A New Compactness Metric for Gerrymandering Identification

• In Event: Poster Session: Political Methodology & Political Science Education & Civic Engagement
  In Poster Session: Poster Session: Political Methodology

Abstract

Drawing legislative boundaries is one fundamental task for the functioning of the political system in the United States. Analyzing the form and structure of legislative boundaries, therefore, is instrumental to understanding many political phenomena and their geographic dynamics. Gerrymandering, that is the manipulation of electoral district boundaries to favor particular group interests through “packing” and “cracking”, has been stubbornly difficult to eliminate despite decades of great efforts from political scientists, mathematicians, legal scholars, and engaged citizens. Even though racial gerrymandering against language minorities has been practically claimed unconstitutional and largely prevented, partisan gerrymandering is still prevalent. While one can argue that districting is political by nature and gerrymandering also reflects, to a certain extent, the composition of the underlying constituents, obvious and extreme gerrymanders that generate weird-shaped boundaries suppress the representation of local communities and become a stain on the merit of democracy. To fight the practice of gerrymandering, numerous quantitative metrics have been proposed to characterize and identify gerrymandered districting maps. Of the two main categories of gerrymandering metrics or testing, one is based on the deviation of the election results from those implied by the popular vote, for example, the efficiency gap. However, these metrics can only be used after elections, which apparently bear huge political cost as they would invalidate the whole election if legally supported. More significantly, these election results-derived metrics essentially converge to the popular vote and ultimately suggest the abolishment of the electoral college system. The other category directly measures the compactness of the boundaries and can be applied without election information. Existing compactness measurements for gerrymandering, however, target at particular aspects of gerrymandered shapes such as elongation, indentation, bizarreness, or dispersion without adequately integrating them with spatial context. Gerrymandered shapes are geometrically complex with multidimensional characteristics, yet most of those geometry-based metrics can only address one aspect and fail to consider the geographic context such as population and sub-population distribution, external constraints, and internal topology. Most significantly, they only rank districts without offering a cut-off value to consistently identify gerrymandered boundaries. This paper presents a quantitative gerrymandering metric that delineates the compactness of legislative districts with the consideration of population, constraints, and topology. The metric is based on a series of spatially exclusive, maximum population-enclosing circles and cumulatively calculates their relative proximity to the district center using the spatial network paths within its boundaries. It renders a coherent integration of roundness, convexity, closeness, and spatial context, therefore is more comprehensive and more intuitive than existing metrics. Most noticeably, the metric features a natural threshold of zero for gerrymandering identification, which can conservatively but directly and unambiguously identify gerrymandered boundaries. Applying the new metric to the U.S. congressional districts, historically and comparatively, exemplifies its differences from existing metrics and also illustrates the necessity and value of coherently combine multiple aspects of gerrymandering in a single shape compactness metric.

Author

• Shipeng Sun, Hunter College