Can ranked-choice voting elect the least popular candidate?

TL;DR

This paper investigates whether instant runoff voting (IRV) tends to elect the least popular candidate, analyzing theoretical models, simulations, and real election data to assess the frequency of such outcomes.

Contribution

It provides a comprehensive analysis of IRV's tendency to select the weakest candidate across multiple models and empirical data, highlighting conditions under which this occurs.

Findings

IRV can select the weakest candidate, but rarely (under 5% probability).

Polarized electorates increase the chance of weakest candidate victory.

Outcomes are generally rare across most models and conditions.

Abstract

We analyze how frequently instant runoff voting (IRV) selects the weakest (or least popular) candidate in three-candidate elections. We consider four definitions of ``weakest candidate'': the Borda loser, the Bucklin loser, the candidate with the most last-place votes, and the candidate with minimum social utility. We determine the probability that IRV selects the weakest candidate under the impartial anonymous culture and impartial culture models of voter behavior, and use Monte Carlo simulations to estimate these probabilities under several spatial models. We also examine this question empirically using a large dataset of real elections. Our results show that IRV can select the weakest candidates under each of these definitions, but such outcomes are generally rare. Across most models, the probability that IRV elects a given type of weakest candidate is at most 5\%. Larger probabilities arise only when the electorate is extremely polarized.