A Spatiotemporal Compactness Pattern Analysis of Congressional Districts to Assess Partisan Gerrymandering: A Case Study with California and North Carolina

Compactness of a congressional district is a traditional principle in adjudicating gerrymandering claims in political redistricting. During the last decade, many states have used compactness as an important criterion to constrain the presence of gerrymandering in the redistricting process. In this study, we conducted an array of spatiotemporal analyses aiming to evaluate the changes in compactness between the 112th and 113th Congressional districting plans in California and North Carolina, two states that have been well known for their heavy gerrymandering for years. We employed classic shape-based compactness measures, moment-of-inertia-based measures, and measures of partisan bias to assess the districting plans from multiple angles, including irregularity of district boundaries, spatial dispersion, population-weighted shape dispersion, and partisan symmetry. This new and combined use of spatial measures evidenced remarkable increases on the average compactness scores for California's Congress, suggesting general alleviation of the bipartisan gerrymandering in the previous plan. On the contrary, the partisan gerrymandering in North Carolina intensified in the current map, indicated by the substantial decline in the compactness scores for a majority of the districts. Analysis of partisan bias in the districting plans suggested a very slight bias toward Democrats in California in both districting plans. In North Carolina, the partisan advantage shifted from Democrats to Republicans during redistricting. Comparative analysis between the two families of spatial measures revealed the superiority of the moment of inertia family to the classic shape-based indexes for measuring compactness of congressional districts.