标题： 重新审视选区计划的紧凑性 显示英文标题

标题： Revisiting Compactness for District Plans

摘要： 现代采样方法创建了在离散紧凑性评分上表现良好的选区地图集合，而Polsby-Popper和其他基于形状的评分对于构建公平的地图和诉讼不公平的地图仍然高度相关。本文的目标有两个。首先，我们引入了基于人口加权的形状评分，并展示了这种评分在何种精确意义上介于基于形状的评分和离散评分之间。其次，我们引入了ReCom采样方法的一种修改，该方法生成具有改进的基于形状的紧凑性评分的地图集合。 显示英文摘要

摘要： Modern sampling methods create ensembles of district maps that score well on discrete compactness scores, whereas the Polsby-Popper and other shape-based scores remain highly relevant for building fair maps and litigating unfair ones. The aim of this paper is twofold. First, we introduce population-weighted versions of shape-based scores and show a precise sense in which this interpolates between shape-based and discrete scores. Second, we introduce a modification of the ReCom sampling method that produces ensembles of maps with improved shape-based compactness scores.