k-means Approach to Legislative Redistricting

Redistricting is a necessary and important process in any democratic society. Modern tools used by legislatures for apportionment of districts are heavily outdated and rely on archaic algorithms. Most use manual redrawing of lines, while others use simulators that simply switch neighborhoods between districts at random until constraints are met. In this document, I outline an attempt to provide a more direct and modern approach by using a modified k-means algorithm. Applying Lloyd’s algorithm to redistricting results in mostly contiguous districts that meet two of the three main constraints for legislative districts in the US. However, LLoyd’s algorithm does not account for population density and therefore creates districts with large disparities in population. My proposed modification adds a heuristic after the update step to account for the current size of the districts. By penalizing districts that already have large populations, the modified algorithm provides a better population distribution. The redistricting by the modified kmeans algorithm converged quickly when there were fewer than 28 districts, but showed significant errors for higher numbers of districts.