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] 将多数投票在两种备选方案上的应用刻画为满足若干简单公理的唯一偏好投票方法。本文证明，通过在梅公理的基础上增加一些理想的公理，我们可以唯一地确定如何在三种备选方案上进行投票（暂不考虑平局处理）。具体而言，我们增加了两个公理，要求投票方法应能缓解“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，表明任何满足我们扩展公理集（包括一些弱同质性和保序性公理）的偏好投票方法，在所有三备选方案选举中都必须从极小极大获胜者中选择。当应用于多于三种备选方案时，我们的公理集还能将极小极大法与其他已知的、在三备选方案下与极小极大法一致或对其细化的投票方法区分开来。