在具有多样性目标的择校中实现平衡表示
Achieving Balanced Representation in School Choice with Diversity Goals
AI总结：
本文研究一对一约定下单个学校的学生选择问题，发现现有算法导致不同类型组合学生间不平衡，提出平衡表示属性及满足四大基本属性的选择函数，并利用流网络方法提升计算效率。
摘要：
在多样性约束下进行学生安置是全球的常见做法。本文研究了一对一约定下单个学校的学生选择问题，其中学生可属于多种类型，但仅根据一种类型计数一次。尽管经济学和计算机科学中的现有算法旨在帮助学校实现多样性目标和优先级，但我们证明这些方法会导致不同类型组合的学生之间出现显著不平衡。为解决此问题，我们引入了平衡表示这一新属性，确保所有类型及类型组合的公平表示。我们提出了一种简单的选择函数，唯一满足四个基本属性：最大多样性、无浪费、无正当嫉妒和平衡表示。以往研究主要基于二分图算法，我们则采用流网络方法。该方法提供了更紧凑的问题形式化，并显著提高了计算效率。此外，我们提出了在二分图和流网络框架内实现该选择函数的高效算法。
英文摘要：
Student placements under diversity constraints are a common practice globally. This paper addresses the selection of students by a single school under a \emph{one-to-one convention}, where students can belong to multiple types but are counted only once based on one type. While existing algorithms in economics and computer science aim to help schools meet diversity goals and priorities, we demonstrate that these methods can result in significant imbalances among students with different type combinations. To address this issue, we introduce a new property called \emph{balanced representation}, which ensures fair representation across all types and type combinations. We propose a straightforward choice function that uniquely satisfies four fundamental properties: maximal diversity, non-wastefulness, justified envy-freeness, and balanced representation. While previous research has primarily focused on algorithms based on bipartite graphs, we take a different approach by utilizing flow networks. This method provides a more compact formalization of the problem and significantly improves computational efficiency. Additionally, we present efficient algorithms for implementing our choice function within both the bipartite graph and flow network frameworks.
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。
