Instant Runoff Voting and the Reinforcement Paradox

TL;DR

This paper investigates the reinforcement paradox in instant runoff voting, showing IRV's high susceptibility to this paradox through theoretical conditions, simulations, and real-world data analysis.

Contribution

It provides necessary and sufficient conditions for the reinforcement paradox in three-candidate IRV elections and evaluates its frequency via simulations and empirical data.

Findings

IRV is highly susceptible to the reinforcement paradox in three-candidate elections.

Necessary and sufficient conditions for the paradox are established.

Simulations and real-world data show the paradox occurs with notable frequency.

Abstract

We analyze the susceptibility of instant runoff voting (IRV) to a lesser-studied paradox known as a \emph{reinforcement paradox}, which occurs when candidate $X$ wins under IRV in two distinct elections but $X$ loses in the combined election formed by merging the ballots from the two elections. For three-candidate IRV elections we provide necessary and sufficient conditions under which there exists a partition of the ballot set into two sets of ballots such that a given losing candidate wins each of the sub-elections. Applying these conditions, we use Monte Carlo simulations to estimate the frequency with which such partitions exist under various models of voter behavior. We also analyze the frequency with which the paradox occurs in a large dataset of real-world ranked-choice elections to provide empirical probabilities. Our general finding is that IRV is highly susceptible to this paradox in three-candidate elections.