We analyze the susceptibility of instant runoff voting (IRV) to a lesser-studied paradox known as a \emph{reinforcement paradox}, which occurs when candidate $X$ wins under IRV in two distinct elections but $X$ loses in the combined election formed by merging the ballots from the two elections. For three-candidate IRV elections we provide necessary and sufficient conditions under which there exists a partition of the ballot set into two sets of ballots such that a given losing candidate wins each of the sub-elections. Applying these conditions, we use Monte Carlo simulations to estimate the frequency with which such partitions exist under various models of voter behavior. We also analyze the frequency with which the paradox occurs in a large dataset of real-world ranked-choice elections to provide empirical probabilities. Our general finding is that IRV is highly susceptible to this paradox in three-candidate elections.

翻译：我们分析了即时决选投票（IRV）对一种较少研究的悖论（称为“增强悖论”）的敏感性，该悖论发生在以下情况：候选人$X$在两个不同的选举中均通过IRV获胜，但在将这两个选举的选票合并后的联合选举中，$X$却落败。对于三候选人IRV选举，我们提供了充分必要条件，描述如何在选票集合上划分出两个子集，使得某个特定落选候选人在每个子选举中获胜。应用这些条件，我们使用蒙特卡洛模拟来估计在不同选民行为模型下此类划分存在的频率。我们还利用一个大型真实世界排序选举数据集分析该悖论发生的频率，以提供经验概率。我们的主要发现是，在三候选人选举中，IRV对此悖论高度敏感。