Susceptibility to strategic voting: a comparison of plurality and instant-runoff elections

Advocates of the instant-runoff voting system (IRV, a.k.a. ranked-choice voting) often argue that it is less susceptible to strategic voting than plurality. Is this true? More generally, how should we define and measure a voting system’s susceptibility to strategic voting? Previous research in this area is unsatisfying, largely because it ignores the uncertainty voters face when they vote. We introduce a better approach and use it to show that IRV elections are far less susceptible to strategic voting than plurality elections given preference data from 160 election surveys and realistic assumptions about uncertainty and voter behavior. The difference arises partly because, as other voters vote more strategically, strategic voting incentives tend to increase in plurality but decrease in IRV. The methods we introduce can be used to study other properties of voting systems when voters are strategic. This version: September 9, 2020. Thanks to Steve Callander, Gary Cox, Justin Grimmer, Matias Iaryczower, Paul Klemperer, Dimitri Landa, Gregory Martin, David Myatt, Karine van der Straeten, and seminar audiences at Trinity College Dublin, the Toulouse School of Economics, the Democracy and Polarization Lab at Stanford University, and the ECPR Standing Group on Strategic Interactions for valuable feedback. Thanks to Mats Ahrenshop, Tak Huen Chau, and Tom Robinson for research assistance. Some of the computing for this project was performed on the Sherlock cluster. We would like to thank Stanford University and the Stanford Research Computing Center for providing computational resources and support that contributed to these research results. Earlier versions were circulated starting June 2019 under the title “Comparing strategic voting incentives in plurality and instant-runoff elections”. †Nuffield College and Department of Politics and International Relations, University of Oxford, UK. email: andrew.eggers@nuffield.ox. ac.uk †Stanford University. email: tnowacki@stanford.edu In recent years, the instant-runoff voting system (IRV) has been a popular reform proposal in several countries. In IRV (also known by several other terms, including ranked-choice voting and the alternative vote2), voters rank the candidates and the winner is determined by successively eliminating less-popular candidates. Large-scale referendums to replace plurality voting with IRV failed in the UK in 2011 and British Columbia in 2018 but succeeded in San Francisco in 2002, Maine in 2016, and New York City in 2019. According to its advocates, IRV chooses winners with broader support, discourages negative campaigning, and minimizes strategic voting, among other benefits.3 Although many aspects of IRV elections have now been studied (e.g. Farrell and McAllister, 2006; Fraenkel and Grofman, 2006; Horowitz, 2006; McDaniel, 2016; John, Smith and Zack, 2018; McDaniel, 2018), previous research leaves some important questions unanswered. Consider IRV’s resistance to strategic voting, which is sometimes offered as its most important advantage over plurality.4 When a candidate is eliminated in IRV, ballots ranking that candidate first are effectively transferred to the next-ranked candidate. This suggests that the incentive to abandon hopeless candidates is lower in IRV than in plurality. But IRV allows for other types of strategic voting, some rather perverse: for example, one might help elect one’s preferred candidate by ranking one’s least-preferred candidate first (e.g. Fishburn and Brams, 1983; Dummett, 1984). It remains an open question whether, for realistic assumptions about the circumstances voters face in real elections, the opportunities for strategic voting are (as advocates claim) more constrained in IRV than in plurality. In this paper, we seek to rigorously assess the common claim that IRV is less susceptible to strategic voting than plurality. We define a voting system’s susceptibility to strategic voting as the expected benefit to the voter from voting strategically (i.e. casting the expected-utility maximizing vote) instead of voting sincerely (i.e. simply reporting the sincere preference). To IRV’s other names include ranked-choice voting (RCV), the alternative vote (AV), preferential voting, singletransferable vote (STV), and the Hare system. We use instant-runoff voting because the term is widely used and more descriptive than “ranked-choice voting” or “the alternative vote”. See e.g. FairVote’s “Ranked Choice Voting 101” at https://www.fairvote. org/rcv#rcvbenefits, visited 1 August 2020. For example, the first argument offered in favor of IRV by UK Deputy Prime Minister Nick Clegg in parliamentary testimony in advance of the 2011 UK referendum was that IRV “stops people from voting tactically and second-guessing how everybody else will vote in their area. ” See “The Coalition Government’s programme of political and constitutional reform: Oral and written evidence”, 15 July 2010, HC 358-i, published 22 October 2010 (link).