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Analyzing Legislative Roll Call Data via Markov-chain Monte Carlo: Testing the Party Discipline Hypothesis

Political scientists make extensive use of ``roll call'' data (the recorded votes of deliberative bodies such as legislatures and courts). Via various data reduction techniques, roll call data generate estimates of (1) legislators' preferred positions in a low-dimensional ideological space; (2) the ideological content of the proposals considered (and passed into law) by the deliberative body. Since roll call data sets are large (either in the number of legislators, the number of votes, or both), roll call analysis often involves estimating thousands of parameters (the analysis of data from standardized tests with Rasch models gives rise to a similar problem).

Markov chain Monte Carlo methods have emerged as an attractive computing strategy for the analysis or roll call data. Moreover, an explicitly Bayesian approach provides an elegant way to improve identifiability (via proper priors), and to make the statistical analysis of roll call data more substantively interesting. In particular, hierarchical models let us bring auxiliary or ``expert'' information about legislators and proposals to bear on the analysis, integrating measurement and tests of structural models of legislative behavior. I will also dwell on issues concerning identifiability and Bayesian computation in the high-dimensional context of roll call analysis. The applications are drawn from recent U.S.~congresses, past U.S. congresses (the passage of the civil rights legislation in the 1960s) and the Supreme Court.