Strategy-Proof Social Choice Correspondences and Single Peaked Preferences

Abstract

We examine social choice correspondences (SCCs) -mappings from preference profiles to sets of alternatives- that satisfy strategy-proofness and unanimity when individuals are endowed with single-peaked preferences over alternatives, preferences over sets are consistent with Expected Utility Theory, uniform prior probabilities, and Bayesian Updating. Leveraging the relation between SCCs and probabilistic decision schemes -mappings from preference profiles to lotteries over alternatives-we extend the results by Ingalagavi and Sadhukhan (2023, Journal of Mathematical Economics 109, 102912). In one-dimensional spaces of alternatives, only the union of two single-valued strategy-proof SCCs satisfy strategy-proofness and unanimity. In multidimensional convex spaces of alternatives, only unions of up to two dictatorships satisfy both properties.