The probability of casting a pivotal vote in an Instant Runoff Voting election

Abstract

I derive the probability that a vote cast in an Instant Runoff Voting election will change the election winner. I show that there can be two types of pivotal event: direct pivotality, in which a voter causes a candidate to win by ranking them, and indirect pivotality, in which a voter causes one candidate to win by ranking some other candidate. This suggests a reason that voters should be allowed to rank at most four candidates. I identify all pivotal events in terms of the ballots that a voter expects to be cast, and then I compute those probabilities in a common framework for voting games. I provide pseudocode, and work through an example of calculating pivotal probabilities. I then compare the probability of casting a pivotal vote in Instant Runoff Voting to single-vote plurality, and show that the incentives to vote strategically are similar in these two systems.

Sincere, Strategic, or Something Else? The Impact of Ranked-Choice Voting on Voter Decision Making Processes

“…However, according to others, RCV should make voters at least as strategic or more strategic than under FPTP (Baltz, 2022;Dummett, 1984;English House of Commons, 2010;Jesse, 2000;Kilgour et al, 2020;Laslier, 2016;Leonhardt, 2021;Reilly, 2021). Further, researchers find high levels of strategic voting in RCV elections, with approximately twothirds RCV elections analyzed having at least 50% strategic voting (Kilgour et al, 2020).…”

“…Some research argues that there are increased incentives to vote sincerely in RCVover FPTP (Bartholdi & Orlin, 1991;Buisseret & Prato, 2022;Drutman & Strano, 2021;Eggers & Nowacki, 2023;Green-Armytage, 2011;Simmons et al, 2022). Others instead argue that RCV may cause voters to behave more strategically (Baltz, 2022;Dummett, 1984;English House of Commons, 2010;Jesse, 2000;Kilgour et al, 2020;Laslier, 2016;Leonhardt, 2021;Reilly, 2021). These arguments suggest that it is "inherent" to RCV that voters would be strategic with their decision making, or at least RCV creates the opportunity for them to be (Leonhardt, 2021;Reilly, 2021).…”