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. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid 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, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways.

翻译：梅定理[K. O. May, Econometrica 20 (1952) 680-684]刻画了二元备选方案中的多数投票作为满足若干简单公理的唯一偏好投票方法。本文通过向梅公理体系补充若干合理公理，可唯一确定三元备选方案的投票规则。具体而言，我们新增了两条公理：投票方法应缓解"搅局者效应"并避免所谓的"强缺席悖论"。我们证明了一个定理：任何满足我们扩充公理集（包含弱同质性公理与保存公理）的偏好投票方法，在所有三选方案选举中均与最小最大投票一致，除了可能在少数概率极低的临界选举中存在平局及不同破平方式的情况。