Fair政治和教育分区的最小胜利幅度
Minimizing Margin of Victory for Fair Political and Educational Districting
摘要：
在许多实际情况下，为了更好地管理，将种群划分为不相交的组，例如，将选民划分为政治选区，将雇员划分为部门，将学生划分为学区，等等。然而，任意地将人们分组可能会导致有偏见的分区，引起人们对政治选区划分中的gerrymandering，学校中的种族隔离等问题的关注。为了解决这些问题，本文将这些问题概念化在投票场景中，提出了公平分配问题，将一组对候选人有偏好的人分成k组，使得任何一组的最大胜利幅度最小。我们还提出了公平连通区的问题，另外需要每个组连接。我们表明，公平分配问题是NP-完全的多数表决，即使我们只有3个候选人，但承认多项式时间算法，如果我们假设k是一些常数或每个人都可以移动到任何组。相反，我们表明，公平连通区问题是NP-完全的多数表决，即使我们只有2个候选人和k = 2。最后，我们提出了启发式算法的问题，并显示其有效性，在英国的政治选区和降低种族隔离在美国的公立学校。
英文摘要：
In many practical scenarios, a population is divided into disjoint groups for better administration, e.g., electorates into political districts, employees into departments, students into school districts, and so on. However, grouping people arbitrarily may lead to biased partitions, raising concerns of gerrymandering in political districting, racial segregation in schools, etc. To counter such issues, in this paper, we conceptualize such problems in a voting scenario, and propose FAIR DISTRICTING problem to divide a given set of people having preference over candidates into k groups such that the maximum margin of victory of any group is minimized. We also propose the FAIR CONNECTED DISTRICTING problem which additionally requires each group to be connected. We show that the FAIR DISTRICTING problem is NP-complete for plurality voting even if we have only 3 candidates but admits polynomial time algorithms if we assume k to be some constant or everyone can be moved to any group. In contrast, we show that the FAIR CONNECTED DISTRICTING problem is NP-complete for plurality voting even if we have only 2 candidates and k = 2. Finally, we propose heuristic algorithms for both the problems and show their effectiveness in UK political districting and in lowering racial segregation in public schools in the US.
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。
