Fairmandering：公平优化政治选区划分的列生成启发式算法
Fairmandering: A column generation heuristic for fairness-optimized political districting
摘要：
美国赢者通吃的国会选区制度使政治家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绘制无偏见的地图，忽略政治和人口输入，而是简单地优化紧凑性。我们声称，这是一个有缺陷的方法，因为紧凑性和公平性是正交的质量，并引入一个可扩展的两阶段的方法来显式优化任意分段线性定义的公平性。第一阶段是一个随机的分治列生成启发式产生指数数量的不同的区计划，通过利用图分割问题的组成结构。这个地区集合形成了对主选择问题的输入，以选择要包括在最终计划中的地区。我们的解耦设计允许在定义公平对齐的目标函数时具有前所未有的灵活性。管道是任意并行化，是灵活的，以支持额外的重划分约束，并可以应用于广泛的其他区域化问题。在有史以来规模最大的一次对国会选区的整体研究中，我们使用我们的方法来了解可能的预期结果的范围，以及这一范围对公平的潜在定义的影响。
英文摘要：
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.
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