Re:[EM] Gerrymandering

[Alex Small]

Probably the simplest measure I can think of, and the most easy to justify
(at least in a simple case) is the average perimeter of each district.

Simple case:  Suppose that we have a square region with uniform population
density.  Draw a straight line that divides it in half.

Here's an obvious gerrymander:

 __________
|        | |
|   _  _|  |
|  /|_|    |
|  \  ____ |
|   | |  | |
|   |_| _| |
|______|___|

(I don't know if I got the area exactly 50-50, but you get the point.)

Those two districts give a much higher average perimeter.  Now, I realize
that people want districts to respect city and county lines, give fair
representation to ethnic minorities, represent distinct economic interests,
and solve every other problem under the sun, so maybe simple rectangles
aren't the best solution.  But trying to solve all those problems with
single-member districts requires King Solomon.  PR is much easier.

(Yes, I realize that I just preached to the choir.)

Alex Small