Facilitating Compromise in Redistricting with Transfer Distance Midpoints

Abstract

States in the United States redraw their electoral district boundaries every 10 years. This redistricting process can be contentious and has long-lasting consequences for political representation. To reduce bias in the redistricting process, some states require bipartisan commissions; however, bipartisan commissions can still involve partisan tension if the political parties cannot compromise. We propose an optimization framework to facilitate compromise between two redistricting stakeholders. This framework seeks a midpoint between two stakeholder plans with respect to a distance metric. A midpoint can help the stakeholders visualize a potential compromise that incorporates district structure common to both of their proposed plans. First, we consider multiple distance metrics and evaluate whether midpoints with respect to these metrics are achievable and align with redistricting requirements. Then we formulate a mixed-integer linear program to find a midpoint (or any fractional point) between two given plans with respect to the transfer distance. This formulation incorporates district structure from both given plans by fixing variables; consequently, it is possible to solve some realistically sized instances exactly in reasonable amounts of time. We present experiments on grid instances and Missouri’s congressional redistricting instance to demonstrate how this method can quickly generate compromise options that align with redistricting requirements. Funding: This material is based on work supported by the National Science Foundation Graduate Research Fellowship Program [Grant DGE-1746047]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2023.0029 .