POSITIVELY RESPONSIVE COLLECTIVE CHOICE RULES AND MAJORITY RULE: A GENERALIZATION OF MAY'S THEOREM TO MANY ALTERNATIVES |
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| Authors: | Sean Horan Martin J Osborne M Remzi Sanver |
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| Institution: | 1. Université de Montréal and CIREQ, Canada;2. University of Toronto, CanadaPlease address correspondence to: Martin J. Osborne, Department of Economics, University of Toronto, 150 St. George Street, Toronto, ON M5S 3G7, Canada (CA). E‐mail: .;3. Université Paris‐Dauphine, Université PSL, CNRS, LAMSADE, France;4. We thank Salvador Barberà, Jean‐Pierre Beno?t, Felix Brandt, Markus Brill, Donald E. Campbell, Christopher Dobronyi, John Duggan, Justin Kruger, Hervé Moulin, Matías Nú?ez, and Maurice Salles for discussions and comments. We are grateful also to a referee and the editor for suggestions that led us to improve the article. In particular, they pushed us to significantly tighten the results. Horan's work was partly supported by FRQSC. Sanver's work was partly supported by the projects ANR‐14‐CE24‐0007‐01 “CoCoRICo‐CoDec” and IDEX 5. ANR‐10‐IDEX‐0001‐02 PSL* “MIFID.” |
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| 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. |
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