Using a Density-Variation/Compactness Measure to Evaluate Redistricting Plans for Partisan Bias and Electoral Responsiveness

The clear association between population density and partisan preference in elections suggests that redistricting plans would be better aligned with principles of partisan fairness if there were a deliberate effort to balance population density across legislative districts. To balance population density without sacrificing geometric compactness, we define a density-variation/compactness (DVC) measure that can serve as a one-number summary of a proposed redistricting plan. After analyzing voter registration data from California to guide the choice of a specific DVC measure, we evaluate its performance in both actual and hypothetical redistricting plans using election data from Texas during the past decade. Using a well-established political-science model of the relationship between legislative representation and the proportion of votes received, higher DVC scores corresponded to estimates of partisan bias with smaller magnitude across a range of redistricting scenarios; meanwhile, contrary to expectations that reduced partisan bias would be accompanied by reduced electoral responsiveness, there was no discernible pattern between DVC scores and estimates of electoral responsiveness. Although there are apt to be multiple considerations in choosing a redistricting plan, we discuss how the use of DVC measures could provide a check on attempts to introduce partisan bias into the redistricting process.