Political districting to minimize cut edges
Political districting to minimize cut edges
复制标题
DOI：
10.1007/s12532-022-00221-5
复制
发表时间：
2022-04
影响因子：
6.3
通讯作者：
Hamidreza Validi;Austin Buchanan
中科院分区：
文献类型：
--
作者：
Hamidreza Validi;Austin Buchanan
在构建政治选区规划时，突出的标准包括人口平衡、邻接性和紧凑性。区划计划的紧凑程度通常通过“眼球测试”来判断，已通过许多方法进行量化，例如，长度-宽度、Polsby-Popper和转动惯量。这篇文章认为切割边的数量，最近在重新划分的文献中得到了支持，作为紧凑性的衡量标准，因为它很简单，并且与眼球测试合理地一致。我们研究了在种群平衡和邻接性约束下最小化割边数目的风格化问题。利用本文提出的整数规划技术，可以将美国所有的县级实例(以及一些地区级实例)解为最优。我们的技术扩展到最小化加权切割边(例如，最小化区域周长)或施加紧致性约束。所有数据、代码和结果都在GitHub上。
When constructing political districting plans, prominent criteria include population balance, contiguity, and compactness. The compactness of a districting plan, which is often judged by the “eyeball test”, has been quantified in many ways, e.g., Length-Width, Polsby-Popper, and Moment-of-Inertia. This paper considers the number of cut edges, which has recently gained traction in the redistricting literature as a measure of compactness because it is simple and reasonably agrees with the eyeball test. We study the stylized problem of minimizing the number of cut edges, subject to constraints on population balance and contiguity. With the integer programming techniques proposed in this paper, all county-level instances in the USA (and some tract-level instances) can be solved to optimality. Our techniques extend to minimizeweightedcut edges (e.g., to minimize district perimeter length) or to impose compactnessconstraints. All data, code, and results are on GitHub.