We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).
Strategy-proofness, Lexicographically separable preferences, Generalized random dictatorship
Economics | Economic Theory
Journal of Mathematical Economics
CHATTERJI, Shurojit; ROY, Souvik; and SEN, Arunava.
The Structure of Strategy-Proof Random Social Choice Functions over Product Domains and Lexicographically Separable Preferences. (2012). Journal of Mathematical Economics. 48, (6), 353-366. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1405
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