The Moderating Effect of Instant Runoff Voting

TL;DR

This paper provides a theoretical proof that instant runoff voting tends to elect more moderate candidates than plurality voting in a one-dimensional preference model, supported by computational validation.

Contribution

It introduces a formal theory of exclusion zones in IRV, demonstrating its moderating effect and connecting voting outcomes to geometric and stick-breaking models.

Findings

IRV favors moderate candidates under symmetric voter distributions

Plurality voting can elect extreme candidates, unlike IRV

Theoretical and computational analysis confirms IRV's moderating effect

Abstract

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.