Note: this is more of a thought experiment than a serious suggestion -- the number of states and districts is not a power of two for one thing, and there are problems with long, skinny districts -- but it does show an automated way of coming up with a single apportionment answer, and it might point to a method we can agree on.
To illustrate, assume we want to break up the United States into 64 states, or perhaps Canada and Mexico have combined with the United States to form a North Americal Union and we want to divide the Union into 64 regions. Find the population centroid for the country, then find the geographic centroid. Draw the great circle that runs between them and continue until the line reaches both borders. You now how two clearly defined sections of roughly equal population. Find the population and geographic centroids for each of these sections, draw another great circle line for each set, and continue until you have 64 states (regions). Each "state" should have *roughly* equal area and population. (I say "roughly" because of the teeter-totter effect -- a small group of people far away will balance a larger group nearby -- which is why I have it going through the geographic centroid as well.) As an alternative, you could use the point where the north-south population median crosses the east-west population median, then take the line between that and the geographic centroid. In either case, everyone who followed the definition accurately would end up with the same result, regardless of party. Instead of a power of two, we could redo the lower 48 contiguous states. Ignoring Alask and Hawaii, cut the country in thirds -- Pacific, Atlantic, and Central -- with equal populations, and the borders defined by longitude lines (in other words, find the line of longitude where one third of the population of the country is west of the line, and then find another where one third of the population is east of the line. Those two lines will divide the country cleanly). Within these three regions, find the population and geographic centroids, draw lines through them, and repeat until each region has 16 "states," giving a total of 48 states. We can keep going within these states until each state has 8 districts, or 384 districts plus Alaska and Hawaii, as opposed to 435 districts we have now. (We could of course do the same thing with lines of latitude -- north, middle, and south -- and divide each region into 16 parts, but lines of latitude are not great circles, and the regions would be more elongated to begin with). As mentioned above, one of the problems is that you could easily end up with long, skinny, not-at-all-compact districts. Another problem is the districts would completely ignore present political, historical, racial, and geographic groupings -- it might take a thin sliver out of the center of a city but extend far out into rural areas, and across our present state boundries. On the other hand, each district would be a simple, closed, and convex figure, with a near-minimum of jaggedness, and there would be only one result possible for each census. The tesselations would also make a cool mosaic (grin). If the results were too strange -- districts stretching acrossed time zones or shaped like slivers of glass -- the population centroid of each district could be used as a "seed" result, with an algorithm moving census blocks between districts to make each each district more compact. This would allow some variability, but the "seeds" would limit the amount of gerrymandering possible. Michael Rouse [EMAIL PROTECTED]
