Can statistical models capture Mamdani's success? Social choice, ranked-choice voting, and model fit, with an application to the 2025 New York City Democratic Primary

Abstract

Ranked-choice voting is increasingly prevalent in elections. An extensive literature in social choice theory -- the study of collective decision-making with the goal of making compromises among disparate opinions -- considers theoretical and empirical properties of various election procedures. Recently, a sub-literature on rationalizability, led by social choice theorists and computer scientists, makes explicit connections between social choice rules and maximum likelihood estimation. This paper further illuminates connections between social choice and statistical summaries of data. We begin by studying rationalizability from a statistical perspective, expanding existing results to realistic voting contexts and deriving statistical details necessary for model estimation and assessment. We then apply our work to ranked-choice votes from the 2025 New York City Democratic mayoral primary election. We demonstrate how rationalizing models impose unrealistic distributional assumptions and thus exhibit poor fit to voting data. Additionally, we show that non-rationalizing models meaningfully elucidate heterogeneous voter preferences. Our work demonstrates the inability of rationalizing models to capture key features of distributions of preferences in political elections, depriving analysts of fundamental uses, such as inference, typically associated with statistical modeling. Conversely, we show that statistical modeling can capture nuanced voter preferences by paying careful attention to plausible data-generating mechanisms.