A Bayesian mixture model captures temporal and spatial structure of voting blocs within longitudinal referendum data

Abstract The estimation of voting blocs is an important statistical inquiry in political science. However, the scope of these analyses is usually restricted to roll call data where individual votes are directly observed. Here, we examine a Bayesian mixture model with Dirichlet-multinomial components to infer voting blocs within longitudinal referendum data. This model infers voting bloc mixture within municipalities using state-level data aggregated at the municipal level. As a case study, we analyze the vote totals of Maine referendum questions balloted from 2008 to 2019 for 423 municipalities. Using a birth–death Markov chain Monte Carlo approach to inference, we recover the posterior distribution on the number of voting blocs, the support for each question within each bloc, and the blocs’ mixture within each municipality. We find that these voting blocs are structured by geography and largely consistent across the study period. The model finds that blocs exhibit both spatial gradients and discontinuities in their structure. Examining the statistical fit of the model, we uncover a small number of questions that show inconsistency with the statewide bloc structure and note that the content of these questions relates to specific regions. We conclude with possible statistical extensions, connections to other statistical frameworks in political science, and detail possible locations for model applications.