[EM] Theoretical Gerrymandering Solution

[Steven Barney]

Many of the states are now focusing on the gerrymandering or redistricting problem. It seems to me that one possible solution may be to require that length of boundaries of all the state senate districts in the state, for example, have the minimum, or close to the minimum sum total. My intuition is that this would mean that the districts would have to be as close to being regular polygons as possible, since, for example, the 4 sided polygon with the shortest boundary is a square, and the infinite sided polygon with the shortest boundary is the circle. Is this a good idea?

If we had to redistrict a rectangular state, such as Wyoming, it seems to me that might be a reasonable possible solution. However, I am concerned about irregular states, such as, say, Wisconsin, which includes a lot of squiggly border lines and even some islands. I don't even know if this is a mathematically solvable problem. What do you think?


Steve Barney