Measuring the circularity of congressional districts

Balázs Nagy () and Szilvia Szakál
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Balázs Nagy: Department of Mathematics, Corvinus University of Budapest, Budapest, Hungary
Szilvia Szakál: Department of Mathematics, Corvinus University of Budapest, Budapest, Hungary

Society and Economy, 2020, vol. 42, issue 3, 298-312

Abstract: Shape analysis has special importance in the detection of manipulated redistricting, which is called gerrymandering. In most of the US states, this process is made by non-independent actors and often causes debates about partisan manipulation. The somewhat ambiguous concept of compactness is a standard criterion for legislative districts. In the literature, circularity is widely used as a measure of compactness, since it is a natural requirement for a district to be as circular as possible. In this paper, we introduce a novel and parameter-free circularity measure that is based on Hu moment invariants. This new measure provides a powerful tool to detect districts with abnormal shapes. We examined some districts of Arkansas, Iowa, Kansas, and Utah over several consecutive periods and redistricting plans, and also compared the results with classical circularity indexes. We found that the fall of the average circularity value of the new measure indicates potential gerrymandering.

Keywords: redistricting; circularity measure; Hu moment invariants; gerrymandering; political manipulation; United States congressional districts (search for similar items in EconPapers)
JEL-codes: D72 (search for similar items in EconPapers)
Date: 2020
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