An extension of May’s Theorem to three alternatives

Axiomatizing Minimax voting

Bibliographic Data

ID21470611
AuthorsWesley H Holliday (0000-0001-6054-9052, University of California, Berkeley), Eric Pacuit (0000-0002-0751-9011, University of Maryland, College Park, corresponding author)
Year2026
Volume66
Issue2
Pages395-422
Publication date2026-03-01
Open AccessYes
TypeARTICLE
VenueSocial Choice and Welfare (JOURNAL)
Journal identifiersISSN: 0176-1714 • E-ISSN: 1432-217X
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s00355-025-01598-7
OpenAlexW4411282053
LanguageEN
References cited51

May’s Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May’s axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). In particular, we add two axioms stating that the voting method should mitigate spoiler effects and the so-called strong no show paradox . We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, must choose from among the Minimax winners in all three-alternative elections. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives

Arrow's impossibility theorem · Economics · International political economy · Macroeconomics · Mathematical economics · Minimax · Political science · Public finance · Social choice theory · Voting · Computer Science · Game Theory and Applications · Game Theory and Voting Systems · Law · Logic, Reasoning, and Knowledge · Mathematics

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