Half a croissant, on a plate, with a sign in front of it saying '50c'
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A mathematical rule to limit gerrymandering
  [vote for,

I understand that a lot of redistricting is done by computer algorithms these days, but I couldn't find any details on how it's done, and I suspect it may still vary state to state, and I still hear outrageous stories of gerrymandered districts now and then. Here's a way of cutting down the number with a uniform rule, perhaps to be written into federal law. Notice that geometrical shapes can be characterized by a number equal to the perimiter squared divided by the area. Call this the crookedness number. This value is independent of the actual size of the shape. For example, for a square, CN=16. For a hexagon, it's slightly over 10. More convuluted shapes will have higher CNs, and for weird "banana" or "line" shaped districts the value will go up rapidly. So you can simply demand that no election district can have a CN value exceeding a certain amount. Not sure what that should be--maybe 30 or 40, which still allows some crookedness at the edges, but would get rid of some of the worst examples which look more like fractals than compact areas.

Mind you, I'm actually more in favor of proportional representation myself, which may reduce or eliminate the need for redistricting at all, but barring that the above rule could limit the worst abuses.

scottinmn, Oct 18 2002

Area of a Hexagon http://www.drking.w...gons/misc/area.html
for those checking the math [krelnik, Oct 18 2002, last modified Oct 04 2004]

Improved legislative redistricting http://www.halfbake...ive_20redistricting
link to supercat's older idea that uses same formula [krelnik, Oct 04 2004]

Example of gerrymandering http://www.thinkmaj...3illustration.shtml
For those lucky enough to live in countries where this doesn't happen, here's an example of what is being discussed. The outline on the linked map is Georgia's current 13th Congressional district. [Worldgineer, Oct 04 2004]


       Just calling it "crookedness" makes me grin. Here, a smile shaped croissant.
lurch, Oct 18 2002

       Excellent. I've no time for the math, but whatever messes up the lines drawn by politicians gets my vote.
rabbit, Oct 18 2002

       PR won't solve all ills - you will still need to re-draw the boundaries when certain areas get too populous, but generally a nice idea.
PeterSilly, Oct 18 2002

       //For a hexagon, it's slightly over 10.//   

       Actually it is about 13.87 for a hexagon. The theoretical minimum CN would be for a circle, which is 4 PI.   

       Despite the math error, I'm giving you a croissant because I'm all for pie.
krelnik, Oct 18 2002

       One man, one vote. I volunteer to be the one man, and I will have the one vote. Problem solved.
8th of 7, Oct 18 2002

       Thanks for the correction krelnik, I knew I shouldn't have have done that off the top of my head. Circles would get a CN of about 12.56, but of course they can't fill a 2d area so the hexagon value is a better baseline figure to consider. It also occurred to me that exceptions may have to be made for geographical reasons, as when the district border is formed by a convoluted coastline, river, or similar features. But the presumption should be that a high CN would be gerrymandering unless a good purely geographical reason to the contrary can be given.
scottinmn, Oct 18 2002

       Keep in mind, [rabbit], that re-districting is just other lines drawn by other politicians. I'm all for reform, but sometimes programs touted as reforms actually make things worse.
snarfyguy, Oct 28 2002

       //It also occurred to me that exceptions may have to be made for geographical reasons, as when the district border is formed by a convoluted coastline, river, or similar features.//   

       I would handle this by allowing the person drawing the districts to have part which extends outside the area of interest (state or whatever). "Area" credit would only be given for the portion of the "drawn district" which was actually legally part of the district, but the perimeter measurement would be of the drawn--not actual--area.   

       Sorry if that's unclear--what I'm getting at would actually be easier to figure than to explain.
supercat, Oct 28 2002

       The product of a normalized crookedness (so that the crookedness of hexagons is made equal to one) times another quantity (lets call the unfairness) which measures how districts are sometimes split up could give a quantity we could call the "contrivance".
talldave, Jun 07 2004


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