Colloquium on the Reinforcement Paradox at Wellesley College

On April 3, the Wellesley College Math Department will host IMD affiliate Dr. David McCune for his colloquium talk entitled “Instant Runoff Voting and the Reinforcement Paradox.” See his bio and abstract for the talk below. The talk will take place at 4:00 pm in H401.

Dr. McCune is an Associate Professor of Mathematics in the Department of Mathematics and Data Science at William Jewell College. He received his PhD in geometric group theory and semigroup theory from the University of Nebraska-Lincoln in 2011. His research interests include apportionment theory and social choice theory, with an emphasis on the computational and empirical aspects of these fields. He is passionate about making these fields accessible to non-mathematical audiences.

Abstract: We analyze the susceptibility of instant runoff voting (IRV) to a funny electoral quirk known as a 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. Using 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.

Join us on April 3 for a lively discussion of instant runoff voting and the reinforcement paradox. Stay tuned for more events throughout the rest of the semester and beyond!