Strategy-Proof Social Choice Correspondences and Single Peaked Preferences

Carmelo Rodríguez à Lvarez ()
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Carmelo Rodríguez à Lvarez: Instituto Complutense de Análisis Económico (ICAE), Universidad Complutense de Madrid (Spain).

No 2025-04, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

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.

Keywords: Strategy-Proofness; Single-Peaked Preferences; Union Min-Max Social Choice Correspondences. (search for similar items in EconPapers)
JEL-codes: C71 C78 D71 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2025
New Economics Papers: this item is included in nep-des
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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