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Strategy-Proof Social Choice Correspondences and Single Peaked Preferences

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  • Carmelo Rodríguez à lvarez

    (Instituto Complutense de Análisis Económico (ICAE), Universidad Complutense de Madrid (Spain).)

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.

Suggested Citation

  • Carmelo Rodríguez à lvarez, 2025. "Strategy-Proof Social Choice Correspondences and Single Peaked Preferences," Documentos de Trabajo del ICAE 2025-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:2504
    Note: This paper greatly benefited from thorough and exhaustive comments of two anonymous referees and the Associate Editor. Financial support from Agencia Estatal de Innovaci´on, Ministerio de Ciencia, Innovaci´on, y Universidades (Proyectos PID2020-118022GB-100, PID2022-138706NB-100, PID-2023- 151783NB- 100) is gratefully acknowledged.
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    References listed on IDEAS

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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