A Theory of Status-Mediated Inequity Aversion

Abstract

We introduce a new social utility function which relates inequity aversion to social status, effort, and ability. The basic idea is as follows: Actors do not suffer from inequality but from inequity relative to a fair share that reflects some normative orientation the actors have internalized. In this regard we advocate the rule of proportionality which states that rewards should be proportional to some standard of comparison. We apply this social utility function to various games from non-cooperative and cooperative game theory and interpret the results with respect to the effects of social status on behavioral outcomes.

Keywords:

• behavioral economics
• fairness
• inequity aversion
• status

We thank André Casajus, Frank Huettner, Thomas Voss, two anonymous referees, and the editor for critical comments on earlier drafts of this paper. Thanks to the participants of the “Seminar on Rational Choice Sociology: Theoretical Contributions and Empirical Applications” at the Venice International University, December, 3–7, 2007 for valuable comments on the involved topics. Financial support from the German Research Foundation (DFG LI 1730/2-1) is gratefully acknowledged.

Notes

¹A reference group is a group of people that might be used by an individual for comparisons with regard to relevant characteristics such as status, effort, ability, or payoffs. There is a long research tradition in social psychology and sociology on the determinants of reference groups and related processes such as social comparisons and relative deprivation (e.g., Stouffer, 1949; Festinger, 1954; Davis, 1959; Adams, 1963; Runciman, 1966; Merton, 1968; Pollis, 1968). However, it is an empirical question what determines a reference group from an individual's point of view. In the following, we study social interactions as they are influenced by social comparisons inside given reference groups and do not deal with the question of reference-group formation.

²For convenience, we typically refer to s as a measure of social status. However, recall from the introduction that s might actually be a measure of effort or ability. The interpretation of this parameter depends on the specific application. With regard to social status it has to be mentioned that status characteristics can be measured by quantitative variables (cardinal or ordinal) such as wealth and beauty and qualitative variables (binary or polytomous) such as gender and ethnicity (cf. Jasso, 2001). Although qualitative variables may not have an inherent status-related ordering such an ordering can often be assumed (e.g., in some societies women have a lower status compared to men). Note that the application of the rule of proportionality requires a standard of comparison (parameter s) that is measured on a ratio scale which is unique up to a linear transformation. Nevertheless, the SMIA-utility function can also be used in case of an ordinal status variable by determining the outcomes of a game for the whole range of order-preserving vectors s. Of course, these procedure leads to less sharp predictions compared to predictions based on a ratio-scaled status variable. However, it is quite intuitive that people' normative orientations relating material outcomes with status are more ambiguous if confronted with a mere ordering instead of a metric status variable.

³The word “almost” refers to the fact that even if the reference group consists of two players with equal status, compared with the F/S-function, the SMIA-utility function allows for a more differentiated weighting of the social disutility terms.

⁴For the purpose of parsimony, we use the notion “status orientation of actor i” for both α _i,1 + β _i,1 and α _i,2 + β _i,2. Typically, it refers to the former sum.

⁵Actually, (V(α, β, s), d(α, β, s)) has to satisfy some technical properties such as convexity of V(α, β, s) to qualify as a primitive of a bargaining problem. In the following, we assume that the inequalities , , and

hold. The latter inequality characterizes the convexity of the induced bargaining set, V(α, β, s), given the former two inequalities. These two inequalities in turn are well-known from our discussion of the shape of indifference curves. They assure that the branch of the indifference curve where some actor obtains more than his status-fair share has a nonpositive slope. If these assumptions hold, any induced bargaining problem, (V(α, β, s), d(α, β, s)), satisfies the requirements for the application of the Nash bargaining solution.

⁶The bargaining solution ϕ satisfies the axiom of independence of irrelevant alternatives if and only if, for any two bargaining problems (V, d) and (V′, d), we have

⁷In the remainder of the paper we employ the following standard notation: Given some strategy profile a, the vector denotes the strategy profile where player i uses his strategy instead of a _i and all other players use their strategies according to a.