Retiring $\Delta$DP: New Distribution-Level Metrics for Demographic Parity

Demographic parity is the most widely recognized measure of group fairness in machine learning, which ensures equal treatment of different demographic groups. Numerous works aim to achieve demographic parity by pursuing the commonly used metric $\Delta DP$. Unfortunately, in this paper, we reveal that the fairness metric $\Delta DP$ can not precisely measure the violation of demographic parity, because it inherently has the following drawbacks: \textit{i)} zero-value $\Delta DP$ does not guarantee zero violation of demographic parity, \textit{ii)} $\Delta DP$ values can vary with different classification thresholds. To this end, we propose two new fairness metrics, \textsf{A}rea \textsf{B}etween \textsf{P}robability density function \textsf{C}urves (\textsf{ABPC}) and \textsf{A}rea \textsf{B}etween \textsf{C}umulative density function \textsf{C}urves (\textsf{ABCC}), to precisely measure the violation of demographic parity in distribution level. The new fairness metrics directly measure the difference between the distributions of the prediction probability for different demographic groups. Thus our proposed new metrics enjoy: \textit{i)} zero-value \textsf{ABCC}/\textsf{ABPC} guarantees zero violation of demographic parity; \textit{ii)} \textsf{ABCC}/\textsf{ABPC} guarantees demographic parity while the classification threshold adjusted. We further re-evaluate the existing fair models with our proposed fairness metrics and observe different fairness behaviors of those models under the new metrics.