Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#352187] of Gregory J. Herschlag

Papers Published

  1. Herschlag, G; Kang, HS; Luo, J; Graves, CV; Bangia, S; Ravier, R; Mattingly, JC, Quantifying Gerrymandering in North Carolina, Statistics and Public Policy, vol. 7 no. 1 (January, 2020), pp. 30-38, Informa UK Limited [doi]
    (last updated on 2021/12/03)

    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.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320