The probability of casting a pivotal vote in an Instant Runoff Voting election

I derive the probability that a vote cast in an Instant Runoff Voting election will change the election winner. I show that there can be two types of pivotal event: direct pivotality, in which a voter causes a candidate to win by ranking them, and indirect pivotality, in which a voter causes one candidate to win by ranking some other candidate. This suggests a reason that voters should be allowed to rank at most four candidates. I identify all pivotal events in terms of the ballots that a voter expects to be cast, and then I compute those probabilities in a common framework for voting games. I provide pseudocode, and work through an example of calculating pivotal probabilities. I then compare the probability of casting a pivotal vote in Instant Runoff Voting to single-vote plurality, and show that the incentives to vote strategically are similar in these two systems.