Polarization in the States

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Peter Orzsag on State Legislative Polarization.  A very good summary of the research, but it emphasizes the role of residential and geographic sorting a bit much for my taste. 

Some of my recent (and very tentative) work with  Boris Shor, Chris Warshaw, Chris Tausanovitch, and Jonathan Rodden sheds some light on the question of the role of residential sorting (beyond my general skepticism borne of the null findings for Gerrymandering).

In our presentation at the American Political Science Association (unfortunately there is not yet a manuscript), we used Tausanovitch and Warshaw's estimates of 245,000 voter ideal points to construct measures of the distribution of voter preferences in every Senate.  We then combined this data with my and Boris's data on state senator ideal points to estimate the relationship between within-district voter heterogeneity and polarization.  A taste of our findings is available after thr jump.
First, we looked for an aggregate relationship between polarization within the states and the number of heterogeneous districts (those with greater than average standard deviations of voter preferences).  As the figure below shows, there is a strong aggregate relationship between district heterogeneity and polarization.

Of course, an aggregate relationship could possibly emerge if there is a relationship between state-level heterogeneity and polarization (which there appears to be).  So we then focused on individual districts.  Here we estimate the "intra-district divergence" -- the predicted difference between Democratic and Republican state senators in otherwise similar districts.  We allow this gap to vary with a number of factors including district heterogeneity (again measured as the standard deviation of voter ideal points).  The next figure plots the predicted divergence as a function of heterogeneity.

Note that there is a strong and precisely estimated relationship between heterogeneity and divergence.  The effect is large enough to explain substantial amount of the variance in party divergence across states.

So what does this mean for the debate on residential and geographic sorting?  Of course, these finding do not rule out that such sorting may matter.  But they do suggest that how voters are polarized within districts may matter far more than how they are polarized across districts.  Our results also suggest that attempts to offset geographic sorting by creating heterogeneous "strange bedfellows" districts will likely backfire.

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