Egalitarianism under Incomplete

The paper aims at extending the egalitarian principle to environments with asymmetric information. It starts by emphasizing the accrued difficulty of deriving axiomatic results under incomplete information, given that incentive constraints and asymmetric beliefs restrict the shape of the feasible sets of interim utilities. Particularly, natural axioms of anonymity, efficiency and monotonicity are shown to be incompatible on the class of quasi-linear social choice problems. Then, a natural adaptation of Kalai’s (Econometrica, 1977, Theorem 1) axioms are shown to lead to a partial characterization of a natural extention of the lex-min solution. Next, I prove that, in each social choice problem, there is a unique way of rescaling the participants’ interim utilities so as to make this solution compatible with ex-ante utilitarianism. These two criteria coincides in the rescaled utilities exactly at the incentive efficient mechanisms that maximize Harsanyi and Selten’s (Management Science, 1972) weighted Nash product. These concepts are illustrated on classical examples of profit-sharing, public good production and bilateral trade. The richness of the topic of social choice under incomplete information is illustrated by considering two alternative extensions of the egalitarian principle – one based on an idea of equity from the point of view of the individuals themselves (given their private information) instead of an uninformed third party (social planner or arbitrator), and another notion based on the idea of procedural justice. ∗The paper beneficiated from stimulating discussions with David Perez-Castrillo and David Wettstein. Financial support from the National Science Foundation (grant SES-0851210) is gratefully acknowledged. †Department of Economics, Brown University. Email: [email protected]