Disagreement and Dimensionality: A Beta Process Approach to Estimating Dimensionality of Ideal Points in the U.S. Congress
Abstract: Roll call scaling techniques, such as NOMINATE and IDEAL, are empirical standards for studies of voting behavior within legislative bodies. Though ideal point estimation techniques are frequently used, the theoretical implications of assumptions made in order to empirically estimate ideal points provide cause for concern. One assumption that is frequently leveraged in studies of legislatures is that ideal points are best represented in one or two dimensions. This assumption is key for further usage of ideal points in formal models and examinations of elite polarization. Despite the importance of this assumption, the dimensionality of the ideal point space is often simply fixed to fit theoretical expectations or tested using subjective post-hoc tests. In this paper, I propose a method for properly modeling the dimensionality of the ideal point space using a beta-Bernoulli Bayesian nonparametric prior. This prior structure allows for the number of dimensions and ideal point estimates to be modeled simultaneously. I apply this model to all sessions of the U.S. House (1st-114th) and show that there is little evidence for the the low dimension conjecture in U.S. roll call scaling models. While the dimensionality of the policy space has decreased over recent sessions, the current estimates are not atypical and previous periods of the U.S. Congress have exhibited similar levels of high party level voting. This paper provides a meaningful examination of dimensionality in the U.S. Congress and shows how seemingly innocuous assumptions in the scaling procedures can lead to inappropriate inferences about legislative behavior.