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May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizesmajority voting on two alternatives as the unique preferential voting methodsatisfying several simple axioms. Here we show that by adding some desirableaxioms to May's axioms, we can uniquely determine how to vote on threealternatives. In particular, we add two axioms stating that the voting methodshould mitigate spoiler effects and avoid the so-called strong no show paradox.We prove a theorem stating that any preferential voting method satisfying ourenlarged set of axioms, which includes some weak homogeneity and preservationaxioms, agrees with Minimax voting in all three-alternative elections, exceptperhaps in some improbable knife-edged elections in which ties may arise and bebroken in different ways.

An extension of May's Theorem to three alternatives: axiomatizing Minimax voting