Can ranked-choice voting elect the least popular candidate?

2026-02-24

AI Summary

This study investigates whether Instant-Runoff Voting (IRV) can elect the least preferred candidate in three-candidate elections. Through theoretical analysis and Monte Carlo simulations—employing the Impartial Anonymous Culture model, the Impartial Culture model, and spatial models—and supplemented by extensive real-world election data, the paper provides the first systematic assessment of the probability that IRV selects one of four types of “weakest” candidates under diverse voter behavior assumptions. The findings confirm that IRV does carry a non-zero risk of electing the least popular candidate, though this occurs with a probability typically below 5%. The likelihood rises significantly only under highly polarized voter distributions, thereby offering quantitative evidence supporting the robustness of IRV in most practical scenarios.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• ranked-choice voting
• instant runoff voting
• least popular candidate
• weakest candidate
• election outcomes

Innovation

• instant runoff voting
• weakest candidate
• social choice theory
• Monte Carlo simulation
• empirical election analysis