Let Them Eat Pie: Addressing Sample Selection in Multiparty Elections

Abstract

Elections are central to the study of politics. When studying parties’ vote shares across districts, scholars are encouraged to use compositional-outcome models in order to test their theories about what factors shape the dynamics of electoral support. Existing compositional modeling approaches incorrectly deal with scenarios in which not all parties compete in every electoral district. Because unobserved factors that affect a party’s decisions to contest a district are likely correlated with its performance in districts where the party fielded candidates, failing to account for partial contestation is likely to result in sample selection bias. Addressing sample selection in a compositional setting is challenging because the outcomes are in log-ratio form, and thus the errors often deviate from normality. To deal with these issues, we introduce a novel maximum likelihood approach which accounts for this type of sample selection and demonstrate through simulations that our method outperforms commonly used solutions, including the conventional Heckman correction. We illustrate the utility of our approach by analyzing the 2017 and 2019 U.K. parliamentary elections in English constituencies.