New characterizations of strategy-proofness under single-peakedness

Andrew Jennings, Rida Laraki, Clemens Puppe and Estelle Varloot ()
Additional contact information
Andrew Jennings: Public Integrity Foundation, Phoenix
Rida Laraki: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, University of Liverpool, UM6P - Université Mohammed VI Polytechnique = Mohammed VI Polytechnic University [Ben Guerir]
Clemens Puppe: TH - Universität Karlsruhe, HSE - Higher School of Economics [Perm] - MAI - National research university
Estelle Varloot: University of Liverpool

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Abstract: We provide novel representations of strategy-proof voting rules applicable when voters have uni-dimensional single-peaked preferences. In particular, we introduce a 'grading curve' representation which is particularly useful when introducing variable electorates. Our analysis recovers, links and unifies existing results in the literature, and provides new characterizations when strategy-proofness is combined with other desirable properties such as ordinality, participation, consistency, and proportionality. Finally, the new representations are used to compute the strategy-proof methods that maximize the ex-ante social welfare for the L 2-norm and a uniform prior. The resulting strategy-proof welfare maximizer is the linear median (or 'uniform median'), that we also characterize as the unique proportional strategy-proof voting rule.

Keywords: Mathematics; Subject; Classification; 91B12; Voting; Theory; •; 91B14; Social; Choice (search for similar items in EconPapers)
Date: 2023-08-28
Note: View the original document on HAL open archive server: https://hal.science/hal-04304821v1
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Citations: View citations in EconPapers (1)

Published in Mathematical Programming, 2023, ⟨10.1007/s10107-023-02010-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04304821

DOI: 10.1007/s10107-023-02010-x

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