Quantifying Gerrymandering in North Carolina

ABSTRACT

By comparing a specific redistricting plan to an ensemble of plans, we evaluate whether the plan translates individual votes to election outcomes in an unbiased fashion. Explicitly, we evaluate if a given redistricting plan exhibits extreme statistical properties compared to an ensemble of nonpartisan plans satisfying all legal criteria. Thus, we capture how unbiased redistricting plans interpret individual votes via a state’s geo-political landscape. We generate the ensemble of plans through a Markov chain Monte Carlo algorithm coupled with simulated annealing based on a reference distribution that does not include partisan criteria. Using the ensemble and historical voting data, we create a null hypothesis for various election results, free from partisanship, accounting for the state’s geo-politics. We showcase our methods on two recent congressional districting plans of NC, along with a plan drawn by a bipartisan panel of retired judges. We find the enacted plans are extreme outliers whereas the bipartisan judges’ plan does not give rise to extreme partisan outcomes. Equally important, we illuminate anomalous structures in the plans of interest by developing graphical representations which help identify and understand instances of cracking and packing associated with gerrymandering. These methods were successfully used in recent court cases. Supplementary materials for this article are available online.

KEYWORDS:

• Common Cause v. Rucho
• Gerrymandering
• Monte Carlo sampling
• Redistricting

Acknowledgments

A preliminary version of the results presented in this article were first reported to the arXiv repository (Bangia et al. 2017). Bridget Dou and Sophie Guo were integral members of the Quantifying Gerrymandering Team and have significantly influenced this work. Mark Thomas, and the Duke Library GIS staff helped with data extraction. Robert Calderbank, Galen Reeves, Henry Pfister, Scott de Marchi, and Sayan Mukherjee have provided help throughout this project. John O’Hale procured the 2016 election Data. Tom Ross, Fritz Mayer, Land Douglas Elliott, and B.J.Rudell invited us observe the Beyond Gerrymandering Project and this work relies on what we learned there.

Funding

The Duke Math Department, the Information Initiative at Duke (iID), the PRUV, and Data + undergraduate research programs provided financial and material support.