How much of an incentive to vote strategically is there in instant runoff voting?

The instant-runoff voting system (IRV) has recently been a popular reform proposal in several countries. In IRV (also known as ranked-choice voting and the alternative vote), voters rank the candidates and the winner is determined by successively eliminating less-popular candidates. IRV was on the ballot in referendums held in the United Kingdom and British Columbia and is currently in use in federal elections in Australia, congressional elections in Maine and Alaska and numerous city elections across the US—including New York City and San Francisco. 

In this paper we aim to rigorously assess the common claim that IRV is less susceptible to strategic voting than plurality; to do so, we develop concepts and tools that can help address other questions about voting systems and strategic voting.

Strategic voting in plurality and instant-runoff voting

Advocates of IRV claim that it permits voters to cast their ballot in line with their sincere preferences. This stands in contrast to plurality elections, where widespread strategic incentives in multi-candidate elections are a well-known phenomenon: if my preference ordering among candidates is A > B > C, but only B and C have a realistic chance of winning, I have an incentive to abandon A and vote for B in the hope of increasing the odds of B winning against C. In IRV, on the other hand, there may be no harm in ranking A first: if A gets eliminated, my vote transfers to B and my second preference still contributes to the probability of B winning against C in the final round.

However, we know from social choice theory that no (non-dictatorial) electoral system is fully immune to strategic voting. That is, there exist some situations—even under IRV—in which I am better off voting insincerely. For instance, if A and B are equally likely to advance to the runoff, but only B has a chance of beating C in the final round (e.g. by way of being the centrist candidate), I may be better off casting my first preference for B with the intention of avoiding the worst outcome (C being elected). It remains an open question how prevalent and how strong these types of incentives are under IRV.

Measuring Strategic Voting Incentives

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 measure susceptibility to strategic voting in realistic scenarios, we start with preference data from 160 election surveys (a total of around 220,000 voters); we then compute, for each voter in each survey, whether and to what extent the voter would benefit from voting strategically given a range of assumptions about how well the voter is able to anticipate the outcome (i.e. uncertainty) and how widespread strategic voting is among other voters in the survey. By doing this both for plurality and for IRV and averaging across surveys, we generate measures of each voting system’s susceptibility to strategic voting. 

Our new method to measure strategic voting incentives contributes two innovations. First, to our knowledge we are the first to assess susceptibility to strategic voting while taking into account the uncertainty that voters face at the time they decide how to vote. Second, we model voters’ beliefs in a way that accounts for strategic behavior by other voters.

Results

Our analysis shows that, for a wide range of assumptions, IRV is less susceptible to strategic voting on average than plurality voting, although the opportunities to benefit from strategic voting in IRV may be more widespread than previously recognized. If we assume that voters have relatively precise beliefs about election outcomes and strategic voting is not widespread, the average gain in expected utility from voting strategically (rather than always sincerely) is about five times higher in plurality compared to IRV; that gap becomes wider when we assume that voters have less precise beliefs about election outcomes and strategic voting is more widespread.

We also find evidence that informed voters might find ample opportunities for strategic voting in IRV: when beliefs are precise and other voters vote sincerely, the proportion of voters who benefit from strategic voting is higher on average in IRV, and much higher for some preference profiles (even though the benefit from voting strategically is smaller than in plurality). But when beliefs become less precise, or when other voters vote more strategically, these opportunities for strategic voting tend to disappear. Our baseline analysis holds fixed voter preference distributions as the voting system changes, but in extensions we show that the main conclusions are robust to allowing the voting system to affect preferences or the number of parties competing.

Conclusion

We introduced a new approach to evaluating voting systems’ susceptibility to strategic voting that addresses important shortcomings in previous work—in particular, our approach takes into account ex ante uncertainty about the election result and relaxes the assumption that others vote sincerely. While we focus on the comparison between IRV and plurality given the prominence of IRV in many recent electoral reform proposals, our method can be extended to study and compare other electoral systems, too.