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

Correctly measuring district preferences is crucial for empirical research on legislative responsiveness and voting behavior. This article argues that the common practice of using presidential vote shares to measure congressional district ideology systematically produces incorrect estimates. I propose an alternative method that employs multiple election returns to estimate voters' ideological distributions within districts. I develop two estimation procedures—a least squared error model and a Bayesian model—and test each with simulations and empirical applications. The models are shown to outperform vote shares, and they are validated with direct measures of voter ideology and out-of-sample election predictions. Beyond estimating district ideology, these models provide valuable information on constituency heterogeneity—an important, but often immeasurable, quantity for research on representatives— strategic behavior.