On Monday, a three-judge federal panel reaffirmed its earlier decision that North Carolina’s congressional map is unconstitutionally gerrymandered and ordered further proceedings to determine how to replace it before the November election.
If these districts are replaced by the court, this November would mark the first time this decade that North Carolina congressional elections would be conducted with maps that are not unconstitutional.
As North Carolina-based scholars, we have brought our expertise to bear on the legal and quantitative problems at the heart of this gerrymandering litigation. These efforts have included developing and applying mathematical methods, providing expert testimony and filing amicus briefs. We have reason to believe that the latest North Carolina ruling, along with the methods supporting it, will be upheld by the Supreme Court and provide a path forward to fight future gerrymanders.
A key analytic method used in this case is our idea to generate thousands of alternative district maps complying with neutral, nonpartisan redistricting criteria. Using historical voting data, we determine the district-level partisan makeup of each compliant map. The overall collection of compliant maps, called an “ensemble,” allows us to determine a typical range of results based on the partisan makeup at the district level.
We can use this range to test whether the enacted map falls within this typical range. Maps that are extreme outliers when compared to the ensemble are labeled partisan gerrymanders.
For instance, among our 24,518 maps and considering 2012 election votes, no map had as many Democrats packed in North Carolina’s three most Democratic districts (Districts 1, 4 and 12) or as many Republicans in the next three most Democratic districts (Districts 2, 9 and 13) as the current plan. This could have profound implications for the election outcome.
This ensemble method, developed by us and others, has several scientific strengths.
First, unlike other methods, we make no assumptions about what the result of an election should have been; instead the ensemble, along with the state’s geopolitical make-up, reveals the range of typical election results. The ensemble also reveals the structural bias in a state’s electoral system; for example, systematic disparities between the residential patterns of Republicans and Democrats. In this way, we are able to distinguish between natural partisan geography and partisan bias that disenfranchises voters.
Additionally, our method separates the often politically charged discussion of redistricting criteria from the more mechanical procedure of generating an ensemble. While guidance from the courts, legislation and tradition can be brought to bear on the debate over redistricting criteria, experts in statistical and geographic computation can evaluate alternative methods of generating compliant maps.
Several research groups, including ours, are investigating how best to generate these ensembles. Once generated, the ensemble serves as a baseline for analyzing the allegedly gerrymandered map, and this analysis may vary depending on the legal question at hand. Thus, each of the three components of our method — specifying redistricting criteria, generating the ensemble and analyzing the challenged map — can be critiqued and vetted independently.
Monday’s 321-page decision closely examined and ultimately endorsed our application of this method to the challenged North Carolina congressional redistricting. We were gratified that the judges understood our analysis and visualizations and used them to draw their own opinion, calling the evidence of the legislative defendants’ discriminatory intent and effect both “strong” and “compelling” in 12 of the state’s 13 districts.
In addition to the federal case in North Carolina, a state supreme court decision in Pennsylvania has confirmed the strength of the ensemble method. In League of Women Voters v. Pennsylvania, the court found that the state’s congressional map violated the state constitution’s guarantee of free and equal elections, citing evidence based on localized comparisons to an ensemble of nonpartisan maps.
Our ensemble approach provides a normative standard for measuring partisan gerrymandering. It is informed by a state’s political systems and geopolitical landscape. It can speak to standing, intent and harm. If the courts continue to accept ensemble methods, our democratic institutions will better hear the will of the people as expressed in our votes.
Guy-Uriel Charles is a professor of law at Duke University; Andrew Chin is a professor of law at the University of North Carolina, Chapel Hill; Gregory Herschlag is an assistant research professor of mathematics at Duke; Jonathan C. Mattingly is a professor of mathematics and statistical science at Duke.