I was trying to think of a reasonable definition of the shape of a district such that it would be "reasonably contiguous"
One possibility that occured to me was using the ratio of the length of the border to the square root of the area By using the sqrt, it doesn't matter the size. 2 shapes which are just scaled versions of each other will give the same result. Some examples: Circle: sqrt(pi*r^2)/(2*pi*r) = 0.282 (I think this is the highest possible) Square: sqrt(a^2)/4a = 0.250 2:1 rectangle: sqrt(2*1)/6 = 0.236 3:1 rectangle: sqrt(3*1)/8 = 0.217 4:1 rectangle: sqrt(4*1)/10 = 0.200 5:1 rectangle: sqrt(5*1)/12 = 0.186 9:1 rectangle: sqrt(9*1)/20 = 0.15 A good threshold might be 0.2. This would allow districts with an aspect ratio of 4:1 or less. It would also make it alot harder to have dumbbell shaped districts which are joined by a narrow channel. Two equal circles that are touching wouldn't work. sqrt(2*pi*r^2) / (4*pi*r) = 0.199 In fact, that is another good reason to use 0.2. A circular district could have a "shooter" of length 1.29 times the radius (0 area but just adds to the border length). However, this would also mess up the neighbouring district(s), which would then end up having to be circular too. The rule would be something like "the length of the border of a district shall not be more than five times the square root of the area of the district" ---- election-methods mailing list - see http://electorama.com/em for list info
