Impossibility results show that important fairness measures (independence,
separation, sufficiency) cannot be satisfied at the same time under reasonable
assumptions. This paper explores whether we can satisfy and/or improve these
fairness measures simultaneously to a certain degree. We introduce
information-theoretic formulations of the fairness measures and define degrees
of fairness based on these formulations. The information-theoretic formulations
suggest unexplored theoretical relations between the three fairness measures.
In the experimental part, we use the information-theoretic expressions as
regularizers to obtain fairness-regularized predictors for three standard
datasets. Our experiments show that a) fairness regularization directly
increases fairness measures, in line with existing work, and b) some fairness
regularizations indirectly increase other fairness measures, as suggested by
our theoretical findings. This establishes that it is possible to increase the
degree to which some fairness measures are satisfied at the same time -- some
fairness measures are gradually compatible.

本文探讨了如何在合理的假设下同时满足公正度量（独立性、分离性、充分性）并 / 或提高这些公正度量，引入了公正度量的信息理论形式，并根据这些形式定义了公正度，进一步探讨了这三个公正度的理论关系。在实验部分，使用信息理论表达式作为规范化器以获得三个标准数据集的公正度规范化预测器。实验结果表明，公正规范化直接增加公正度量，并间接增加其他公正度量，这表明在一定程度上可以同时满足某些公正度量。