A Note on Binary Strategy-Proof Social Choice Functions

Achille Basile, Anna De Simone () and Ciro Tarantino
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Achille Basile: Dipartimento di Scienze Economiche e Statistiche, Università Federico II di Napoli, 80126 Napoli, Italy
Anna De Simone: Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università Federico II di Napoli, 80126 Napoli, Italy
Ciro Tarantino: Dipartimento di Scienze Economiche e Statistiche, Università Federico II di Napoli, 80126 Napoli, Italy

Games, 2022, vol. 13, issue 6, 1-19

Abstract: Let Φ n be the set of the binary strategy-proof social choice functions referred to a group of n voters who are allowed to declare indifference between the alternatives. We provide a recursive way to obtain the set Φ n + 1 from the set Φ n . Computing the cardinalities | Φ n | presents difficulties as the computation of the Dedekind numbers. The latter give the analogous number of social choice functions when only strict preferences are admitted. A comparison is given for the known values. Based on our results, we present a graphical description of the binary strategy-proof social choice functions in the case of three voters.

Keywords: binary social choice functions; strategy-proofness; indifference; monotonicity; Dedekind numbers (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2022
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