Calculus of Variations and Geometric Measure Theory

A. Saracco - G. Saracco

A discrete districting plan

created by saracco on 21 Dec 2018
modified on 21 Oct 2019


Published Paper

Inserted: 21 dec 2018
Last Updated: 21 oct 2019

Journal: Netw. Heterog. Media
Volume: 14
Number: 4
Pages: 771--788
Year: 2019
Doi: 10.3934/nhm.2019031

ArXiv: 1812.05047 PDF


The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing the shape of electoral districts in order to win the forthcoming elections. While so far the problem has been treated using continuous analysis tools, it has been recently pointed out that a more reality-adherent model would use the discrete geometry of graphs or networks. Here we propose a parameter-dependent discrete model for choosing an ``optimal'' districting plan. We analyze several properties of the model and lay foundations for further analysis on the subject.

Keywords: Graphs, isoperimetric problem, networks, discrete geometry, gerrymandering