论文标题
（同源）的持久性
The (homological) persistence of gerrymandering
论文作者
论文摘要
我们将持久同源性（拓扑数据分析领域的主要工具）应用于研究选举重新分配。我们的方法将政治区域计划中的地理信息与选举数据结合在一起，以产生持久图。然后，我们能够可视化和分析现代重新分配研究（和法院挑战）中常用类型的计算机生成区域计划的大型集合。我们制定了三个申请：在各个区域的每个范围内进行分区，比较选举并寻求格里曼德的信号。我们的案例研究着重于宾夕法尼亚州和北卡罗来纳州的重新划分，这两个州在过去几年中提出了颁布计划的法律挑战，这引起了广泛的公共利益。 为了解决持续图对投票数据和地区边界扰动的鲁棒性的鲁棒性问题，我们翻译了Cohen-Steiner等人的经典稳定定理。进入我们的环境，发现它可以以易于解释的方式进行措辞。我们伴随理论结合，并进行了经验演示，以说明实践中的图稳定性。
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.
