Quantifying Gerrymandering in North Carolina

Abstract

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that adheres to realistic and non-partisan criteria. Using the sampled redistricting plans and historical voting data, we produce an ensemble of elections that reveal geo-political structure within the state. We showcase our methods on the two most recent districtings of NC for the U.S. House of Representatives, as well as a plan drawn by a bipartisan redistricting panel. We find the two state enacted plans are highly atypical outliers whereas the bipartisan plan accurately represents the ensemble both in partisan outcome and in the fine scale structure of district-level results.Gerrymandering | Redistricting | Monte Carlo Sampling I n the 2012 NC congressional election, over half the total votes went to Democratic candidates, yet only four of the thirteen congressional representatives were Democrats. Furthermore, the most Democratic district had 29.63% margin of victory, whereas the most Republican district had a 13.11% margin of victory. These results may be due to political gerrymandering or, alternatively, be natural outcomes of NC's geo-political structure as determined by the spatial distribution of partisan votes.To probe the geo-political structure and its effect on election outcomes we (i) sample from the space of congressional redistricting plans that adheres to non-partisan redistricting criteria; (ii) we simulate an election with each of our sampled redistricting plans using the actual partisan votes cast by North Carolinians in the 2012 and 2016 congressional elections; and (iii) we aggregate election results to construct the distributions of partisan vote balance on each district and of the congressional delegation's partisan composition. Districts that do not respect typical election results are considered gerrymandered. When a districting is gerrymandered, the congressional delegation's partisan composition may be not representative of what is typical.Having probed the impact of the geo-political structure, we analyze three specific districting plans: the two most recent districting plans of NC for the U.S. House of Representatives and a plan proposed by a bipartisan panel of retired NC judges. By situating the election outcomes of these three districting plans in our sampled ensemble, we determine whether the three districting plans contain unlikely partisan favoritism and thwart the underlying geo-political structure, as expressed by the people's votes, by shifting each district's partisan vote balance significantly away from what is typical. MethodsTo sample from the space of congressional redistricting plans, we construct a family of probability distributions that are concentrated on plans adhering to non-partisan design criteria from proposed legislation. The non-partisan design criteria ensures that

Lattice Studies of Gerrymandering Strategies

“…Whilst Monte Carlo methods have been previously employed for detection of gerrymandering, for instance [Herschlag, 2018;Herschlag et al, 2017], and also towards constructing fair districts, e.g. [Fifield et al, 2015], to our knowledge this is the first study to apply a Monte Carlo approach to look to quantify general features of gerrymandering.…”

Geometry of Graph Partitions via Optimal Transport

“…Ensemble-based redistricting. A growing body of scientific research centers on ensemble-based redistricting, which uses mathematical and algorithmic techniques to generate and analyze a collection of thousands or millions of candidate districting plans that meet some criteria [2,6,7,8,12,21,22]. These methods and analyses are increasingly used as quantitative tools by legal experts, policymakers, and the public at-large to inform debates around redistricting.…”

“…In information theory, the Hamming distance between two binary strings of equal length is the number of positions in which they differ. Inspired by this definition, the authors in [21] compute a notion of Hamming distance between two graph partitions X and Y . Using v ∈ x i to indicate that vertex v belongs to component i of partition X, the Hamming distance is defined as…”

“…The grid graph partitions in §8.2 and the Markov chain sampling in subsections 8.4 to 8.6 rely on the enumerator [36] and GerryChain [28] open source software packages available on GitHub. The spatial and electoral data comes from the Metric Geometry and Gerrymandering Group's mggg-states repository [29], the NHGIS database [26], and the data accompanying [21] from the Quantifying Gerrymandering group [20].…”

Utility Ghost: Gamified redistricting with partisan symmetry

“…In 2018, the Pennsylvania Supreme Court struck down the 2011 congressional map as an unconstitutional partisan gerrymander; here, the plantiffs leveraged Markov Chain-based techniques to sample the space of admissible maps and make informative comparisons with the map in question [5]. This trend of policing partisan gerrymandering in the courts has led to a flurry of relevant mathematical research, primarily in Markov Chain Monte Carlo sampling methods [6,3,9,8,16] and in evaluating various fairness criteria [4,14,1,2,10]. However, in light of recent changes to the U.S. Supreme Court bench, a new approach might be necessary to effectively combat partisan gerrymandering in the future.…”