A related topic is Gerrymandering. This is when Congressional Districts are drawn in complex and contorted fashion in order to include certain neighborhoods and the voters that live there, and exclude others.
Two measures of how badly a District is Gerrymandered are "compactness" and "community".
A compact district is one with a simple shape, with a minimum of irregularities on its boundary. This is a good measure of a district that has not been Gerrymandered. One way to measure compactness is to compare the area of a polygon with its perimeter. A simple polygon, with no "ins and outs" will have a smaller perimeter compared to its area than a polygon that is very complex and contorted, such as the example in Figure 1. This is New York District #7, which I determined from my analysis to be the least compact of all the House districts in the continental United States. It is not so easy to see at this scale, but there are many tiny jagged features along the boundary of this district. The thick red part of its west boundary is actually composed of a long series of very small ins and outs, on the scale of a block or less. This level of small-scale irregularity adds up to a very large perimeter, and a very complex district shape, and suggests that it has been Gerrymandered.
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| Figure 1. New York Congressional District #7 |
A high level of "community" in a District indicates that a District does not suffer too badly from Gerrymandering. "Community" is measured here by how much counties are cut by District lines and separated among various Districts. I determined this by identifying the counties that are cut by at least one District line, then finding the Districts with the most "cut" counties. Figure 2 shows North Carolina District #1. It cuts parts out of 20 counties, and contains no whole counties at all. This district has a very low level of "community", by our definition, and this hints at a lot of Gerrymandering.
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| Figure 2. North Carolina District #1 |
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