Bayesian Social Aggregation With Non-Archimedean Utilities and Probabilities

Abstract

We consider social decisions under uncertainty. Given certain richness conditions, we show that the ex ante social preference order satisfies a Pareto axiom with respect to ex ante individual preferences, along with an axiom of Statewise Dominance, if and only if all agents admit subjective expected utility (SEU) representations with the same beliefs, and furthermore the social planner is utilitarian (i.e. the social utility function is the sum of the individual utility functions). In these SEU representations, the utility functions take values in an ordered abelian group, and probabilities are represented by order-preserving automorphisms of this group. This group may be non-Archimedean; this allows the SEU representations to encode lexicographical preferences and/or infinitesimal probabilities. Relative to earlier results in Bayesian social aggregation, our framework is minimal, with a finite set of states of nature, no structure on the set of social outcomes, and preferences not assumed to be continuous.

JEL Classification: D70, D81