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Applying Voronoi Diagrams to the Redistricting Problem

Summary Gerrymandering is an issue plaguing legislative redistricting. We present a novel approach to redistricting that uses Voronoi and population-weighted Voronoiesque diagrams. Voronoi regions are contiguous, compact, and simple to generate. Regions drawn with Voronoiesque diagrams attain small population variance and relative geometric simplicity. As a concrete example, we apply our methods to partition New York State. Since New York must be divided into 29 legislative districts, each receives roughly 3.44% of the population. Our Voronoiesque diagram method generates districts with an average population of (3.34 ± 0.74)%. We discuss possible refinements that might result in smaller population variation while maintaining the simplicity of the regions and objectivity of the method.