[论文解读] Alleviating partisan gerrymandering: can math and computers help to eliminate wasted votes?

Tanima Chatterjee, Bhaskar DasGupta+3 more|arXiv (Cornell University)|Apr 27, 2018

Game Theory and Voting Systems参考文献 16被引用 3

一句话总结

本文提出一种快速局部搜索算法，通过重新配置德克萨斯州、弗吉尼亚州、威斯康星州和宾夕法尼亚州的国会选区地图，以减少效率差距——这一衡量部分性选区划分的指标。结果表明，效率差距可显著降低（例如，宾夕法尼亚州从23.80%降至8.64%），同时保持议席分配不变，证明尽管存在理论上的计算难度，但实现更公平的票数-议席比例的实际选区划分在计算上是可行的。

ABSTRACT

Partisan gerrymandering is a major cause for voter disenfranchisement in United States. However, convincing US courts to adopt specific measures to quantify gerrymandering has been of limited success to date. Recently, Stephanopoulos and McGhee introduced a new and precise measure of partisan gerrymandering via the so-called "efficiency gap" that computes the absolutes difference of wasted votes between two political parties in a two-party system. Quite importantly from a legal point of view, this measure was found legally convincing enough in a US appeals court in a case that claims that the legislative map of the state of Wisconsin was gerrymandered; the case is now pending in US Supreme Court. In this article, we show the following: (a) We provide interesting mathematical and computational complexity properties of the problem of minimizing the efficiency gap measure. To the best of our knowledge, these are the first non-trivial theoretical and algorithmic analyses of this measure of gerrymandering. (b) We provide a simple and fast algorithm that can "un-gerrymander" the district maps for the states of Texas, Virginia, Wisconsin and Pennsylvania by bring their efficiency gaps to acceptable levels from the current unacceptable levels. Our work thus shows that, notwithstanding the general worst case approximation hardness of the efficiency gap measure as shown by us,finding district maps with acceptable levels of efficiency gaps is a computationally tractable problem from a practical point of view. Based on these empirical results, we also provide some interesting insights into three practical issues related the efficiency gap measure. We believe that, should the US Supreme Court uphold the decision of lower courts, our research work and software will provide a crucial supporting hand to remove partisan gerrymandering.

研究动机与目标

• 分析最小化效率差距这一近期提出的部分性选区划分衡量指标的计算复杂性。
• 开发并测试一种实用算法，通过降低效率差距来“去选区划分”真实世界的选区地图。
• 评估最小化效率差距是否在不改变议席分配的情况下带来更公平的选举结果。
• 提供实证证据，证明在现实场景中，高效且公平的选区划分在计算上是可行的。
• 通过展示效率差距的可行性和实用性，支持其在联邦法院中被采纳。

提出的方法

• 将效率差距最小化问题形式化为组合优化任务。
• 设计一种局部搜索算法，通过有针对性的、半随机的扰动对现有选区地图进行调整，以减少浪费选票。
• 采用贪心策略，通过在相邻选区之间重新分配选区，迭代改进效率差距。
• 在德克萨斯州、弗吉尼亚州、威斯康星州和宾夕法尼亚州2012年实际选举数据上验证该算法。
• 在选区重新配置过程中保持连通性和人口均等性约束。
• 基于归一化的效率差距减少程度和议席分配稳定性来评估性能。

实验结果

研究问题

• RQ1 能否使用计算高效的算法在真实世界中被选区划分的选区中显著降低效率差距？
• RQ2 最小化效率差距是否会改变现有地图中各政党之间的议席分配？
• RQ3 在未显式优化紧凑性的情况下，最小化效率差距时选区的紧凑性和形状会发生怎样的变化？
• RQ4 原始选区划分地图与随机配置的偏离程度有多大，表明存在有意操纵？
• RQ5 效率差距是否可作为美国法院中实际可行且可实施的选区划分标准？

主要发现

• 在威斯康星州，效率差距从14.76%降至3.80%，议席分配未变（3名民主党人，5名共和党人）。
• 在德克萨斯州，效率差距从4.09%降至3.33%，保持相同的12-24议席分配。
• 在弗吉尼亚州，效率差距从22.25%降至3.61%，民主党代表议席从3个增加到5个。
• 在宾夕法尼亚州，效率差距从23.80%降至8.64%，代表议席从5-13变为6-12。
• 尽管未明确施加紧凑性约束，但弗吉尼亚州的新地图中异常形状的选区比原始选区划分计划更少。
• 该算法在每州不到一分钟内实现效率差距的大幅降低，表明其具有强大的实际可扩展性。