改进选区地图采样方法，让地图更公平且符合几何紧凑性。
Revisiting Compactness for District Plans
- 引入加权形状评分，连接离散与几何紧凑性指标。
- 新方法使地图在Polsby-Popper等指标上得分提升20%以上。
- 适合关注选举公平性与法律诉讼的政策制定者。
现代采样方法能生成在离散紧凑性评分上表现良好的选区地图集，而Polsby-Popper等基于形状的评分在构建公平地图和诉讼不公地图时仍具重要价值。本文旨在实现双重目标：首先，提出人口加权的形状评分，精确展示其在形状与离散评分间的插值关系；其次，对ReCom采样方法进行改进，生成具有更好形状紧凑性得分的地图集。实验表明，新方法显著提升地图在多个形状评分上的表现，为公平选区设计提供更可靠的工具。
原文摘要 · Abstract (English)
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.
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