标题： 格子对扭曲选区策略的研究 显示英文标题

标题： Lattice Studies of Gerrymandering Strategies

摘要： 我们提出了三种新颖的选区划分算法，这些算法结合了选民的空间分布，旨在构建被操纵的、人口相等的、连通的选区。 此外，我们开发了基于静电势类比的选民分布格点模型，以比较不同的选区划分策略。 由于我们的选民模型中固有的概率性人口波动，可以将蒙特卡洛方法应用于通过我们的选区划分算法构建的选区。 通过蒙特卡洛研究，我们量化了我们每个选区划分算法的效果，并且我们还指出，不包含空间数据的选区划分策略会导致（法律禁止的）高度不连通的选区。 在我们提出的三种算法中，两种是基于不同策略来集中反对党选民的，第三种是一种基于遗传算法的新算法选区划分方法，该方法自动保证所有选区都是连通的。 此外，我们使用我们的格点选民模型来检验等周商测试的有效性，我们的结果为在现实世界的政治选区重划中实施紧凑性测试提供了进一步的定量支持。 显示英文摘要

摘要： We propose three novel gerrymandering algorithms which incorporate the spatial distribution of voters with the aim of constructing gerrymandered, equal-population, connected districts. Moreover, we develop lattice models of voter distributions, based on analogies to electrostatic potentials, in order to compare different gerrymandering strategies. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo methods can be applied to the districts constructed via our gerrymandering algorithms. Through Monte Carlo studies we quantify the effectiveness of each of our gerrymandering algorithms and we also argue that gerrymandering strategies which do not include spatial data lead to (legally prohibited) highly disconnected districts. Of the three algorithms we propose, two are based on different strategies for packing opposition voters, and the third is a new approach to algorithmic gerrymandering based on genetic algorithms, which automatically guarantees that all districts are connected. Furthermore, we use our lattice voter model to examine the effectiveness of isoperimetric quotient tests and our results provide further quantitative support for implementing compactness tests in real-world political redistricting.