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Consider the task of dividing a state into k contiguous political districts whose populations must not differ by more than one person, following current practice for congressional districting in the USA. A widely held belief among districting experts is that this task requires at least k − 1 county splits. This statement has appeared in expert testimony, special master reports, and Supreme Court oral arguments. In this article, we seek to dispel this belief. To illustrate, we find plans for several states that use zero county splits, that is, all counties are kept whole, despite satisfying contiguity and 1-person deviation. This is not a rare phenomenon; states like Iowa and Montana admit hundreds, thousands, or tens of thousands of such plans. In practice, mapmakers may need to satisfy additional criteria, like compactness, minority representation, and partisan fairness, which may lead them to believe k − 1 splits to be minimum. Again, this need not be true. To illustrate, we conduct short case studies for North Carolina (for partisan fairness) and Alabama (for minority representation). Contrary to expert testimony and Supreme Court oral arguments from Allen v. Milligan (2023), we find that fewer than k − 1 county splits suffices, even when subjected to these additional criteria. This demonstrates our narrow point that k − 1 county splits should not be assumed minimum and also suggests that districting criteria do not conflict as much as people sometimes believe. The optimization methods proposed in this article are flexible and can assist mapmakers in satisfying them.
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This content will become publicly available on March 1, 2026
Political Districting to Minimize County Splits
Political Districting to Minimize County Splits When dividing a state into districts for elections, one traditional criterion is that political subdivisions like counties and cities should not be divided unnecessarily. Some states go as far as to say that the number of county splits should be minimized, but previously there was no scalable exact method for determining this. With new integer programming techniques, Shahmizad and Buchanan exactly compute this minimum number for all states and district types (congressional, state senate, state house) across the USA.
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- Award ID(s):
- 1942065
- PAR ID:
- 10579889
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Operations Research
- Volume:
- 73
- Issue:
- 2
- ISSN:
- 0030-364X
- Page Range / eLocation ID:
- 752 to 774
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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