  How can we probabilistically predict the winner in a ranked-choice election
without all ballots being counted? In this study, we introduce a novel
algorithm designed to predict outcomes in Instant Runoff Voting (IRV)
elections. The algorithm takes as input a set of discrete probability
distributions describing vote totals for each candidate ranking and calculates
the probability that each candidate will win the election. In fact, we
calculate all possible sequences of eliminations that might occur in the IRV
rounds and assign a probability to each.
  The discrete probability distributions can be arbitrary and, in applications,
could be measured empirically from pre-election polling data or from partial
vote tallies of an in-progress election.
  The algorithm is effective for elections with a small number of candidates
(five or fewer), with fast execution on typical consumer computers. The
run-time is short enough for our method to be used for real-time election night
modeling where new predictions are made continuously as more and more vote
information becomes available. We demonstrate the algorithm in abstract
examples, and also using real data from the 2022 Alaska state elections to
simulate election-night predictions and also predictions of election recounts.
