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Understanding political phenomena requires measuring the politicalpreferences of society. We introduce a model based on mixtures of spatialvoting models that infers the underlying distribution of political preferencesof voters with only voting records of the population and political positions ofcandidates in an election. Beyond offering a cost-effective alternative tosurveys, this method projects the political preferences of voters andcandidates into a shared latent preference space. This projection allows us todirectly compare the preferences of the two groups, which is desirable forpolitical science but difficult with traditional survey methods. Aftervalidating the aggregated-level inferences of this model against results ofrelated work and on simple prediction tasks, we apply the model to betterunderstand the phenomenon of political polarization in the Texas, New York, andOhio electorates. Taken at face value, inferences drawn from our model indicatethat the electorates in these states may be less bimodal than the distributionof candidates, but that the electorates are comparatively more extreme in theirvariance. We conclude with a discussion of limitations of our method andpotential future directions for research.

Inferring Population Preferences via Mixtures of Spatial Voting Models