Positively Responsive Collective Choice Rules and Majority Rule: A Generalization of May’s Theorem to Many Alternatives

Sean Horan, Martin Osborne and Remzi Sanver

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: A collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative x is in the set selected by a collective choice rule for some collective choice problem. Now suppose that x rises above another selected alternative y in some individual’s preferences. If the collective choice rule is “positively responsive”, x remains selected but y is no longer selected. 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 (May 1952). If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case 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. Further, no rule satisfies the four conditions for the domain of all preference relations.

Keywords: Majority rule; Condorcet winner; May's theorem; positive responsiveness; Nash independence (search for similar items in EconPapers)
JEL-codes: D70 D71 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2018
New Economics Papers: this item is included in nep-cdm and nep-mic
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES (2019)
Working Paper: Positively responsive collective choice rules and majority rule: A generalization of May’s theorem to many alternatives (2019)
Working Paper: Positively responsive collective choice rules and majority rule: A generalization of May's theorem to many alternatives (2018)
Working Paper: Positively responsive collective choice rules and majority rule: a generalization of May's theorem to many alternatives (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montec:03-2018

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