Unpredictable voters in ideal point estimation

Ideal point estimators are typically based on an assumption that all legislators are equally responsive to modeled dimensions of legislative disagreement; however, particularistic constituency interests and idiosyncrasies of individual legislators introduce variation in the degree to which legislators cast votes predictably. I introduce a Bayesian heteroskedastic ideal point estimator and demonstrate by Monte Carlo simulation that it outperforms standard homoskedastic estimators at recovering the relative positions of legislators. In addition to providing a refinement of ideal point estimates, the heteroskedastic estimator recovers legislator-specific error variance parameters that describe the extent to which each legislator's voting behavior is not conditioned on the primary axes of disagreement in the legislature. Through applications to the roll call histories of the U.S. Congress, the E.U. Parliament, and the U.N. General Assembly, I demonstrate how to use the heteroskedastic estimator to study substantive questions related to legislative incentives for low-dimensional voting behavior as well as diagnose unmodeled dimensions and nonconstant ideal points.