This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents' disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the GGI criterion.

翻译：本文论述稳定的婚姻问题的公平性。本文所研究的理念是,通过普遍化的吉尼指数(GGI)实现公平性。 通用吉尼指数是衡量不平等的一个众所周知的标准,它既包括平等性标准,也包括作为特殊情况的实用性标准。我们表明,确定稳定婚姻,优化GGI关于代理人丧失利用能力的标准,是一个棘手的问题。然后,我们在一般情况下提供了一种多婚制2比2的算法,以及一种精确的算法,在连续数的非零权重使GGI标准平衡的情况下,这种算法是多婚制时间。