2021年佐治亚州国会选区规划的数学量化非响应性
Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan
摘要：
为了审计政治区地图的党派不公正划分，可以通过对地图的集合进行采样来确定党派结果的预期分布的基线。采样的一种方法是使用重划分策略作为指南，以精确地编码地图之间的偏好。这样的偏好会导致重新划分计划的空间上的概率分布，而Metropolis-Hastings方法允许从指定的分布中抽取地图集合。虽然这些方法有很好的理论属性，并成功地检测在法律环境中的gerrymandering，从常用的政策驱动的分布采样往往是计算困难的。到目前为止，还没有一种算法可以用于在通用的重新划分标准下检查地图。在这项工作中，我们通过与ReCom[12]相结合的并行回火方法减轻了Metropolized-sampling技术中的计算挑战，并首次验证了这些技术在全州范围内的选区图的规模上对这些问题是有效的，以便采取更多的政策措施。我们开发这些改进，通过在格鲁吉亚地区计划的第一个案例研究。我们的分析预测，根据颁布的计划，佐治亚州的任何选举都将可靠地选出9名共和党人和5名民主党人。这一结果在很大程度上是固定的，即使公众舆论转向任何一方，制定的计划的党派结果并不符合人民的意愿。在我们的集合中，只有0.12%的$\sim$ 160 K计划同样没有响应。
英文摘要：
To audit political district maps for partisan gerrymandering, one may determine a baseline for the expected distribution of partisan outcomes by sampling an ensemble of maps. One approach to sampling is to use redistricting policy as a guide to precisely codify preferences between maps. Such preferences give rise to a probability distribution on the space of redistricting plans, and Metropolis-Hastings methods allow one to sample ensembles of maps from the specified distribution. Although these approaches have nice theoretical properties and have successfully detected gerrymandering in legal settings, sampling from commonly-used policy-driven distributions is often computationally difficult. As of yet, there is no algorithm that can be used off-the-shelf for checking maps under generic redistricting criteria. In this work, we mitigate the computational challenges in a Metropolized-sampling technique through a parallel tempering method combined with ReCom[12] and, for the first time, validate that such techniques are effective on these problems at the scale of statewide precinct graphs for more policy informed measures. We develop these improvements through the first case study of district plans in Georgia. Our analysis projects that any election in Georgia will reliably elect 9 Republicans and 5 Democrats under the enacted plan. This result is largely fixed even as public opinion shifts toward either party and the partisan outcome of the enacted plan does not respond to the will of the people. Only 0.12% of the $\sim$160K plans in our ensemble were similarly non-responsive.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
