不公正划分选区的（同源）持久性
The (homological) persistence of gerrymandering
摘要：
我们应用持续同源，从拓扑数据分析领域的主导工具，研究选举选区重划。我们的方法结合了地理信息的政治选区规划与选举数据产生的持久性图。然后，我们能够可视化和分析计算机生成的分区计划的类型通常用于现代重新划分研究（和法院的挑战）的大型合奏。我们列出了三个应用程序：在每一个选区的规模划分一个州，比较选举，并寻求gerrymandering的信号。我们的案例研究集中在宾夕法尼亚州和北卡罗来纳州的选区重划，这两个州在过去几年中对已颁布的计划提出了法律挑战，引起了相当大的公众兴趣。为了解决这个问题的持久性图的扰动在投票数据和地区边界的鲁棒性，我们翻译的经典稳定性定理的科恩-施泰纳等人。到我们的设置，并发现它可以措辞的方式，是很容易解释。我们伴随着理论界的实证演示，以说明图在实践中的稳定性。
英文摘要：
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a persistence diagram. We are then able to visualize and analyze large ensembles of computer-generated districting plans of the type commonly used in modern redistricting research (and court challenges). We set out three applications: zoning a state at each scale of districting, comparing elections, and seeking signals of gerrymandering. Our case studies focus on redistricting in Pennsylvania and North Carolina, two states whose legal challenges to enacted plans have raised considerable public interest in the last few years. To address the question of robustness of the persistence diagrams to perturbations in vote data and in district boundaries, we translate the classical stability theorem of Cohen--Steiner et al. into our setting and find that it can be phrased in a manner that is easy to interpret. We accompany the theoretical bound with an empirical demonstration to illustrate diagram stability in practice.
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