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）对一种较少被研究的悖论——即强化悖论——的敏感性。该悖论发生在候选人$X$在两场独立的IRV选举中均获胜，但在将两场选举的选票合并形成的联合选举中$X$却落败的情况。针对三候选人IRV选举，我们给出了充分必要条件，以确定是否存在一种将选票集划分为两个子集的方式，使得某个给定的落败候选人在每个子选举中均获胜。应用这些条件，我们通过蒙特卡洛模拟估算了在不同选民行为模型下此类划分存在的频率。此外，我们分析了大规模真实世界排序选择选举数据集中该悖论发生的频率，以提供经验概率。我们的总体发现是：在三候选人选举中，IRV极易受到此类悖论的影响。