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.

翻译：如何在选票未完全统计的情况下，概率性地预测排名选择制选举的获胜者？本研究提出了一种新颖的算法，旨在预测即时决选（IRV）选举的结果。该算法以描述每位候选人排名得票总数的离散概率分布集合作为输入，计算每位候选人赢得选举的概率。实际上，我们计算了IRV轮次中所有可能发生的淘汰顺序，并为每种顺序分配一个概率。这些离散概率分布可以是任意的，在实际应用中，可通过选举前的民调数据或进行中选举的部分得票统计进行实证测量。该算法适用于候选人数量较少（不超过五人）的选举，能在普通消费级计算机上快速执行。其运行时间足够短，可用于实时选举之夜建模，随着更多投票信息的不断获取，可连续生成新的预测。我们通过抽象示例，并利用2022年阿拉斯加州选举的真实数据演示了该算法，模拟了选举之夜预测以及选举重新计票的预测结果。