[EM] Advantages of Dirichlet Region Districts

Alex Small asmall at physics.ucsb.edu
Thu Jan 15 20:44:03 PST 2004

Forest suggested that election districts should be drawn by defining a
center for each district, and specifying that district i will be the set
of all points which are closer to center i than any other center.  He
suggested that "closer" be measured by (literally) taxicab geometry.

I like this notion of taxicab geometry relying on roads, but I think one
should also specify a limit to resolution.  I wouldn't want to
artificially divide neighborhoods, so I might specify that the only roads
considered for these purposes are those with speed limits of 35 mph or

Also, a question for Forest and others:  Perhaps this was already
addressed and I just missed it, but does the Dirichlet method minimize any
criterion such as total perimeter, or satisfy some criterion regarding
convexity of districts or whatever?

Finally, I do have one reservation about the Dirichlet method:  In order
to achieve (roughly) equal population, one must do a considerable amount
of trial and error, adjusting district centers until the population
variance is below some pre-determined criterion.  Does anybody have
thoughts about how to handle this problem tractably?


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