[EM] Re: Automated districting

Forest Simmons fsimmons at pcc.edu
Mon Jan 12 14:23:01 PST 2004

I suggest (as one of the constraints) that districts should be Dirichlet
regions with respect to some set of defining points, P_1, P_2, P_3, ... ,
P_n, one defining point for each of the n regions.

In other words if you are in district k, then point P_k should be closer
to your residence than any of the other defining points.

If the defining points are the precinct headquarters, then you just vote
at the precinct closest to your home, and you will automatically get the
correct ballot.

If distance is measured with the Euclidean metric, then the districts will
be convex polygons called Voronoi polygons.

A more practical metric would be the "estimated travel time" metric.

Rental cars with GPS systems have software for deciding the estimated
travel time from point A to point B, so we know that this metric can be
standardized and computed effectively.

This Dirichlet region constraint still leaves enough freedom that other
requirements can be met, including the relative equality of the number of
voters in each district.

Minimization of some other quantity (such as total or max travel distance
for voters) subject to these basic constraints could help select from
several proposed configurations.

Just an idea (capable of modification or adaptation)!


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