Ballot Length in Instant Runoff Voting

Abstract

Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than individual votes. In practice, municipalities often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k − 1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide constructions matching these bounds. Additionally, we fully characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections and that longer ballots can favor particular candidates. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.

Ballot Length in Instant Runoff Voting

“…. , 40 with initially full ballots (the heatmaps were qualitatively identical for partial ballots (Tomlinson, Ugander, and Kleinberg 2022)). For general preferences, the probability of selecting the full-ballot IRV winner increases smoothly as ballot length increases.…”

“…The number of candidates in these elections ranges from 3-29 and the number of voters from tens to hundreds of thousands. See the extended version for additional summary statistics of these elections (Tomlinson, Ugander, and Kleinberg 2022). Some of these PrefLib datasets included a small number of ballots with multiple candidates listed at the same rank (0.5% of all ballots), which we omit.…”

“…We note that one third of the elections initially used ballot length of at most four, where it is impossible to have more than three different winners across ballot lengths. An extended version of the paper including all proofs omitted for space is available online (Tomlinson, Ugander, and Kleinberg 2022). Our code and data are available at https://github.com/tomlinsonk/irv-ballot-length.…”