[EM] More on Gerrymander prevention

[Forest Simmons]

On Fri, 22 Mar 2002, Michael Rouse wrote:

> chosing a winner. If there were some clear standard, we could (as others
> have suggested) solicit plans not only from computer models and the parties
> involved, but from ordinary citizens, and then choose the best one. Heck,
> you could have a distributed-processing program like seti at home
> (gerrymander at home? redistrict at home?) so that trillions of different options
> could be tested (complete with cool screensavers) and the best ones
> forwarded to the redistricting boards. If they were obligated by law to
> choose the plan that scores the best by some standard method, computer geeks
> (of which I'm a proud member) could keep the politicians honest.

This idea is similar to Joe Weinstein's, and as Joe said the measure of
goodness doesn't have to be one that can be maximized easily; it only
has to be something than can be effectively computed in individual cases
for purposes of comparison.

Someone (sorry I don't remember who) suggested using average perimeter as
the measure.  The smaller the average perimeter the better.  That would
satisfy Joe's criterion (easy to compute in any specific instance) and
is exactly the right kind of measure of unnecessary zig-zagging.

As Joe also pointed out, there should be some absolute criterion for
admissibility, too.  For this I suggest that each district shape should
have at least one point P in its interior such that for any other point Q,
the straight line segment from P to Q never leaves the district. In other
words a crow flying as the crow flies should be able to get from P to any
other point Q without flying over a piece of some other district.

[The technical name for this condition is "star-like."  But it doesn't
mean that it has to look like a star.]

Any partition of a state into star-like districts would be reasonable, and
this condition is flexible enough to allow following of natural boundaries
when necessary, unlike the more stringent condition of convexity.

Forest