I've been following the latest efforts (in the US) of the GOP to unfairly redraw electoral boundaries and was considering how simple a law could be worded to ensure a more fair allocation of electoral districts. What I came up with is:

  1. All boundary lines must consist of straight line segments
  2. No district may contain an inside angle of greater than 180 degrees
  3. No district may have a major axis greater than 1.5 times its minor axis

I chose the 1.5 number as a starting point. Do the above three restrictions effectively eliminate the tetris/dragon style maps?

Technically you were never a democracy. You were a republic. There are subtle but important differences. Differences notwithstanding, you are still pretty much f**ked. Not that we're that far behind you on the curve.

commented: You're right. Is that a pun as well? (right?) Wow, too far right. +0

A slightly less restrictive but (I hope) still fair policy might be:

  1. All boundary lines must consist of straight line segments
  2. No district may have a major axis greater than 1.5 times its minor axis
  3. The major and minor axes must lie entirely within the district

Any topologists out there who can confirm the fairness of this?

You still have the problem of densely populated liberal cities surrounded by sparsely populated conservative ones. If the main goal is still to have equal numbers of people in each district do you make a donut around the city? Do you slice it up like a pie? Either of those will violate some of your rules.

Another simple solution is to say that the ratio of the perimeter of a district to its area must be below some value. Or that districts must be draw to minimize the total length of perimeter lines around the district.

It seems that a further restriction would be that each district must have a population between two bounds. Densely populated urban areas would have smaller districts. Rural districts would have larger districts. At least my plan would eliminate the jigsaw districts. No plan is perfect but surely we can pick a plan that is fairer than what we have now.