I suggest (as one of the constraints) that districts should be Dirichlet regions with respect to some set of defining points, P_1, P_2, P_3, ... , P_n, one defining point for each of the n regions.
In other words if you are in district k, then point P_k should be closer to your residence than any of the other defining points. If the defining points are the precinct headquarters, then you just vote at the precinct closest to your home, and you will automatically get the correct ballot. If distance is measured with the Euclidean metric, then the districts will be convex polygons called Voronoi polygons. A more practical metric would be the "estimated travel time" metric. Rental cars with GPS systems have software for deciding the estimated travel time from point A to point B, so we know that this metric can be standardized and computed effectively. This Dirichlet region constraint still leaves enough freedom that other requirements can be met, including the relative equality of the number of voters in each district. Minimization of some other quantity (such as total or max travel distance for voters) subject to these basic constraints could help select from several proposed configurations. Just an idea (capable of modification or adaptation)! Forest ---- Election-methods mailing list - see http://electorama.com/em for list info
