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POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES
Author(s) -
Horan Sean,
Osborne Martin J.,
Sanver M. Remzi
Publication year - 2019
Publication title -
international economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.658
H-Index - 86
eISSN - 1468-2354
pISSN - 0020-6598
DOI - 10.1111/iere.12394
Subject(s) - condorcet method , mathematical economics , generalization , independence of irrelevant alternatives , majority rule , set (abstract data type) , social choice theory , mathematics , independence (probability theory) , scoring rule , computer science , voting , artificial intelligence , statistics , law , mathematical analysis , politics , political science , programming language
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.