We study the impact of pre and post processing for reducing discrimination in data-driven decision makers. We first analyze the fundamental trade-off between fairness and accuracy in a pre-processing approach, and propose a design for a pre-processing module based on a convex optimization program, which can be added before the original classifier. This leads to a fundamental lower bound on attainable discrimination, given any acceptable distortion in the outcome. Furthermore, we reformulate an existing post-processing method in terms of our accuracy and fairness measures, which allows comparing post-processing and pre-processing approaches. We show that under some mild conditions, pre-processing outperforms post-processing. Finally, we show that by appropriate choice of the discrimination measure, the optimization problem for both pre and post processing approaches will reduce to a linear program and hence can be solved efficiently.

翻译：我们首先分析预处理方法中公平性和准确性之间的根本权衡,并提议一个基于分流优化方案的预处理模块的设计,该模块可以在原分类者之前添加,这导致对可实现的歧视的基本较低约束,因为结果中的任何可接受扭曲。此外,我们从准确性和公平性方面重新制定现有的后处理方法,以便能够比较后处理和预处理方法。我们表明,在某些温和条件下,预处理优于后处理。最后,我们表明,通过适当选择歧视措施,预处理和后处理方法的优化问题将降低为线性方案,从而可以有效解决。