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：不同训练模型预测中的方差是公平二分类中一个显著但尚未充分探索的误差来源。实践中，某些数据示例的方差大到足以使决策几乎成为任意行为。为探究该问题，我们采用实验方法并做出四项总体贡献：1) 定义一种源自方差的度量指标——自一致性，作为衡量和减少任意性的代理指标；2) 开发一种集成算法，当预测具有任意性时放弃分类；3) 开展迄今规模最大的实证研究，分析方差（相对于自一致性和任意性）在公平二分类中的作用；4) 发布工具包，使美国《住房抵押贷款披露法案》（HMDA）数据集能便捷地用于未来研究。综合而言，我们的实验揭示了关于基准数据集结论可靠性的惊人见解：在考虑预测中存在的任意性程度后——甚至在我们尝试应用任何公平干预措施之前——大多数公平二分类基准已接近公平。这一发现质疑了常见算法公平性方法的实际效用，进而表明我们应重新审视如何在二分类中选择衡量公平性的方式。