In just about every government that requires legislative redistricting, the party that controls the districting draws districts in whatever shapes will maximize their political power, regardless of whether these shapes would be justifiable on any other basis. Oftentimes these districts have very interesting
shapes--sometimes resembling animals--and someone once called such a district a 'gerrymander'.

To prevent this, I would propose that each party is allowed to draw their own redistricting plan, in secret, before it is publicly presented. Each plan would be evaluated by measuring the perimeter of each equal-population district, squaring it, and dividing it by the area. and then computing the sum of those results. The plan with the smallest sum would be the one that was implemented.

If one party tried to gerrymander their districts while the other party drew reasonably-straightforward districts (which nonetheless favored them, if only slightly), the latter party's map would be used, to the latter party's advantage. It would thus be worthwhile for parties to avoid the snaky district boundaries that have come to be so typical in legislative districting today.

A mathematical rule to limit gerrymanderinghttp://www.halfbake...Anti-Gerrymandering Geometrical shapes can be characterized by a number equal to the perimiter squared divided by the area. [LoriZ, Oct 04 2004, last modified Oct 05 2004]

It seems obvious to me that an optimal solution exists, whether you define optimum by minimizing total boundary length, minimizing population variance, maximizing use of existing boundary lines, minimizing district rotational inertia, etc. It is not at all obvious to me how to calculate an optimal solution. Obviously someone knows something about optimization of subdivision, but using a more subjective set of criteria. It would be interesting to try to formulate a set of criteria that minimizes the role of tactics and strategy (i.e. competition) in the redistricting process. Then try to do the same for life. This of course is my own opinion based on my own subjective experience.

Certainly there would exist one or more optimal solutions for any shape of state, where any party proposing one would be guaranteed a "win" [unless the other party chose an exactly-equally-good method, in which case it may be necessary to flip a coin or something]. I suppose it's possible that an optimal solution might impart some noticeable advantage to one party or the other, but I would not expect such advantage to be great in such case.

More likely, even the party whom the 'optimal' solution would favor would try to adjust the district boundaries so as to favor themselves a little more, in the belief that no better solution the other party could come up with would be more advantageous to them. Of course, the other party's goal would be to prove them wrong...

I think Supercat got it right the first time. The formula is very straightforward. One could argue that anyone should be able to submit a redistricting plan si that Democlans would have to compete with Greens, Libertarians, PIRG, or anybody so so inclined.

district lines sometimes follow geographical lines for a reason. In the system you propose wouldn't be possible where one person on one side of a lake had to vote with and be governed by a group on the other side just to make it square? Go fish

//district lines sometimes follow geographical lines for a reason. In the system you propose wouldn't be possible where one person on one side of a lake had to vote with and be governed by a group on the other side just to make it square? Go fish//

It would probably be appropriate to make allowances in the formula for boundaries that follow certain pre-existing natural or political contours. I did not want to overcomplicate the idea with such details, but any implementation should probably include some.

there's a proposed amendment here to put it in the hands of a nonpartisan commission, but in the conservative hellhole of florida, i'm sure they'll pervert that.

i still like the canada and uk tradition of naming districts, and then you add and merge where appropriate. Instead of saying "California 31rd' or something--you can say "berkeley zoo' :)