Although many fairness criteria have been proposed to ensure that machine learning algorithms do not exhibit or amplify our existing social biases, these algorithms are trained on datasets that can themselves be statistically biased. In this paper, we investigate the robustness of a number of existing (demographic) fairness criteria when the algorithm is trained on biased data. We consider two forms of dataset bias: errors by prior decision makers in the labeling process, and errors in measurement of the features of disadvantaged individuals. We analytically show that some constraints (such as Demographic Parity) can remain robust when facing certain statistical biases, while others (such as Equalized Odds) are significantly violated if trained on biased data. We also analyze the sensitivity of these criteria and the decision maker's utility to biases. We provide numerical experiments based on three real-world datasets (the FICO, Adult, and German credit score datasets) supporting our analytical findings. Our findings present an additional guideline for choosing among existing fairness criteria, or for proposing new criteria, when available datasets may be biased.

翻译：尽管已提出许多公平性准则以确保机器学习算法不会展现或放大我们现有的社会偏见，但这些算法训练所用的数据集本身可能存在统计偏差。本文研究了当算法基于有偏数据训练时，若干现有（人口统计学）公平性准则的鲁棒性。我们考虑两种数据集偏差形式：先前决策者在标注过程中产生的错误，以及弱势群体特征测量中的错误。分析表明，某些约束条件（如人口均等）在面对特定统计偏差时能保持鲁棒性，而其他准则（如等赔率）若基于有偏数据训练则会显著违反。我们还分析了这些准则及决策者效用对偏差的敏感性。基于FICO、Adult和德国信用评分数据集三个真实世界数据集的数值实验支持了我们的分析结论。研究结果为在可用数据集可能存在偏差的情况下，选择现有公平性准则或提出新准则提供了额外指导。