When one of the major parties in the United States wins a substantially larger share of the seats than its vote share would seem to warrant, the conventional explanation lies in manipulation of maps by the party that controls the redistricting process. Yet this paper uses a unique data set from Florida to demonstrate a common mechanism through which substantial partisan bias can emerge purely from residential patterns. When partisan preferences are spatially dependent and partisanship is highly correlated with population density, any districting scheme that generates relatively compact, contiguous districts will tend to produce bias against the urban party. In order to demonstrate this empirically, we apply automated districting algorithms driven solely by compactness and contiguity parameters, building winner-take-all districts out of the precinct-level results of the tied Florida presidential election of 2000. The simulation results demonstrate that with 50 percent of the votes statewide, the Republicans can expect to win around 59 percent of the seats without any "intentional" gerrymandering. This is because urban districts tend to be homogeneous and Democratic while suburban and rural districts tend to be moderately Republican. Thus in Florida and other states where Democrats are highly concentrated in cities, the seemingly apolitical practice of requiring compact, contiguous districts will produce systematic pro-Republican electoral bias.
The fear with district design is that the designers could create twisted unnatural districts that ensures a party can win a majority of districts, even if they receive less votes then the opposition.
U.S. congressional districts covering Travis County, Texas (outlined in red) in 2002, left, and 2004, right. In 2003, the majority of Republicans in the Texas legislature redistricted the state, diluting the voting power of the heavily Democratic county by parceling its residents out to more Republican districts.[Wikipedia]
A standard proposed solution to this problem is to take the subjectivity out of drawing districts by requiring districts to be compact(Round). But the authors find that this seemingly fair solution creates a large anti-urban and correspondingly pro-Republican bias unless there are either an absurdly high or absurdly low number of districts.
Republican share of seats after algorithmically creating n compact districts.
The crux of their result lies in a vote-theoretic version of Tobler's law
, that the probability of two voters voting in tandem is roughly inversely proportional to their distance from each other. The paper find empirical evidence of the law in the five elections they looked at.
This is more than just an urban-rural divide because of it's voter-invariance. As can be seen from the map below, there are rural blue counties, and they tend to cluster near other rural blue counties.
Assortative mixing and conformity are the main causes of a Tobler-like relationship that comes to mind. That is to say, either Democrats tend to move away from areas with large numbers of Republicans, or people who live near lots of Democrats tend to conform to local consensus, or a combination of both. Of course, more research is necessary to say which.
But to return to districting, the authors seem to show that a non-trivial consequence of Tobler's law is that placing a compactness restraint on districts produces biased and unrepresentative legislatures.
Then how do we ensure fair and representative districting? Gelman suggests multimember districts as a way around the problem, an idea that Matthew Yglesias has mentioned before. But why not a restraint of the form "If voters from the last election voted under the the proposed districting, the proportion of Democratic seats to Republican seats must be as close as possible to the proportion of Democratic voters to Republican voters"? Of course using Proportional Representation makes this whole issue irrelevant...
Update: Based on questions, I think a summary would be useful:
f we get rid of "funny-looking" districts and make all districts roughly round with equal population, there will be a strong Republican bias. That is to say, some form of gerrymandering(in the form of funny looking districts) is necessary in order to have a representative legislature.
Update 2: In the comments, I wrote the following theoretical explanation for the relationship between Tobler's law and skewed legislatures:
Here's another way to look at it. Suppose that Tobler's law holds (That your probability of voting for the same guy as someone else is inversely proportional with distance) and that your districts have to be roughly circular with equal population(say, 100,000).
Let's consider a district centred in an urban district. Since population density is so high, the circle is going to be pretty small if it's going to have 100,000 people. Because the area is so small, Tobler's law predicts that the variation inside your district is going to be pretty small.
Meanwhile, a suburban district is going to be pretty big, so Tobler's law predicts higher variation in votes then in the smaller district.
The end result is that your urban districts will be really lop-sided, so that the urban party will "waste" most of their votes, leaving the rural party with more seats
The main way around it, is that we have to make our districts funny looking and twisted...which is roughly the status quo, actually. Multimember districts or PR would do it too...