Society is increasingly relying on predictive models in fields like criminal justice, credit risk management, or hiring. To prevent such automated systems from discriminating against people belonging to certain groups, fairness measures have become a crucial component in socially relevant applications of machine learning. However, existing fairness measures have been designed to assess the bias between predictions for protected groups without considering the imbalance in the classes of the target variable. Current research on the potential effect of class imbalance on fairness focuses on practical applications rather than dataset-independent measure properties. In this paper, we study the general properties of fairness measures for changing class and protected group proportions. For this purpose, we analyze the probability mass functions of six of the most popular group fairness measures. We also measure how the probability of achieving perfect fairness changes for varying class imbalance ratios. Moreover, we relate the dataset-independent properties of fairness measures described in this paper to classifier fairness in real-life tasks. Our results show that measures such as Equal Opportunity and Positive Predictive Parity are more sensitive to changes in class imbalance than Accuracy Equality. These findings can help guide researchers and practitioners in choosing the most appropriate fairness measures for their classification problems.

翻译：社会在刑事司法、信用风险管理或招聘等领域日益依赖预测模型。为防止此类自动化系统歧视属于特定群体的人群，公平性度量已成为机器学习在社会相关应用中的关键组成部分。然而，现有公平性度量在设计时仅用于评估受保护群体间预测结果的偏差，而未考虑目标变量类别的不平衡问题。当前关于类别不平衡对公平性潜在影响的研究主要聚焦于实际应用，而非独立于数据集的度量性质。本文研究了在类别与受保护群体比例变化时公平性度量的一般性质。为此，我们分析了六种最常用的群体公平性度量的概率质量函数。同时，我们测量了在不同类别不平衡比例下实现完全公平的概率变化。此外，本文将描述的公平性度量的数据集独立性质与实际任务中的分类器公平性联系起来。研究结果表明，相较于准确率平等性，机会均等与正预测率平等性等度量对类别不平衡的变化更为敏感。这些发现可为研究人员和实践者选择最适合其分类问题的公平性度量提供指导。