Preventing Gerrymandering: A Moving-Knife Algorithm to Draw Districts

• In Event: Redistricting and Representation

Abstract

To prevent gerrymandering of House seats in the U.S. Congress, we describe and apply a moving-knife algorithm (MKA) to draw congressional districts that are nonpartisan and compact. MKA maximizes a measure of geographic compactness, using census data, that precludes political parties from influencing the drawing of district boundaries. It proceeds in the following steps:

1. The minimum bounding circle of a state, which encircles a state as tightly as possible, is drawn, and its Roack score (described next) is computed.

2. The Roack score is the ratio of the area of a state (or smaller entity) to the area of its minimum bounding circle. It ranges between 0 and 1; the greater the Roack score, the more of its area falls within the circle, making it more compact.

3. Starting at the point on the circle due north, 36 points, each 10 degrees apart, are identified on the circumference of the bounding circle.

4. The tangent at each point is computed. One at a time, a line, parallel to the tangent, is moved across a state until it cuts off, as if it were a knife, a portion of the state whose population is that of a single district.

5. Of the 36 districts carved out from the 36 different points around the circle, that district with the largest Roack score is selected as the first district. It is removed from the state, and the procedure is repeated for the diminished state.

6. The procedure is repeated again and again until the state is reduced to only one district, which becomes its last constructed district.

We show that the district with the median Roack score of a state is generally greater than its present score, in some of which gerrymandering occurred following redistricting after the 2000 census. We also show that the closer the Democratic-Republican party split of a state is, the more competitive MKA makes district elections.

To be sure, if a state is predominantly Democratic or Republican, more compact districts will not necessarily be more competitive. But MKA prevents the majority party in a state from deliberating manipulating district boundaries (e.g., by pack-and-crack) to gain an additional advantage. In short, MKA blunts, at least to some extent, the disproportional representation of House seats, especially in competitive states, by creating more compact districts.

Author

• Steven J. Brams, New York University