Optimal Legislative County Clustering in North Carolina

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 the courts have provided guidelines that seek to reduce counties split across districts while also complying with the “one person, one vote” criterion. Under these guidelines, the counties are separated into clusters; each cluster contains a specified number of districts and that are drawn independent from other 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 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. Supplementary materials for this article are available online.

KEYWORDS:

• Gerrymandering
• Optimization algorithm
• Redistricting
• Whole County Provision

Acknowledgments

The authors are thankful to Blake Esselstyn and Eddie Speas bringing this important question to our attention as well as generally educating us about legal and GIS issues involved. This project began as a project in a year long research experience hosted at Duke University for students from the North Carolina School of Science and Mathematics.

Funding

The authors acknowledge support from a grant from Imagine North Carolina First which partially supported GH and the summer work of DC and ZH as well as the Mathematics Department and the Rhodes Information initiative at Duke for hosting this work.

Notes

1 For example, of the 100 counties in North Carolina, Mecklenburg county has enough population to hold 12 State House districts and so must be split to achieve population parity across the other 119 districts.

2 Git repository available at https://git.math.duke.edu/gitlab/gjh/countycluster.git

3 See Section 6 and Appendix C in the supplementary materials for a more thorough discussion of this fact.

4 Annual Estimates of the Resident Population: April 1, 2010 to July 1, 2018, May 2019.

5 This measure was used in the early drafts of this article, but omitted in later drafts.

6 The two 2010 datasets represent only 3 months of population change and the APC was just 0.3%.

7 The possibly preserved Senate clusters are the Lincoln-Cleveland-Gaston county cluster, which is the southeastern light blue 2-district cluster of the leftmost option (A) in Figure 6(a), and the Pitt-Greene county cluster which is the brown central 1-district cluster of the leftmost option (B) in Figure 6(a)

8 The preserved House clusters are the Ashe-Watauga (1 district), Caldwell (1 district), Caswell-Orange (2 districts), Union-Anson (3 districts), Buncombe (3 districts), Macon-Cherokee-Clay-Graham (1 district), Lincoln (1 district), Davidson (2 districts), Iredell (2 districts), Guilford (6 districts), and Alamance (2 districts) clusters; on the map these county clusters are found in Figure 6(b) to be the orange-yellow northern most district with 1 district to the west, the brown single district cluster immediately south of the previous cluster, the northern-most central light blue two district cluster, the green three district cluster on the southern border, the green three district cluster toward the west of the state, the western-most green one district cluster, orange-yellow one district cluster next to the brown 13 district cluster, the central brown 2 district cluster, the bright yellow 2 district cluster to the west of the previous cluster, the bright-yellow 6 district cluster, and the green two district cluster immediately east of the previous cluster, respectively.

9 See Appendix C.2 in the supplementary materials for the exact alterations we make to the algorithm.

10 Legislator’s Guide to North Carolina Legislative and Congressional Redistricting, March 2011.