Al Gore and gerrymandering

Al Gore writes in his new book The Assault on Reason (pp. 238-239), commenting on the fact that U. S. Senators serve for longer terms (six years) than U. S. Representatives (two years):

"Until recently, it followed that House seats turned over more frequently than Senate seats.

In recent years, that juxtaposition has flipped. In the four elections of the new millennium, House members have been reelected an average of 96 percent of the time, compared with Senate members, who have been reelected only 85 percent of the time, according to Rhodes Cook, an expert on election statistics. It is now statistically easier for a House member to be reelected three times in succession than it is for a senator to be reelected once. As a result, the Founder's intention that House members would be on a shorter `leash" and more responsive to the public than the Senate, has been stood on its head."

This is in a chapter in which Gore argues that a lot of what our nation's Founding Fathers stood for has been changed. You might say that it doesn't matter which house is the one that turns over quicker -- but the two chambers are not symmetric. One could distinguish a world in which the Senate was the chamber with more turnover than one in which the House was.

The mathematical content here isn't particularly strong. We can compute that the probability of a House member staying in power for six years (three House terms) is (.96)³, which is 88%; this isn't all that much more than 85%. Still, though, the conventional wisdom is that the House turns over faster than the Senate, so it surprised me to read this.

Of course, the reason why House seats turn over faster than Senate seats is due to gerrymandering. Gerrymandering, for those who don't know, is the practice of devising Congressional districts which are shaped in such a way as to take advantage of how members of the two parties are distributed in space. A particularly egregious example is the second district of Arizona, which is basically two disjoint pieces connected by the Grand Canyon. Nobody lives in the Grand Canyon, because it's a giant hole in the ground. The reason for doing this, of course, is that the people at the eastern and western ends are in the same political party.

I've seen proposals that require a certain amount of "compactness" in a district, usually measured as something like the area of a district over the square of its perimeter; the isoperimetric inequality tells us that this is minimized for a circle, and it's very large for districts like the Arizona 2nd.

There are, in fact, mathematical algorithms to abolish gerrymandering. The one that I linked to is called the "shortest splitline" algorithm; it works by splitting states up into districts by drawing lines which are as short as possible to successively divide the population in half. (I'm simplifying a bit; what I said is only strictly true if the number of districts is a power of two.) This ensures that the districts are at least convex (intuitively, this means they don't have "dents") if the state is; many of them are triangles or quadrilaterals. Since this pays absolutely no attention to the way people tend to vote, it's seen as "impartial".

I'm not sure how I feel about this, though, just because people's settlement patterns don't fall along straight lines. My instinct is to propose a system that tries not to divide counties if at all possible; historically counties in the United States are of roughly uniform size and shape (especially in sparsely settled western states like Nebraska, but even densely populated eastern states like New Jersey or Massachusetts are fairly compact. Furthermore, county lines can't be redrawn nearly as casually as congressional district lines can be. But there are plenty of counties that have a much larger population than a congressional district (roughly 700,000 at the moment), so this isn't perfect either.

Still, it's probably a lot better than the current system.

If you want to get your own experience with gerrymandering, there's something called the redistricting game which is floating around, which has been mentioned by the New York Times and Slashdot.