The Margin of Victory in Ranked-Choice Voting

• In Event: Electoral Systems, Parties, and Representation

Abstract

The margin of victory is one of the most important and well-established concepts in political science that quantifies the closeness of electoral contests. Despite its intuitive nature in first-past-the-post (FPTP)––the vote-share difference between the winner and the runner-up––computing the margin of victory has been known to be both conceptually and computationally challenging in alternative electoral systems. The problem is further exacerbated under ranked-choice voting (RCV), where voters can vote by ranking multiple candidates, and therefore, the notion of the “winner” and the “runner-up” becomes far less clear than under FPTP. We provide the first large-scale computation and analysis of the margin of victory under RCV, leveraging cast vote records from 444 RCV elections in the U.S. along with an efficient optimization algorithm that explores the vast space of counterfactual electoral results. Our publicly available results allow social scientists to study various aspects of RCV. To illustrate, we study electoral competitiveness and its determinants in 2007-2022, finding that the number of candidates negatively affects the margin of victory. Moreover, we also examine incumbency advantage in RCV by integrating a regression-discontinuity design with our results. We conclude by discussing additional applications and theoretical implications for future research.

Authors

• Yuki Atsusaka, University of Houston

• Agustin Vallejo, University of Houston

• Silviya Valeva, Saint Joseph's University