Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T16:54:39.446Z Has data issue: false hasContentIssue false
  • English
  • Français

Partisan gerrymandering with geographically compact districts

Part of:Markov processesStochastic processes

Published online by Cambridge University Press:  16 January 2019

Boris Alexeev and
Dustin G. Mixon
Boris Alexeev*
Affiliation:
The Ohio State University
Dustin G. Mixon*
Affiliation:
The Ohio State University
*
* Postal address: Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA.
* Postal address: Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Bizarrely shaped voting districts are frequently lambasted as likely instances of gerrymandering. In order to systematically identify such instances, researchers have devised several tests for so-called geographic compactness (i.e. shape niceness). We demonstrate that under certain conditions, a party can gerrymander a competitive state into geographically compact districts to win an average of over 70% of the districts. Our results suggest that geometric features alone may fail to adequately combat partisan gerrymandering.

Keywords

GerrymanderingBrownian motion

MSC classification

Primary:60G50: Sums of independent random variables; random walks
Secondary:60J65: Brownian motion

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018, pp. 1046 - 1059
Copyright
Copyright © Applied Probability Trust 2018 

References

[1]Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th edn. Dover, New York, pp. 258–259.Google Scholar
[2]Bernstein, M. and Duchin, M. (2017). A formula goes to court: partisan gerrymandering and the efficiency gap. Notices Amer. Math. Soc. 64, 1020–1024.10.1090/noti1573Google Scholar
[3]Borodin, A. and Salminen, P. (1996). Handbook of Brownian Motion. Birkhäuser, Basel.Google Scholar
[4]Choi, B. S. and Roh, J. H. (2013). On the trivariate joint distribution of Brownian motion and its maximum and minimum. Statist. Prob. Lett. 83, 1046–1053.10.1016/j.spl.2012.12.015Google Scholar
[5]Duchin, M. (2017). Redistricting 101: Metrics for gerrymandering. Tech. Rep. Duke University. Available at http://sites.duke.edu/gerrymandering/files/2017/11/MD-duke.pdf.Google Scholar
[6]Gill v. Whitford, . (2017). U.S. 585, 1b-1161.Google Scholar
[7]Herschlag, G.et al. (2018). Quantifying gerrymandering in North Carolina. Preprint. Available at http://arxiv.org/abs/1801.03783.Google Scholar
[8]Ingraham, C. (2014). America’s most gerrymandered congressional districts. Washington Post, May 15. Available at https://www.washingtonpost.com/news/wonk/wp/2014/05/15/americas-most-gerrymandered-congressional-districts.Google Scholar
[9]Polsby, D. D. and Popper, R. D. (1991). The third criterion: compactness as a procedural safeguard against partisan gerrymandering. Yale Law Policy Rev. 9, 301–353.Google Scholar
[10]Reock, E. C. (1961). Measuring compactness as a requirement of legislative apportionment. Midwest J. Political Sci. 5, 70–74.10.2307/2109043Google Scholar
[11]Soberón, P. (2017). Gerrymandering, sandwiches, and topology. Notices Amer. Math. Soc. 64, 1010–1013.10.1090/noti1582Google Scholar
[12]Smith, J. D. (2014). On Democracy’s Doorstep: The Inside Story of how the Supreme Court Brought, “One Person, One Vote” to the United States. Hill and Wang, New York.Google Scholar
[13]Stephanopoulos, N. O. and McGhee, E. M. (2015). Partisan gerrymandering and the efficiency gap. Univ. Chicago Law Rev. 82, 831–900.Google Scholar
[14]Wisconsin State Legislature Open GIS Data. (2018). WI election data with 2017 wards. Available at https://data-ltsb.opendata.arcgis.com/datasets/2012-2020-wi-election-data-with-2017-wards.Google Scholar