Axioms for Defeat in Democratic Elections

TL;DR

This paper introduces six axioms for defining candidate defeat in democratic elections, showing that the Split Cycle method uniquely satisfies these axioms and addressing Arrow's Impossibility Theorem.

Contribution

It formalizes axioms for electoral defeat, introduces Coherent IIA as a weakening of IIA, and characterizes Split Cycle as the unique method satisfying these axioms.

Findings

Split Cycle uniquely satisfies the six axioms.

Split Cycle is the most resolute defeat method under these axioms.

Split Cycle avoids Arrow's Impossibility Theorem constraints.

Abstract

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem and related impossibility results.