The Margin of Victory in Ranked-Choice Voting

The margin of victory (MOV) is one of the most important and well-established metrics in political science that quantifies the closeness of electoral contests. Despite its intuitive nature in first-past-the-post (FPTP)---half the vote-share difference between the winner and the runner-up, studying the MOV gets challenging under ranked-choice voting (RCV), where voters can vote by ranking multiple candidates and determine the majority winner via a series of candidate elimination and vote transfer. This paper discusses conceptual and computational challenges in studying the MOV in RCV. Utilizing works in computer science, we provide a generalized definition of the MOV as the minimum number of votes that need to be modified to change the election winner. Moreover, we construct an RCV vote margin dataset by providing the first large-scale computation of the MOV under RCV based on the cast vote records from 444 RCV elections and an efficient optimization algorithm that explores the vast space of counterfactual electoral results. We illustrate the utility of our data by studying electoral competitiveness in RCV elections from 2007 to 2022. We also discuss and illustrate the advantages of using RCV margins in the sharp regression-discontinuity design. Our results allow social scientists to study various aspects of RCV.