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Instant runoff voting (IRV) is an increasingly-popular alternative totraditional plurality voting in which voters submit rankings over thecandidates rather than single votes. In practice, elections using IRV oftenrestrict the ballot length, the number of candidates a voter is allowed to rankon their ballot. We theoretically and empirically analyze how ballot length caninfluence the outcome of an election, given fixed voter preferences. We showthat there exist preference profiles over $k$ candidates such that up to $k-1$different candidates win at different ballot lengths. We derive exact lowerbounds on the number of voters required for such profiles and provide aconstruction matching the lower bound for unrestricted voter preferences.Additionally, we characterize which sequences of winners are possible overballot lengths and provide explicit profile constructions achieving anyfeasible winner sequence. We also examine how classic preference restrictionsinfluence our results--for instance, single-peakedness makes $k-1$ differentwinners impossible but still allows at least $\Omega(\sqrt k)$. Finally, weanalyze a collection of 168 real-world elections, where we truncate rankings tosimulate shorter ballots. We find that shorter ballots could have changed theoutcome in one quarter of these elections. Our results highlight ballot lengthas a consequential degree of freedom in the design of IRV elections.

Ballot Length in Instant Runoff Voting