POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES

Sean Horan, Martin Osborne and Remzi Sanver

International Economic Review, 2019, vol. 60, issue 4, 1489-1504

Abstract: 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.

Date: 2019
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https://doi.org/10.1111/iere.12394

Related works:
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)
Working Paper: Positively responsive collective choice rules and majority rule: a generalization of May's theorem to many alternatives (2018)
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