Strategy-Proof Social Choice Correspondences for Conditional Expected Utility Maximizers *

Abstract

We study social choice functions that take preferences over sets as input, when voters evaluate sets according to conditional expected utility obtained from Bayesian updating of a common prior.While under a uniform prior both dictatorial and bidictatorial rules satisfy strategy-proofness and unanimity, we show that this multiplicity is a knife-edge case: for every non-uniform prior, dictatorship is the unique rule satisfying these properties. The argument links set-valued rules to random dictatorship and shows that the probability ratios imposed by non-uniform updating are incompatible with combining the top choices of multiple voters. We also characterize the admissible rules when voters hold heterogeneous subjective priors.