ℓ1-based Bayesian Ideal Point Model for Multidimensional Politics

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 ℓ1 distance. In the Bayesian framework, the use of ℓ1 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.