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The Probability of Casting a Pivotal Vote in an Instant Runoff Voting Election

Published online by Cambridge University Press:  27 January 2025

Samuel Baltz Open the ORCID record for Samuel Baltz [Opens in a new window]
Samuel Baltz*
Affiliation:
Political Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
*
E-mail: [email protected]
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Abstract

If instant runoff voting (IRV) mitigates strategic voting, is that because the rules of the system mechanically reduce strategic opportunities, or because of other more indirect effects? In single-vote plurality elections, a voter can be pivotal if adding one vote to a candidate would cause that candidate to win. In IRV, it is more complicated to identify when one voter can be pivotal. This letter derives all the ways that a single ballot can change the result of an IRV election, for any number of candidates and voters. I obtain an expression for the probability of casting a pivotal vote in IRV by phrasing the probability that any pivotal event occurs as a function of all the rankings cast by other voters. This expression facilitates modeling vote choice in IRV, and enables the estimation of voters’ strategic opportunities in IRV contests between any number of candidates. I present some illustrative simulations estimating pivotal probabilities in both IRV and Single-Member District Plurality for stylized electorates with identical preference structures. These simulations produce similar estimated pivotal probabilities in the two systems, suggesting that these systems may provide similar opportunities to strategically cast a decisive vote.

Keywords

Ranked Choice VotingInstant Runoff Votingpivotal probabilitystrategic votingelectoral systems
Type
Letter
Information
Political Analysis , First View , pp. 1 - 9
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Society for Political Methodology

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Footnotes

Edited by: Jeff Gill

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