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...contemporary American politics. do we know, scientifically, that politics has become more polarized over the past thirty years?
The fact that the members of Congress form overlapping cohorts suggests a possible method to investigate this question. The conservative Rick Santorum recently held the Pennsylvania Senate seat once held by the moderate John Heinz. How can we claim that Santorum was more conservative than Heinz? Heinz served with Arlen Specter, who also served with Santorum. Heinz and Specter had very similar voting records. In contrast, Specter voted with the liberals (or Democrats) much more frequently than Santorum did. Observations like this one form the basis for measuring increases in polarization. Thus replacements like that of Heinz by Santorum in Pennsylvania, or of Ervin by Edwards in North Carolina, are the symptoms of polarization.
By adapting the standard dichotomous-choice model, we have created a procedure for measuring ideology--DW NOMINATE. We have used it to analyze all of the roll-call votes in the first 108 Congresses (1789-2004), a project we discuss in greater detail in our book Ideology and Congress. This procedure is based on a simple geometric model of voting behavior. Each legislator is represented by one point, and each roll call is represented by two points--one for 'yea' and one for 'nay.' These points form a spatial map (maps available at voteview.ucsd.edu and voteworld.berkeley.edu).
Jordan Ellenberg, in "Growing Apart: The Mathematical Evidence for Congress' Growing Polarization,"...
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