One-Dimensional Scaling without Apologies

I propose a fully nonparametric framework for estimation of and inference on the location of political parties in a one-dimensional scale. I derive a novel balance condition sufficient for identification and consistent estimation of the parties’ order and a weaker error rate condition that partially identifies the order. Capitalizing on recent advances in testing moment inequalities, I propose a strong and weak specification test of the one-dimensional model. These tests can also be interpreted as tests of a weak sufficient condition for the existence of a majority-core party. Under stronger cardinal assumptions on preferences, I rely on arguments from revealed preference theory to execute similar tests efficiently, obviating the need for confidence set construction using an approximating grid of party locations. I illustrate these techniques using Comparative Study of Electoral Systems survey data on the German party system.