Partition Decomposition for Roll Call Data
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In this paper we bring to bear some new tools from statistical learning on the analysis of roll call data. We present a new data-driven model for roll call voting that is geometric in nature. We construct the model by adapting the "Partition Decoupling Method," an unsupervised learning technique originally developed for the analysis of families of time series, to produce a multiscale geometric description of a weighted network associated to a set of roll call votes. Central to this approach is the quantitative notion of a "motivation," a cluster-based and learned basis element that serves as a building block in the representation of roll call data. Motivations enable the formulation of a quantitative description of ideology and their data-dependent nature makes possible a quantitative analysis of the evolution of ideological factors. This approach is generally applicable to roll call data and we apply it in particular to the historical roll call voting of the U.S. House and Senate. This methodology provides a mechanism for estimating the dimension of the underlying action space. We determine that the dominant factors form a low- (one- or two-) dimensional representation with secondary factors adding higher-dimensional features. In this way our work supports and extends the findings of both Poole-Rosenthal and Heckman-Snyder concerning the dimensionality of the action space. We give a detailed analysis of several individual Senates and use the AdaBoost technique from statistical learning to determine those votes with the most powerful discriminatory value. When used as a predictive model, this geometric view significantly outperforms spatial models such as the Poole-Rosenthal DW-NOMINATE model and the Heckman-Snyder 6-factor model, both in raw accuracy as well as Aggregate Proportional Reduced Error (APRE).
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