The impossibility theorem of fairness is a foundational result in the algorithmic fairness literature. It states that outside of special cases, one cannot exactly and simultaneously satisfy all three common and intuitive definitions of fairness - demographic parity, equalized odds, and predictive rate parity. This result has driven most works to focus on solutions for one or two of the metrics. Rather than follow suit, in this paper we present a framework that pushes the limits of the impossibility theorem in order to satisfy all three metrics to the best extent possible. We develop an integer-programming based approach that can yield a certifiably optimal post-processing method for simultaneously satisfying multiple fairness criteria under small violations. We show experiments demonstrating that our post-processor can improve fairness across the different definitions simultaneously with minimal model performance reduction. We also discuss applications of our framework for model selection and fairness explainability, thereby attempting to answer the question: who's the fairest of them all?

该论文研究算法公平性的不可能定理，提出了一种基于整数规划方法的框架，可以同时满足多种公平标准，并在模型性能减少的情况下改善公平性，以及探讨了模型选择和公平性可解释性的应用。

公平性的极限挑战：谁是最公平的？