Instant Runoff Voting and the Reinforcement Paradox
For election designers and social choice theorists, this work quantifies a previously understudied vulnerability of IRV, showing it is more common than expected.
The paper analyzes the reinforcement paradox in instant runoff voting (IRV), where a candidate wins in two separate elections but loses when the ballots are combined. Using Monte Carlo simulations and real-world data, they find IRV is highly susceptible to this paradox in three-candidate elections.
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.