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Gerrymandering and convexity. (English) Zbl 1272.97059

Summary: Convexity-based measures of shape compactness provide an effective way to identify irregularities in congressional district boundaries. A low convexity coefficient may suggest that a district has been gerrymandered, or it may simply reflect irregularities in the corresponding state boundary. Furthermore, the distribution of population within a district can either amplify or lessen the effects of boundary irregularities. As such, it is essential to take both population data and state boundaries into account when using convexity coefficients to detect gerrymandering. The boundary-adjusted convexity coefficient provides an efficient way to do so, and it yields results similar to the shortest-path approach.

MSC:

97M70 Behavioral and social sciences (aspects of mathematics education)
97M40 Operations research, economics (aspects of mathematics education)
91B12 Voting theory
91F10 History, political science
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