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 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, 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.

翻译：梅定理[K. O. May, Econometrica 20 (1952) 680-684]将多数投票刻画为满足若干简单公理的唯一偏好投票方法，适用于两个候选方案。本文证明，通过在梅公理基础上增加若干理想公理，我们能够唯一确定三候选方案的投票规则（不考虑平局处理）。特别地，我们引入两条公理：投票方法应缓解“搅局者效应”并避免所谓的“强不参与悖论”。我们证明了一个定理：任何满足我们扩展公理体系（包含弱齐次性与保序性公理）的偏好投票方法，在所有三候选方案选举中都必须从极小极大获胜者中选出结果。当应用于超过三个候选方案时，我们的公理体系还能将极小极大方法与其他已知投票方法区分开来——这些方法在三候选方案场景中与极小极大方法重合或为其精细化扩展。