Analyzing the U.S. senate in 2003: Similarities, clusters, and blocs

In this paper, we apply information theoretic measures to voting in the U.S. Senate in 2003. We assess the associations between pairs of senators and groups of senators based on the votes they cast. For pairs, we use similarity-based methods, including hierarchical clustering and multidimensional scaling. To identify groups of senators, we use principal component analysis. We also apply a discrete multinomial latent variable model that we have developed. In doing so, we identify blocs of cohesive voters within the Senate and contrast it with continuous ideal point methods. We find more nuanced blocs than simply the two-party division. Under the bloc-voting model, the Senate can be interpreted as a weighted vote system, and we are able to estimate the empirical voting power of individual blocs through what-if analysis.