Back again (I don’t waste my life sleeping too much). The shortest splitline method is all fine and well (and sounds really cool) but I thought maybe I could do better. Somewhat surprisingly, yes, I think.
First of all, we are going to have to deal with the fact that the earth is more or less spherical. So the curse of the armchair cartographers is upon us, and probably some folks will thus begin talking about “Great Circles,” and I hope most of that can be avoided.
The shortest splitline seems to have some issues, but it goes like this (I think, but could be mistaken): Phase one, you start with some odd-shaped geographical patch of land, and then find the shortest distance between two points where you can divide it into two equal areas. Then in the same fashion, divide each of those two into two equal areas, and so on. (This is over-simple, since we are not reckoning with the number of voters.) The first problem is that the actual “shortest distance” is not perfectly easy to define, since some tiny grain of sand could alter everything about the entire shape, but in the real world, this is not an issue very often. But if you really want to get into the real nitty-gritty you soon find yourself in the land of fractals and chaos theory. But what you really want is to divide the patch of land (at the shortest distance) into two areas having an equal number of (registered) voters. And so on. What results looks something like a broken pane of plate glass. And my best guess is that if one person were to move from one of these areas to another, that could change the entire configuration. You can see where this is going.
Let’s begin from the ground up talking about those thin, one-foot, square vinyl floor tiles. If you have four of them you can easily fit them together to make a bigger four-by-four square, or even go on to make a three-by-three, or a 4’x4’, and so on. So let’s just do that, and we find that the edges where the tiles meet are continuous straight lines, and if we orient ourselves by deciding that we are at an intersection where the line in front of us is facing “north,” that behind us is “south,” to the left is “west,” and to the right is “east.” Now if we want, we can “shift” one column of tiles to the north or south, and then we will find that, unless we move them just far enough that the edges align perfectly again, the edges of these moved tiles will form “T” “intersections” instead of “plus sign” “intersections.” And then this will lock the whole “floor” up so that no pieces can move either east nor west. But we can still “shift” any of the “north-south” columns as much as we like. Likewise, if we shift any row of tiles “east” or “west,” that will lock the pattern so no tiles can be shifted “north” nor “south.”
But we can do even more than this. As long we go either “north-south” or “east-west” (but we cannot do both at once) we can make the tiles as short or as long as we want. So, for a political application example, if we need (14) “districts,” I think we don’t want (2) north-south, by (7) east-west districts because that’s just too crazy. But we can have (3) north-south, by (4) east-west districts (for a total of (12)), plus (2) “at-large” candidates (for a total of (14)), which is more “regular” since (7) is more than twice as big as (2), but (4) is not more than twice as big as (3). (I think we should use reasonably same-size whole numbers for this.) (or we could choose (4) north-south, by (3) east-west districts – more on that later). Now, as per the previous paragraph, we can “slide” either the north-south or the east-west bounds, but not both – you’ll see. Since we have only (3) north-south, but (4) east-west, I think we should position the (3) north-south (“static”) lines to have equal numbers of voters, and then “slide” the east-west bounds into (4) equal-number-of-voters rectangles in each of the (3) north-south columns.
Actually, the north and south may object to being treated differently than the east and west. So maybe we need (2 static) north-souths with (3 sliding) east-wests – plus (2 static) east-wests with (3 sliding) north-souths, for another total of twelve districts, then plus the (2) at-large for the total of (14). Damn that was hard!
Now the earth is spherical, but this just makes no difference. Cadastral land surveyors usually get away with treating the earth as flat, but people who design long highways or navigate long-distance cannot. And any conventional “globe” will treat the world as a giant orange with “wedges” or “sections,” and the earth’s dimensions are mostly defined by the distance between, and orientation of its north and south poles. “Lines of latitude” run in circles east and west, and never intersect with each other, while “lines of longitude” run north and south, and they all intersect at both the north and south poles. This scheme is essentially modeled after the orange fruit, the north pole and south pole being analogous to the oranges stem scar and distal fruit tip with the “lines of longitude” forming the “wedges” or “sections.” While the “lines of longitude” and “lines of longitude” form square-like shapes near the equator and trapezoid-like shapes near the poles, they can still be statically positioned and can slide just like the square vinyl tiles to adjust for voting populations. Each voter will find themself within exactly two of the districts created by this scheme. But since more than one north-south district will generally overlap more than one east-west one, and vice-versa, each candidate must chose one of their districts to run in.
This scheme will produce “regionality” – all district bounds will be “close to home,” and people moving from district to district will not induce complete rearrangement of the district dimensions.