ℓ 1 -based Bayesian Ideal Point Model for Multidimensional Politics

Abstract

Ideal point estimation methods in the social sciences lack a principled approach for identifying multidimensional ideal points. We present a novel method for estimating multidimensional ideal points based on ℓ 1 distance. In the Bayesian framework, the use of ℓ 1 distance transforms the invariance problem of infinite rotational turns into the signed perpendicular problem, yielding posterior estimates that contract around a small area. Our simulation shows that the proposed method successfully recovers planted multidimensional ideal points in a variety of settings including non-partisan, two-party, and multi-party systems. The proposed method is applied to the analysis of roll call data from the United States House of Representatives during the late Gilded Age (1891-1899) when legislative coalitions were distinguished not only by partisan divisions but also by sectional divisions that ran across party lines.