Applying Voronoi Diagrams to the Redistricting Problem Mav10.2007 Abstract Gerrymandering is an issue plaguing legislative redistricting resulting from inade- uate regulation. Here, we present a novel approach to the redistricting problem, an approach that uses a state's population distribution to draw the legislative bound aries. Our method utilizes Voronoi and population-weighted Voronoiesque diagrams and was chosen for the simplicity of the generated partition: Voronoi regions are con- tiguous, compact, and simple to generate. We found regions drawn with voronoiesque diagrams attained small population variance and relative geometric simplicity. As a concrete example, we applied 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 generated 29 regions with an average population of (3.34+0.74)%. We discuss several refinements that could be made to the methods presented which may result in smaller population variation between re gions while maintaining the simplicity of the regions and objectivity of the method Finally, we provide a short statement that could be issued to the voters of New York state to explain our method and justify its fairness to themApplying Voronoi Diagrams to the Redistricting Problem May 10, 2007 Abstract Gerrymandering is an issue plaguing legislative redistricting resulting from inade￾quate regulation. Here, we present a novel approach to the redistricting problem, an approach that uses a state’s population distribution to draw the legislative bound￾aries. Our method utilizes Voronoi and population-weighted Voronoiesque diagrams, and was chosen for the simplicity of the generated partition: Voronoi regions are con￾tiguous, compact, and simple to generate. We found regions drawn with Voronoiesque diagrams attained small population variance and relative geometric simplicity. As a concrete example, we applied 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 generated 29 regions with an average population of (3.34 ± 0.74)%. We discuss several refinements that could be made to the methods presented which may result in smaller population variation between re￾gions while maintaining the simplicity of the regions and objectivity of the method. Finally, we provide a short statement that could be issued to the voters of New York state to explain our method and justify its fairness to them. 1