After surfing the web for information on how to divide maps without gerrymandering, I think I found a standard that won't offend most people.
The ideal district under most standards has the following features: 1. Equal Population 2. Contiguous 3. Compact If we were to define the ideal districting map to be a centroidal Voronoi diagram where each Thiessen polygon has the same number of people, then the map that comes closest to this standard should be the one we choose. (See http://www.math.iastate.edu/gunzburg/voronoi.html#quan and http://www.cs.ubc.ca/~ajsecord/npar2002/html/stipples-node2.html for examples -- phrases like "Voronoi diagram" and "Thiessen polygon" look impressive, but the ideas behind them are easy to understand.) In practice, we would say something like "The districting map of the (country, state, county, city) shall be a Voronoi tessellation where each polygon contains equal (population, citizens, adults, voters) and the cumulative distance between Voronoi generators and Voronoi centroids is minimized." By their nature, these polygons are contiguous and compact -- they are also convex, simply shaped, and just look nice (which may not seem important, but federal judges view gerrymandering as they do pornography -- "They know it when they see it"). Just as important is having the ability to compare two or more competing plans with a set standard, and allowing interested citizens and groups of citizens to offer their own plans. On the down side, these polygons ignore roads, rivers, and ridges, communities, city limits and county lines, etc. And while they are easy to calculate for most states, states like New York, Florida, Texas, and *especially* California might be looking at a problem that is impossible to solve exactly -- and redistricting an entire country (not necessarily the U.S.), we would have to settle for "excellent" rather than "perfect" districting. Still, "excellent" is better than the "godawful" method we have now. Michael Rouse [EMAIL PROTECTED]
