Evolutionary algorithms for solving single- and multiple-objective political redistricting problems: The case study of Poland

Abstract

We propose novel evolutionary algorithms for solving single- and multi-objective political redistricting problems. The objectives include population equality, compactness of districts, deviation from the current districting, and an expected number of mandates attainable by some parties. The former two ensure the constructed solutions are reasonable, while the latter pair is meaningful for the post-analysis on how the alternation of existing districts may affect election outcomes. We operate on data concerning geography, demography, and politics in Poland. The experiments reveal that our algorithms efficiently handle the four-objective variant of the problem. In a single test run, we evaluate around one million solutions in nearly two hours on an average class computer, which is satisfactory given the problem’s complexity. The methods construct high-quality non-dominated solutions, outperforming the current districting and revealing the trade-offs between the objectives. The post-analysis allows us to observe connections between the expected number of mandates and the remaining three objectives. Specifically, attaining a greater number of mandates requires more significant changes in delineating the districts and potential violations of constraints. We also exhibit that the space for possible political manipulations increases when more districts can be determined.