Giving Order to Districts: Estimating Voter Distributions with National Election Returns

Abstract

This article argues that the common practice of using presidential vote shares to measure congressional district ideology is logically flawed. I propose two alternative methods - a classical and Bayesian model - that employ multiple election returns to estimate voters' ideological distributions within districts. Simulations and empirical applications demonstrate that the proposed models outperform direct vote shares, and they externally validate estimates of district ideology. Moreover, by generating estimates of districts' variances, these models also provide information on constituency heterogeneity, a quality that is perhaps equally valuable for understanding representatives' strategic behavior.