所有的政治都是地方性的：通过地方公平重新划分选区
All Politics is Local: Redistricting via Local Fairness
摘要：
在本文中，我们建议使用本地公平的概念，审计和排名重划计划。给定一个选区重划计划，一个偏离群体是一个人口平衡的连续区域，其中大多数人都有相同的利益，并且在各自的选区中占少数;这样一组人对选区重划计划的制定方式有合理的抱怨。没有偏离组的重新划分计划被称为局部公平。我们发现，审计一个给定的计划，本地公平的问题是NP完全的。我们提出了一个MCMC的审计方法，以及重新划分计划的排名。我们还提出了一个基于动态规划的算法，我们使用的审计问题，证明我们的MCMC方法的有效性。使用这些工具，我们测试本地公平的真实世界的选举数据，表明它确实是可能的，找到计划，几乎或完全本地公平。此外，我们表明，这样的计划可以产生，而牺牲很少的紧凑性和现有的公平措施，如竞争力的地区或席位份额的计划。
英文摘要：
In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of the same interest and in the minority of their respective districts; such a set of individuals have a justified complaint with how the redistricting plan was drawn. A redistricting plan with no deviating groups is called locally fair. We show that the problem of auditing a given plan for local fairness is NP-complete. We present an MCMC approach for auditing as well as ranking redistricting plans. We also present a dynamic programming based algorithm for the auditing problem that we use to demonstrate the efficacy of our MCMC approach. Using these tools, we test local fairness on real-world election data, showing that it is indeed possible to find plans that are almost or exactly locally fair. Further, we show that such plans can be generated while sacrificing very little in terms of compactness and existing fairness measures such as competitiveness of the districts or seat shares of the plans.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
