I assume most people know that, in the U.S., the States are divided up into "districts" for various political reasons. One major reason is that the laws, the Constitution, and the U.S. Census require each state to be able to appoint some certain number of Representatives to the U.S. House of Representatives, based on each state's population. And at least theoretically, each district is supposed to contain (very nearly) the same number of voters. However, the way in which each state is geographically divided up (the "shape" of the districts) can readily provide whatever regime performs the occasional redistricting scheme with tremendous advantages (this is called "gerrymandering"). And, unfortunately, whatever regime happens to be in power gets to dictate redistricting schemes (the courts occasionally attempt to remedy the very most flagrant abuses).
This has inspired comrade Warren D. Smith to come up with a "shortest splitline districting method". This method is algorithmic in nature, so it may be expected to remove any influence whatever regime happens to be in power may have in determining redistricting schemes. Overlooking some minuscule, readily remediable edge cases (such as off-by-one dilemmas), I will attempt to describe this method. I will ignore the complication that the earth is round and not flat for now. With the shortest splitline method, you take a map of the relevant region or state and find the shortest straight line that divides it into two geographic parts that contain an equal number of voters. Then you divide each of those two parcels into two more such parts until you have the requisite number of equally populated parcels corresponding to the required number of Representatives. And this is purely algorithmic and should be expected to eliminate the influence of whatever political regime happens to be in power. So far, so good.
But there are a few hairy edges. Actually, every redistricting plan developed by this method seems to somewhat resemble a broken pane of flat transparent glass. One has every expectation that each result is due to a totally chaotic process. In fact, it could reasonably expected that if a few voters should move in or out of any one district, the entire pattern of the plan would likely shift into a completely different pattern of division of districts. This could be quite disconcerting. Also, geography is notoriously (not to mention historically) fractal. What this leads to is that two algorithms that are sensitive to differing scales of measurement (one perhaps being sensitive to tiny incursions of territory that the other ignores, the potential number of these tiny features being virtually infinite) could very possibly generate two dramatically different redistricting plans. And the whole process really seems to provide a wonderful playground for chaos theorists. But this troubled me.
So after months of perplexity, I came across a few interesting things. Let's begin with a few thought experiments, which I will describe now. Let us obtain sixteen typical red building blocks, or to avoid heavy lifting, sixteen dominoes. These are easy to move around, since they are three dimensional rectangles (actually called "cuboids"). Now, let us arrange them to all have the same orientation, so if each one is, say, two inches by four inches, the total arrangement of all sixteen will be 4*2" by 4*4". OK this is nice. Suppose we have laid them on the floor in front of us and their east side is to our right, their west side is to our left, their north is farthest away, and their south side is closest to us. The north to south groups of blocks we will call "columns", and the east to west groups of blocks we will call "rows". Now suppose we move any one of the columns north by half an inch. This will lock all of the rows from moving either east or west. Or, if we were to move any row east by half an inch, we will lock all of the columns from moving north or south. Well this is a problem, as we can move all of the columns north or south as much as we like, or all of the rows east or west all we like, but we must choose one way of movement or the other, and cannot have both. Or... can we?
The earth is round, so we must deal with arc segments rather than straight line segments, but this makes no difference in the end. Latitude and longitude will work just the same way as Cartesian coordinates for our purposes. I will favor north-south distinctions over east-west distinctions simply because of minor climate distinctions. So let's say that some state, by virtue of population numbers, is entitled to ten Representatives. 10 = 2*5. So first dividing north to south, we could define five latitudes, each with an equal number of voters. Every voter in each of those latitudes gets to vote for potential Representatives who live in their latitude. Hopefully using strategic hedge simple score voting. But there are still two longitudes, and of course they are selected to have an equal number of voters. So each voter gets to vote in essentially two elections, one in which they get to choose a latitudinal Representative, and another in which they get to choose a longitudinal Representative. This is easy if each voter, who will automatically live in two kinds of districts, will have two ballots, one for each (overlapping) district.
This could be further rationalized. There could be three latitudinal, and three longitudinal elections, and one at-large election (there could be a rule requiring the number of latitudes and longitudes to be no greater than twice one or the other). This has great precedence since, for example, the state of Texas has often had at-large Representatives, mostly due to geographical impediments.
This would make the algorithmic determination of districts vastly simpler. And would also make districting far more coherent to the voters.