Ex post fairness and ex ante fairness in social preferences under risk

We extend the domain of social preferences, which depend on not only one’s outcomes but also vectors of outcomes of all other agents, from deterministic outcome vectors to lotteries over outcome vectors. First, we axiomatically characterize a class of utility functions which satisfies the expected utility theory and reversal of order as far as these two requirements are consistent with ex post fairness and ex ante fairness. Based on this class, we characterize three classes of utility functions which additionally satisfy ex ante fairness, inequality-aversion, and ex post fairness for probability mixture, respectively. Finally, we characterize our main class of utility functions which satisfies these axioms. Saito (2013) also axiomatizes social preferences on lotteries over the outcome vectors which are an extension of the utility functions proposed by Fehr and Schmidt (1999). We characterize a wider class of utility functions which explains heterogeneous attitudes of how much the decision maker cares about ex ante fairness and ex post fairness toward each agent. Moreover, we provide an additional axiom under which our class of utility functions coincides with Saito’s class of utility functions. We reveal that the axiom requires that the attitudes are the same among all the agents.