by the simple tradeoff for individuals conforming

to a norm rather than attributed to the true opinions of people.

4.4. When are norms representative of true opinions?

Social norms may originate in traditions, historical institutions, authority, individual stances, or

any mixture of those. This means that a norm may not necessarily represent the average public

stance. Think for example of traffic rules. They determine that speeding is not allowed, which

means that the “norm” (judicially defined) is to keep to the speed limit and those who violate it

may get fined. Still many people drive faster than the limit and much fewer stay under. This

means that speed limits are not representative of what people do in practice. People may of

course prefer to have speed limits, as they know that things will get out of hand otherwise. Thus,

they may opt for joint rules that they will not themselves follow.

Now, what if people indirectly vote when they declare a stance? What will the norm then be? To

be precise, what will the norm be if it equals the average declared opinion in society? We are in

particular interested in whether the norm will then also represent the average of the true opinions

in society.

Assume for simplicity that the true opinions are distributed uniformly between 0 and 1. For the

norm to be representative of the true opinions it will then have to be located at the center, at ½.

Let’s now heuristically investigate whether the norm can be located somewhere else than at the

center (for a complete mathematical investigation see Michaeli and Spiro, 2012).

Assume that the norm is located to the left of the center, say at 0.3. Then the distribution of true

opinions can be divided into two sub-ranges, one that is symmetric around the norm (this is the

range [0,0.6]) and one that lies only at one side of the norm (the range [0.6,1]). Due to the

symmetry of the first sub-range, and due to the fact that only the distance between the true

opinion and the social norm matters, the distribution of the declared stances of the individuals in

this sub-range must also be symmetric around the norm, i.e., the norm would be the average

stance for this sub-range. Thus, the only way for the norm to be the average of all public stances

in society (and not just of those individuals with true opinions in this sub-range) is that the

stances of the individuals in the other sub-range ([0.6,1]) would also be symmetrically distributed

around the norm. Since individuals from this sub-range would never choose a stance lower than

the norm at 0.3 , the only scenario in which the norm is the average of all stances and is located

at 0.3 is that in which all individuals in the sub-range [0.6,1] fully conform (i.e., choose 0.3 as their

public stance). In light of our analysis, this cannot happen in liberal societies, because then small

deviations from the norm bear no social pressure, hence there is no incentive to fully conform.

The significance of this result is that in liberal societies we should expect that if a social norm is

representative of declared stances then it is also representative of true opinions.

What about orthodox societies then, will the norm be representative of true opinions there too?

The answer is not necessarily. In orthodox societies we may get a norm that is located

somewhere towards the edges. The intuition is that, unlike in liberal societies, orthodoxy creates

the possibility of full conformity if society is tight enough. That is, if the social pressure is heavy.

The norm can then be located at any place that guarantees full conformity by those with stances

far from it. This also means that orthodox societies may be history dependent; if a skewed norm

has once been created it may hold “indefinitely”, while liberal societies will over time converge to

a more representative norm. An example of skewed norms is voting and public expressions in

very authoritarian societies like North Korea. The norm there may well be representative of

declared stances; it is the true opinions that the norm presumably does not represent.

4.5. The effect of curvature on a model of peer pressure

We will now divert slightly from the previous model setup and instead give a flavor of other

insights that can be gained by looking at the curvature of preferences. Kandel and Lazear (1992)

have a paper on the effect of peer pressure on the effort exerted by partners who share their

profits. In particular, they investigate the effect of mutually imposed punishments on deviations

from the work norm, in either direction, on the actual effort exerted by partners. They justify this

assumption by stating that “reduced effort means lower income for each of the other partners,

but effort above their own levels may shame them.” By using a quadratic function for the peer

pressure (i.e., a special case of convex pressure), they show that in equilibrium all partners would

choose the same level of effort, and this chosen level equals the level that would be chosen in the

absence of peer pressure. This result gives an insight on the limits of peer pressure in shaping

effort decisions by partners who share their profits.

However, additional insights can be gained by looking at a variation of their convexity

assumptions. That is, assume that peer pressure is concave. Additionally, assume that the cost of

effort is concave too, so that getting out of bed in the morning is very painful, but staying one

additional hour at work once there is less so (Kandel and Lazear assume instead that this cost is

convex). By some back of the envelope calculations, it can be shown that for a partnership of

two there can be equilibrium where only one of the partners exerts effort while the other is idle.

At the same time they will put pressure on each other, where the hard worker will blame the

other for not working enough while the non-worker will complain of the partner working too

much.

What is the intuition behind this result? Well, since the partners are pressuring each other in a

concave manner, there is no point to accommodate the other person just a little bit. Then, given

that her partner already exerts effort, the non-worker may as well keep not working if the

additional gain from hard work is low7. Meanwhile, given that actually she is the sole worker, less

work effort on the side of the hard worker will make for large falls in productivity. So also she is

better off accepting this lot.

Note that such an outcome can emerge even if both partners have exactly the same preferences.

It means that under such conditions creating partnerships is probably not a good idea after all.

Whether the assumption of concave pressure and effort costs is more reasonable than the convex

alternative is hard to say. It is essentially an empirical question. But as long as there is no

empirical evidence in favor of any one of them, both cases may be interesting to analyze

theoretically.

7 This comes from decreasing returns to scale which is a standard assumption in production theory and is also used by Kandel and Lazear (1992).

5. Concluding remarks

The aim of this paper has been to connect the mathematical terms of convexity and concavity to

societal traits, to argue that including these distinctions makes sense from a descriptive point of

view, and finally to demonstrate that additional insights can be gained by analyzing societies that

differ in the way they treat large deviations compared to small deviations from the norm. To this

end the paper is far from exhaustive. It has rather given a flavor of the type of analysis that can

be made, and the type of insights that can be gained. We believe that there is a large amount of

other applications where this mode of analysis is useful. If this paper can somehow spur research

in that direction then our aim has been achieved. Furthermore, we have provided mostly

anecdotal motivation for how the models are constructed and for the ensuing analytical results.

There should be plenty of scope to test these conclusions empirically. As norms and, in particular,

the distinction between true and revealed opinions is hard to observe in most real settings,

possibly the most appropriate way to do so is through experiments.

References

Brock, W.A., & Durlauf, S.N. (2001). Discrete Choice with Social Interactions. Review of Economic

Studies, 68, 235-260.

Clark, A. E., & Oswald, A. J. (1998). Comparison-concave utility and following behaviour in

social and economic settings. Journal of Public Economics, 70, 133-155.

Eguia, J.X. (2011). On the Spatial Representation of Decision Profiles. Economic Theory.

doi:10.1007/s00199-011-0669-8

Gelfand, M.J., et al. (2011). Differences between Tight and Loose Cultures: A 33-Nation Study.

Science, 332, 1100–1104.

Herrmann, B., Thöni, C., & Gächter, S. (2008). Antisocial Punishment across Societies. Science,

319, 1362–1367.

Kandel, E., & Lazear, E. P. (1992). Peer Pressure and Partnerships. The Journal of Political Economy,

100 (4), 801-817.

Kuran, T. (1989). Sparks and prairie fires: A theory of unanticipated political revolution. Public

Choice, 61 (1), 41-74.

Lindbeck, A., Nyberg, S., & Weibull, J. W. (2003). Social norms and Welfare State Dynamics.

Journal of the European Economic Association, 1 (2,3), 533-542.

Michaeli, M., & Spiro, D. (2012). The Distribution of Revealed Preferences under Social Pressure.

Discussion Paper no. 609, the Center for the Study of Rationality.

Figure 1:

Society 1

Society 2

Society 3