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Fairmandering: A column generation heuristic for fairness-optimized political districting
arXiv - CS - Discrete Mathematics Pub Date : 2021-03-21 , DOI: arxiv-2103.11469
Wes Gurnee, David B. Shmoys

The American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries. Existing computational solutions mostly focus on drawing unbiased maps by ignoring political and demographic input, and instead simply optimize for compactness. We claim that this is a flawed approach because compactness and fairness are orthogonal qualities, and introduce a scalable two-stage method to explicitly optimize for arbitrary piecewise-linear definitions of fairness. The first stage is a randomized divide-and-conquer column generation heuristic which produces an exponential number of distinct district plans by exploiting the compositional structure of graph partitioning problems. This district ensemble forms the input to a master selection problem to choose the districts to include in the final plan. Our decoupled design allows for unprecedented flexibility in defining fairness-aligned objective functions. The pipeline is arbitrarily parallelizable, is flexible to support additional redistricting constraints, and can be applied to a wide array of other regionalization problems. In the largest ever ensemble study of congressional districts, we use our method to understand the range of possible expected outcomes and the implications of this range on potential definitions of fairness.

中文翻译:

费尔曼德(Fairmandering):针对公平性优化的政治区划的列生成启发法

美国的“全胜制”国会选区系统使政治人物能够通过操纵选区边界来设计选举结果。现有的计算解决方案主要集中在通过忽略政治和人口统计输入来绘制无偏地图,而是简单地进行紧凑性优化。我们认为这是一种有缺陷的方法,因为紧致性和公平性是正交性质,并且引入了可扩展的两阶段方法来明确优化公平性的任意分段线性定义。第一个阶段是随机化的分治列生成启发式算法,它通过利用图划分问题的组成结构来生成指数数量的不同区域规划。该区域集合构成对主选择问题的输入,以选择要包括在最终计划中的区域。我们的解耦设计在定义公平对齐的目标函数时提供了前所未有的灵活性。该管道可以任意并行化,可以灵活地支持其他重新分配约束,并且可以应用于其他各种区域化问题。在有史以来规模最大的国会选区研究中,我们使用我们的方法来理解可能的预期结果的范围以及该范围对公平的潜在定义的影响。并可以应用于其他许多区域化问题。在有史以来规模最大的国会选区研究中,我们使用我们的方法来理解可能的预期结果的范围以及该范围对公平的潜在定义的影响。并可以应用于其他许多区域化问题。在有史以来规模最大的国会选区研究中,我们使用我们的方法来理解可能的预期结果的范围以及该范围对公平的潜在定义的影响。
更新日期:2021-03-23
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