Yet another Congressional redistricting proposal

Yet another Congressional redistricting proposal, from Brian Olson.

This proposal is based on the theory that the "best" districting proposal is the one which has the shortest sum of distances from people to the center of their districts.

It sounds like a good idea, but I'm not sure how one would actually find this. Olson claims to. But his program runs by taking the current districting and perturbing it (he has video showing this), which means that the maps look like the current maps. Gerrymandering becomes a bit more difficult because you can't have districts that are oddly shaped. But, for example, the city of Austin, Texas (with a population which is very nearly that of one congressional district, and is politically quite different from the surrounding areas) is shared between three districts in both the old and new maps.

Of course, Olson's method didn't say it wouldn't do that, and in fact Olson addresses the question of his method breaking up communities in his FAQ. But I also wonder if he's only finding a local minimum for the sum of the distance to the centers, while the global minimum might lie with a map that looks radically different. The space of possible districtings of a state is very-high-dimensional so this is the sort of thing one has to worry about. Olson in fact proposes an Impartial Redistricting Amendment which would enshrine this criterion -- but how do we know that his program, or any other program, actually implements it?

What might be interesting is to just assign each census block in a state to a district at random and then run the algorithm. The problem with that is that there's no way the district lines would end up falling in the same place every time.

(Found at O'Reilly Radar, via Statistical Modeling, etc., the full name of which I'm tired of typing.)