  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).
