It is widely accepted that biased data leads to biased and thus potentially unfair models. Therefore, several measures for bias in data and model predictions have been proposed, as well as bias mitigation techniques whose aim is to learn models that are fair by design. Despite the myriad of mitigation techniques developed in the past decade, however, it is still poorly understood under what circumstances which methods work. Recently, Wick et al. showed, with experiments on synthetic data, that there exist situations in which bias mitigation techniques lead to more accurate models when measured on unbiased data. Nevertheless, in the absence of a thorough mathematical analysis, it remains unclear which techniques are effective under what circumstances. We propose to address this problem by establishing relationships between the type of bias and the effectiveness of a mitigation technique, where we categorize the mitigation techniques by the bias measure they optimize. In this paper we illustrate this principle for label and selection bias on the one hand, and demographic parity and ``We're All Equal'' on the other hand. Our theoretical analysis allows to explain the results of Wick et al. and we also show that there are situations where minimizing fairness measures does not result in the fairest possible distribution.

翻译：学界普遍认为，有偏差的数据会导致模型产生偏差，进而可能引发不公平。为此，研究者已提出多种数据与模型预测偏差度量指标，以及旨在通过设计学习公平模型的偏差缓解技术。尽管过去十年间涌现了大量缓解技术，但学界对其适用条件仍缺乏深入理解。近期，Wick等人通过合成数据实验表明，在某些情境下，当以无偏数据为基准进行测量时，偏差缓解技术反而能生成更精确的模型。然而，由于缺乏严谨的数学分析，这些技术在何种条件下有效依然悬而未决。我们拟通过建立偏差类型与缓解技术有效性之间的关联来攻克这一难题——其中，我们根据缓解技术所优化的偏差度量指标对其进行分类。本文以标签偏差和选择偏差为一方，以人口均等和"众生平等"准则为另一方，阐释该原理。理论分析不仅能够解释Wick等人的实验结果，还揭示出在某些情境下，最小化公平度量指标未必能生成最公平的分布。