Why Weight? A Cluster-Theoretic Approach to Political Districting

Political districting has been one of the most contentious issues within American politics over the last two centuries. Since the landmark case of Baker v. Carr, in which the United States Supreme Court ruled that the constitutionality of a state’s legislated districting is within the jurisdiction of a federal court, many within academia have attempted to produce a rigorous system for determining a set of districts for a given state. In this paper, we attempt to improve upon these past efforts. We propose both a modified form of classical K-means clustering and an interesting algorithm called the shortest-splitline algorithm to accomplish impartial redistricting. As an example, we apply our methods to redistricting the state of New York, and, as further examples, to Texas and Colorado. Both methods use only population density data and state boundaries as inputs and run in a feasible amount of time. Our criteria for successful redistricting include contiguity, compactness, and sufficiently uniform population. The K-means method produces districts similar to convex polygons and the splitline method guarantees that the resulting districts have piecewise linear boundaries. The K-means method has the advantage of allowing seeding of the district centers. The centers of the generated districts then roughly correlate to the existing districts, by proper seeding, but the resulting boundaries are vastly simpler.