[extropy-chat] POL: Gerrymandering and Geometry: A Tiling Problem?

Greg Burch gregburch at gregburch.net
Wed Dec 10 14:53:57 UTC 2003


This will be largely of interest to U.S. subscribers, since it is premised on a provision of the U.S. Constitution.

Listening to a piece on NPR this morning about the on-going battles over Congresssional redistricting in the wake of the 2000 census, I was struck by the idea that Congressional redistricting can be viewed as a classic tiling problem.  

Article I, Sec. 2 of the Constitution calls for the (partially) proportional division of seats in the House of Representatives according to population.  (The caveat arises from the fact that each state must have at least one seat, and some states don't have enough population to qualify for that according to a nation-wide even apportionment.)  This provision has been ammended and fine-tuned over the years, and has now resulted in both a complex mathematical problem, and a political problem.  A very good resource explaining the process can be found at:

http://www.census.gov/population/www/censusdata/apportionment.html

Now, state legislatures are given the task of redrawing congressional district lines to apportion seats according to population within a state.  This becomes a partisan political opportunity that has come to have the name "gerrymandering" for historical reasons, in which the majority party in the state legislature draws the geographic boundaries of the congressional districts to try to maximize the number of national congressional seats their party can garner.

Here's my question: is it possible to devise an algorithm that would create an ideal tiling based on the restraint of having the same number of voters in each district, given an uneven geographic distribution of voters, but MINIMIZING the ratio of the surface area of each tile (congressional district) to its defining border and perhaps also minimizing the number or negative angles in the shape of the border?

Here's a chance to implement the idea discussed in Max More's recent essay about trying to employ reason to improve political processes.

Greg Burch
My blog: http://www.gregburch.net/burchismo.html



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