Strategy-proof social choice correspondences for conditional expected utility maximizers

Abstract

We analyze strategy-proof rules that select sets of alternatives based on voters' preferences over those sets. Sets of alternatives represent social choices pending a final resolution and voters are expected utility maximizers that assign probabilities to alternatives within each set using Bayesian updating from a common prior probability assessment. If there are at least three alternatives, then, for generic priors, only dictatorial rules are strategy-proof and unanimous. However, when the prior probability assessment assigns equal probability to all alternatives, strategy-proofness also permits rules that select the set of best elements determined by two fixed voters.