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Multi-balanced redistricting

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Abstract

The one person–one vote principle for political redistricting requires balancing populations across districts. We address the matter of simultaneously balancing a second attribute across districts, proving that this is always possible to within reasonable tolerances. Feasibility is demonstrated by formulating the problem as a constrained partitioning problem on graphs. The resulting computational results demonstrate the practicality of obtaining dual-balanced districts whose balance for both attributes is well within reasonable deviations from the ideal values. Applications include attempts to avoid differential population growth leading to malapportionment between decennial census counts or simultaneously balancing total and voting-age populations.

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Data availability

The raw data used in this paper is publicly available from [20, 21] and https://redistrictingdatahub.org. Replication code for the empirical experiments is available at [14].

Notes

  1. https://redistrictingdatahub.org.

  2. This is sometimes referred to as “eligible-voter” redistricting where the plans are balanced according to citizen, voting-age population, or CVAP.

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Acknowledgements

E. K. was supported by the Ellen Hauge Abelson Scholarship for undergraduate research from the Washington State University College of Arts and Sciences.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA

    Daryl DeFord

  2. Washington State University, Program in Data Analytics, Pullman, WA, USA

    Elliot Kimsey

  3. Department of Mathematics, University of North Dakota, Grand Forks, ND, USA

    Ryan Zerr

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  1. Daryl DeFord
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  2. Elliot Kimsey
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Correspondence to Daryl DeFord.

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Conflict of interest

D. D. has previously served as an expert in redistricting cases. E. K. and R. Z. have no conflicts to report.

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DeFord, D., Kimsey, E. & Zerr, R. Multi-balanced redistricting. J Comput Soc Sc 6, 923–941 (2023). https://doi.org/10.1007/s42001-023-00217-8

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