New characterizations of strategy-proofness under single-peakedness

• Published in: Mathematical programming Vol. 203; no. 1-2; pp. 207 - 238
• Main Authors: Jennings, Andrew B., Laraki, Rida, Puppe, Clemens, Varloot, Estelle M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Analysis; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Computer Science; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Participation; Quantitative Finance; Representations; Theoretical; Voting; Participation; Proportionality; 91B12 Voting Theory; Single-peaked preferences; Voting; Linear/uniform median; Consistency; 91B14 Social Choice; Strategy-proofness; Mathematics Subject Classification 91B12 Voting Theory • 91B14 Social Choice
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-023-02010-x

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.