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Positively responsive collective choice rules and majority rule: A generalization of May’s theorem to many alternatives,

Horan, Sean; Osborne, Martin; Sanver, Remzi (2019), Positively responsive collective choice rules and majority rule: A generalization of May’s theorem to many alternatives,, International Economic Review, 60, 4, p. 1489-1504. 10.1111/iere.12394

Type
Article accepté pour publication ou publié
Date
2019
Journal name
International Economic Review
Volume
60
Number
4
Publisher
Wiley
Pages
1489-1504
Publication identifier
Metadata
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Author(s)
Horan, Sean
Osborne, Martin
Sanver, Remzi
Abstract (EN)
May's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.