Envy and Altruism: Contrasting Bivariate and Univariate Prospect Preferences

• Published date: 01 April 2017
• DOI: http://doi.org/10.1111/sjoe.12168
• Author: Guy Kaplanski,Haim Levy
• Date: 01 April 2017

Scand. J. of Economics 119(2), 457–483, 2017

DOI: 10.1111/sjoe.12168

Envy and Altruism: Contrasting Bivariate

and Univariate Prospect Preferences∗

Guy Kaplanski

Bar-Ilan University, Ramat Gan 52900, Israel

guykap@biu.ac.il

Haim Levy

The Hebrew University, Jerusalem 91905, Israel

mshlevy@mscc.huji.ac.il

Abstract

We compare prospect ordering with and without envy and altruism. We find that envy

can induce a violation of the univariate first-degree stochastic dominance (FSD), and thus

a violation of the classic expected utility monotonicity axiom. Surprisingly, altruism can

also violate FSD preferences. The intuitive explanation of the result in the case of altruism

hinges on the sign of the mixed derivative of the bivariate preference: the individual might

prefer a certain correlation between her wealth and her peer group’s wealth, and is therefore

willing to violate FSD as long as the outcomes of the two parties are ordered according to

her preferences. When investments are considered, envy and altruism can distort not only

preferences but also actual choices.

Keywords: Efficient set; expected money burning; social presence; stochastic dominance

JEL classification:D64; D81; G11

I. Introduction

The expected utility paradigm of von Neumann and Morgenstern (1953)

assumes a self-interested individual who acts to maximize the expected

utility defined by her wealth. In this study, we compare prospect ordering

(preferences) according to this classic paradigm to prospect ordering in

which both the individual’s wealth and the peer group’s aggregate wealth

affect preferences. Thus, we explore the possible economic distortion in-

duced by envy or altruism, when the distortion is measured relative to the

preference in the self-interest univariate expected utility model. In the clas-

sic paradigm, we have a univariate preference, as the individual’s utility is

affected by a single factor – the individual’s wealth. When the individual’s

utility is affected by two factors – the individual’s wealth and the peer

∗The authors acknowledge the helpful comments and suggestions of two anonymous referees.

We thank the Kruger Center for the Finance of the Hebrew University for its financial

support.

CThe editors of The Scandinavian Journal of Economics 2015.

458 Envy and altruism

group’s wealth – we have a bivariate preference. In this study, we compare

the univariate and bivariate preference frameworks, while focusing on the

possible economic distortion due to envy or altruism on preference ordering

and choices.

A prospect represents a distribution (univariate or bivariate) of future

outcomes. We define a univariate prospect as a prospect that depends solely

on the individual’s future wealth, and a bivariate prospect as a prospect that

depends on both the individual’s wealth and the wealth of the peer group.

Generally, economic models that consider the bivariate expected utility

model incorporate the effect of the peer group’s wealth by employing a

specific bivariate preference, so the results are limited.1In this study, we

employ the first-degree stochastic dominance (FSD) approach to compare

the univariate and bivariate preference orderings. As FSD relies only on

partial information on preferences, the main results of this study are general

and do not hinge on specific preferences. Nevertheless, the bivariate case

partial ordering depends on the sign of the mixed derivative. Therefore, we

characterize the partial ordering of all prospects with partial information as

regards envy and altruism, as well as the mixed derivative, and we explore

the possible economic distortion of envy and altruism.

As envy and altruism can have different meanings, for simplicity’s sake

in the discussion we refer to envy and altruism as general attitudes in

the context of bivariate preferences. Thus, envy and altruism describe

negative and positive attitudes towards the peer group’s wealth, respec-

tively, regardless of the source of those attitudes. Whenever one’s welfare

decreases with an increase in one’s peer group’s wealth, we refer to one’s

attitude as envy, and whenever one’s welfare increases, we refer to one’s

attitude as altruism. These definitions are consistent with the more general

social preference approach and, in particular, with the empirical evidence

on self-centered inequality aversion (i.e., when one cares about inequity in

one’s own payoff relative to the payoffs of others). This is equivalent to

being envious when one’s wealth is below the peer group’s wealth, and to

being altruistic when it is above the peer’s group wealth. As the analy-

sis is forward-looking and the outcomes are random variables, our results

relate to the case of social preferences under risk (Bolton et al., 2005)

and, in particular, to inequality in expected outcomes rather than in actual

outcomes (Trautmann, 2009).

The analysis distinguishes between preferences and actual choices. In

the simpler scenario, the individual’s choice has no effect on the peer

group’s wealth distribution. This scenario includes the important case of

1The most common functions employed in the literature are the power utility function and the

additive preference, where the effect of the peer group is additive and the mixed derivative

is always zero.

CThe editors of The Scandinavian Journal of Economics 2015.