Multiobjective Optimization for Politically Fair Districting: A Scalable Multilevel Approach

• 成果类型: Article
• 署名作者: Swamy, Rahul; King, Douglas M.; Jacobson, Sheldon H.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2311
• 发表日期: 2023
• 页码: 536-562
• 关键词: electoral bias; algorithms; contiguity; COMPETITION

摘要

Political districting in the United States is a decennial process of redrawing the boundaries of congressional and state legislative districts. The notion of fairness in political districting has been an important topic of subjective debate, with district plans affecting a wide range of stakeholders, including the voters, candidates, and political parties. Even though districting as an optimization problem has been well studied, existing models primarily rely on nonpolitical fairness measures such as the compactness of districts. This paper presentsmixed integer linear programming (MILP) models for districting with political fairness criteria based on fundamental fairness principles such as vote-seat proportionality (efficiency gap), partisan (a)symmetry, and competitiveness. A multilevel algorithm is presented to tackle the computational challenge of solving large practical instances of these MILPs. This algorithm coarsens a large graph input by a series of graph contractions and solves an exact biobjective problem at the coarsest graph using the epsilon-constraint method. A case study on congressional districting in Wisconsin demonstrates that district plans constituting the approximate Pareto-front are geographically compact, as well as efficient (i.e., proportional), symmetric, or competitive. An algorithmically transparent districting process that incorporates the goals of multiple stakeholders requires a multiobjective approach like the one presented in this study. To promote transparency and facilitate future research, the data, code, and district plans aremade publicly available.