Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary. To investigate this problem, we take an experimental approach and make four overarching contributions: We: 1) Define a metric called self-consistency, derived from variance, which we use as a proxy for measuring and reducing arbitrariness; 2) Develop an ensembling algorithm that abstains from classification when a prediction would be arbitrary; 3) Conduct the largest to-date empirical study of the role of variance (vis-a-vis self-consistency and arbitrariness) in fair binary classification; and, 4) Release a toolkit that makes the US Home Mortgage Disclosure Act (HMDA) datasets easily usable for future research. Altogether, our experiments reveal shocking insights about the reliability of conclusions on benchmark datasets. Most fair binary classification benchmarks are close-to-fair when taking into account the amount of arbitrariness present in predictions -- before we even try to apply any fairness interventions. This finding calls into question the practical utility of common algorithmic fairness methods, and in turn suggests that we should reconsider how we choose to measure fairness in binary classification.

翻译：不同训练模型预测结果的方差是公平二值分类中一个显著但尚未充分探索的误差来源。实践中，某些数据样本的方差过大，以至于决策实际上可视为任意选择。为探究此问题，我们采用实验方法并做出四项总体贡献：1）定义了一种基于方差的自洽性指标，用于衡量和减少任意性；2）开发了一种集成算法，在预测结果具有任意性时放弃分类；3）开展了迄今最大规模的经验研究，探讨方差（相对于自洽性和任意性）在公平二值分类中的作用；4）发布了一个工具包，便于未来研究使用美国住房抵押贷款披露法案（HMDA）数据集。总体而言，我们的实验揭示了关于基准数据集结论可靠性的惊人发现：在考虑预测结果中存在的任意性程度之后（甚至在我们尝试应用任何公平性干预措施之前），大多数公平二值分类基准已接近公平。这一发现对常见算法公平性方法的实际效用提出了质疑，进而表明我们应重新审视如何选择度量二值分类中的公平性。