Re: Redistricting: Problem and Proposed Solution

[David Farber <dave () farber net>]

Begin forwarded message:

From: George Sadowsky <george.sadowsky () gmail com>
Date: February 15, 2007 2:05:47 PM EST
To: dave () farber net
Cc: Stephen Unger <unger () cs columbia edu>
Subject: Re: [IP] Redistricting: Problem and Proposed Solution

Dave,

For IP if you like.

In 1964 I worked with Morris Davis of Yale University when he was  
appointed Special Master to the Connecticut Supreme Court to assist  
in resolving a politically charged discussion of how to redistrict  
Connecticut (6 Congressional districts, 169 towns) in anticipating of  
the 1966 national elections.

Along with my colleagues (of whom I remember Lois Frampton and Mike  
Hooven) and Morris, we investigated two methods of quasi-automatic  
redistricting not based upon any political considerations.  The first  
was a rather elegant iterative linear programming method originally  
developed and used by Jim Weaver and Sid Hess in Delaware in which  
one estimated initial centers of the districts and them iteratively  
moved the centers and adjusted the boundaries to minimize the squares  
of the distances from the 169 Connecticut towns to those centers.  
Convergence and connectedness were always achieved, although the  
algorithm did not guarantee it.  The result depended upon the initial  
centers chose, but only minimally, and the resulting districts,  
perhaps surprisingly, perhaps not, conformed roughly to sensible  
population groupings.

The second method depended upon repetitive scanning of the population  
centers by a combination of latitudinally and longitudinally scanning  
the towns and aggregating their populations.  That work is described  
in "Legislative Districting by Computer," Jurimetrics, Vol. 8, No. 4,  
June 1968, pp. 77-98.  The methodology is cruder than that of Weaver  
and Hess, but in fact gave quite reasonable (from the Court's point  
of view) results.  The stability of the results using this method was  
slightly less that Weaver-Hess depending upon scanning direction, and  
we did not investigate solution stability based upon various  
rotations of the coordinate space.

Use of the two methods gave the Court what it wanted: a number of  
solutions that were based upon logic separate from any political  
considerations, and they used those solutions to fashion the final  
result.  Of course, each of these solutions had political  
implications, but none of them remotely approached the contorted,  
twisted districts that we observe these days resulting from  
redistricting efforts.

Regards,

George

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 At 11:49 AM -0500 2/15/07, David Farber wrote:
> Begin forwarded message:
>
> From: Stephen Unger <unger () cs columbia edu>
> Date: February 15, 2007 11:22:46 AM EST
> To: Dave Farber <dave () farber net>, ip () v2 listbox com
> Subject: Redistricting: Problem and Proposed Solution
>
> Redistricting is a perennial (used to be every decade, but now
> cropping up more often) problem that significantly distorts the
> political arena. For example, there are a number of states where,
> despite having received many fewer total votes in elections for the  
> House,
> the Republicans have won most of the seats as a result of
> gerrymandering.  (Of course BOTH parties have done this sort of thing
> for two centuries.)
>
> Setting rules for redistricting is very difficult, even in
> principle. But there is a very nice mathematical solution that is
> inherently neutral,leaving no room for manipulation.
>
> I have just posted an article describing the problem and solution  
> on my
> blog at:
> http://www1.cs.columbia.edu/~unger/myBlog/endsandmeansblog.html
>
> (An earlier posting on the blog is a somewhat revised version of my
> e-voting article.)
>
> Steve
> ............



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