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

TL;DR

This paper extends May's Theorem to three alternatives by adding axioms that ensure the voting method mitigates spoiler effects and avoids the no show paradox, ultimately characterizing Minimax voting.

Contribution

It introduces new axioms that uniquely determine Minimax voting for three alternatives, extending May's Theorem beyond two options.

Findings

Minimax is uniquely characterized under the new axioms for three alternatives.

The axioms distinguish Minimax from other voting methods for more than three options.

The approach mitigates spoiler effects and avoids the strong no show paradox.

Abstract

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.