用罗尔斯公平原则解决高校招生中的非线性多样性匹配难题
Rawlsian many-to-one matching with non-linear utility
- 基于罗尔斯公平理念，最大化最差学院的效用
- 证明经典稳定匹配在非线性效用下可能不存在
- 提出确定与随机算法，适合公平分配场景
我们研究一类多对一匹配问题，如高校招生，其中每所学院可录取多名学生。与经典模型不同，学院通过非线性效用函数评估学生群体，以捕捉其多样性。在此设定下，我们发现经典稳定匹配可能不存在。为此，我们提出基于罗尔斯公平原则的替代解法，旨在最大化各学院间的最低效用。我们设计了确定性和随机性算法，迭代提升最差学院的匹配结果，为稳定性无法保证时提供一种可行的公平分配方法。
原文摘要 · Abstract (English)
We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture diversity between them. In this setting, we show that classical stable matchings may fail to exist. To address this, we propose alternative solution concepts based on Rawlsian fairness, aiming to maximize the minimum utility across colleges. We design both deterministic and stochastic algorithms that iteratively improve the outcome of the worst-off college, offering a practical approach to fair allocation when stability cannot be guaranteed.
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