  Instant runoff voting (IRV) is an increasingly-popular alternative to
traditional plurality voting in which voters submit rankings over the
candidates rather than single votes. In practice, elections using IRV 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 a
construction matching the lower bound for unrestricted voter preferences.
Additionally, we characterize which sequences of winners are possible over
ballot lengths and provide explicit profile constructions achieving any
feasible winner sequence. We also examine how classic preference restrictions
influence our results--for instance, single-peakedness makes $k-1$ different
winners impossible but still allows at least $\Omega(\sqrt k)$. 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. Our results highlight ballot length
as a consequential degree of freedom in the design of IRV elections.
