The use of spatial models for inferring members' 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 Euclidean policy space. However, the geometry of Euclidean spaces (even multidimensional ones) cannot fully 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 for not going far enough for them. This paper introduces a new class of spatial voting models in which preferences live in a circular policy space. Such geometry for the latent space is motivated by both theoretical (the so-called "horseshoe theory" of political thinking) and empirical (goodness of fit) considerations. Furthermore, the circular model is flexible and can approximate the one-dimensional version of the Euclidean voting model when the data supports it. We apply our circular model to roll-call voting data from the U.S. Congress between 1988 and 2019 and demonstrate that, starting with the 112th House of Representatives, circular policy spaces consistently provide a better explanation of legislators's behavior than Euclidean ones and that legislators's rankings, generated through the use of the circular geometry, tend to be more consistent with those implied by their stated policy positions.
