Inter‐person Separation: A New Objective Standard for Evaluating the Spatial Fairness of Political Redistricting Plans

Abstract

The fundamental basis for territorial political representation is the presumption that people share greater common interests with others in closer geographic proximity than with people farther away. This principle is found in U.S. legal requirements that districts for the House of Representatives and state legislatures should not needlessly divide “communities of interest” and should be “reasonably compact.” We propose a new objective standard to evaluate spatial fairness of redistricting plans: the extent to which a delineation minimizes total distance between all pairs of people assigned to the same district. To date, the legal standard of compactness has primarily been thought of in terms of the shapes of political districts, but boundary shape may have little correspondence with how populations are actually clustered and dispersed. Inter‐person separation, by contrast, provides a direct, intuitive metric for evaluating the congruence of districting plans with the territorial basis of political representation. To operationalize an inter‐person separation standard, we propose a model and present a heuristic method for delineating comparator districting schemes. We apply the standard to the current U.S. Congressional Districts in the states of Arizona and North Carolina to demonstrate how inter‐person separation could be used to develop and vet future redistricting plans.

An iterative local search based hybrid algorithm for the service area problem

“…However, 4 h of computation time were used to solve the problem instances with 150 units and 6 territories. Plane et al (2019) proposed a minimum inter-person separation model for political districting. For instances with 6 × 6 grids can be solved optimally or near-optimally in 6.30-53,632.22 s. Kong et al (2019) formulated a center-based allocation model with flow-based constraints on district contiguity to solve the districting problem.…”