Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans
Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans
复制标题
用于平衡和紧凑重划区计划抽样的顺序蒙特卡罗
DOI：
10.1214/23-aoas1763
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
K. Imai
中科院分区：
文献类型：
--
作者：
Cory McCartan;K. Imai
在约束下对图形分区的随机采样已成为评估立法重新划分计划的流行工具。分析师通过将提议的重新分配计划与采样的替代计划进行比较，检测到党派的群体。为了成功应用，采样方法必须扩展到与许多地区的大型地图，结合现实的法律约束，并准确地从选定的目标分布中进行采样。不幸的是，大多数现有方法在这三个领域中至少有一个。我们提出了一种新的顺序蒙特卡洛（SMC）算法，该算法从选择的目标分布中汲取了代表性的重新分配计划。由于它产生了几乎独立的样本，因此SMC算法可以有效地探索重新分配计划的相关空间，而不是现有的Markov Chain Monte Carlo算法。我们的算法可以同时纳入在现实世界中常见的重新划分问题中通常施加的几个约束，包括同等的人口，紧凑性和行政界限的保存。我们通过使用可以列举所有重新分配计划的小地图来验证所提出的算法的准确性。然后，我们应用SMC算法来评估相关方在宾夕法尼亚州最近的备受瞩目的重新分配案例中提交的几个地图的党派含义。开源软件可用于实施提出的方法。
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled alternative plans. For successful application, sampling methods must scale to large maps with many districts, incorporate realistic legal constraints, and accurately sample from a selected target distribution. Unfortunately, most existing methods struggle in at least one of these three areas. We present a new Sequential Monte Carlo (SMC) algorithm that draws representative redistricting plans from a realistic target distribution of choice. Because it yields nearly independent samples, the SMC algorithm can efficiently explore the relevant space of redistricting plans than the existing Markov chain Monte Carlo algorithms that yield dependent samples. Our algorithm can simultaneously incorporate several constraints commonly imposed in real-world redistricting problems, including equal population, compactness, and preservation of administrative boundaries. We validate the accuracy of the proposed algorithm by using a small map where all redistricting plans can be enumerated. We then apply the SMC algorithm to evaluate the partisan implications of several maps submitted by relevant parties in a recent high-profile redistricting case in the state of Pennsylvania. Open-source software is available for implementing the proposed methodology.
DOI：
10.1073/pnas.1617540114
发表时间：
2017-03-14
影响因子：
11.1
作者：
Chikina, Maria;Frieze, Alan;Pegden, Wesley
通讯作者：
Pegden, Wesley