  Understanding political phenomena requires measuring the political
preferences of society. We introduce a model based on mixtures of spatial
voting models that infers the underlying distribution of political preferences
of voters with only voting records of the population and political positions of
candidates in an election. Beyond offering a cost-effective alternative to
surveys, this method projects the political preferences of voters and
candidates into a shared latent preference space. This projection allows us to
directly compare the preferences of the two groups, which is desirable for
political science but difficult with traditional survey methods. After
validating the aggregated-level inferences of this model against results of
related work and on simple prediction tasks, we apply the model to better
understand the phenomenon of political polarization in the Texas, New York, and
Ohio electorates. Taken at face value, inferences drawn from our model indicate
that the electorates in these states may be less bimodal than the distribution
of candidates, but that the electorates are comparatively more extreme in their
variance. We conclude with a discussion of limitations of our method and
potential future directions for research.
