Optimal Legislative County Clustering in North Carolina

TL;DR

This paper introduces an algorithm to optimally cluster North Carolina counties for legislative districts, ensuring compliance with legal guidelines and analyzing the stability and uniqueness of current districting choices.

Contribution

The work presents a novel algorithm that enumerates all optimal county clusterings under legal constraints, aiding transparent and fair redistricting.

Findings

Enacted clusters are optimal but not unique.

The algorithm lists all possible optimal clusterings.

Projected future clusters based on population changes.

Abstract

North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Carolina legislature and courts have provided guidelines that seek to reduce counties split across districts while also complying with the "one person, one vote" criteria. Under these guidelines, the counties are separated into clusters. The primary goal of this work is to develop, present, and publicly release an algorithm to optimally cluster counties according to the guidelines set by the court in 2015. We use this tool to investigate the optimality and uniqueness of the enacted clusters under the 2017 redistricting process. We verify that the enacted clusters are optimal, but find other optimal choices. We emphasize that the tool we provide lists \textit{all} possible optimal county clusterings. We also explore the stability of clustering under changing statewide populations and project what the county clusters may look like in the next redistricting cycle beginning in 2020/2021.