Spherical Latent Factor Model

Abstract

The use of spatial models for inferring member's preferences from voting data has become widespread in the study of deliberative bodies such as legislatures. Most established spatial voting models assume that ideal points belong to a (possibly multidimensional) Euclidean policy space. However, the geometry of Euclidean spaces cannot accommodate situations in which members at the opposite ends of the ideological spectrum reveal similar preferences by voting together against the rest of the legislature. This kind of voting behavior can arise, for example, when extreme conservatives oppose a measure because they see it as being too costly, while extreme liberals oppose it as for not going far enough for them. This paper introduces a new class of spatial voting models in which preferences live in a circular space. Our formulation includes the one-dimensional version of the Euclidean model as a special (limiting case), allowing the data to inform us about the geometry of the underlying space. A circular structure for the latent space is motivated by both theoretical (the so-called horseshoe theory'' of political thinking) and empirical (goodness of fit) considerations. In particular, by applying the model to roll-call voting data from the U.S. Congress between 1988 and 2019, we demonstrate that circular latent spaces provide a better explanation for the political process in the House of Representatives than Euclidean models, that policy spaces have become increasingly circular in recent years (and, especially, since 2010), and that legislators's rankings generated through the use of the circular geometry tend to be more consistent with their stated policy positions.