Multiobjective Optimization for Politically Fair Districting: A Scalable Multilevel Approach

Gerrymandering has been a fundamental issue in American democracy for more than two centuries, with significant implications for electoral representation. Traditional optimization models for political districting primarily model nonpolitical fairness metrics such as the compactness of districts. In “Multiobjective Optimization for Politically Fair Districting: A Scalable Multilevel Approach,” Swamy, King, and Jacobson propose optimization models that explicitly incorporate political fairness objectives using political data from past elections. These objectives model fundamental fairness principles such as vote-seat proportionality (efficiency gap), partisan (a)symmetry, and competitiveness. They propose a solution strategy, called the multilevel algorithm, that solves large instances of the problem using a series of matching-based graph contractions. A case study on congressional districting in Wisconsin demonstrates that district plans balance the interests of the voters and the political parties. 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 presents mixed 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 ϵ − 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