  As artificial intelligence plays an increasingly substantial role in
decisions affecting humans and society, the accountability of automated
decision systems has been receiving increasing attention from researchers and
practitioners. Fairness, which is concerned with eliminating unjust treatment
and discrimination against individuals or sensitive groups, is a critical
aspect of accountability. Yet, for evaluating fairness, there is a plethora of
fairness metrics in the literature that employ different perspectives and
assumptions that are often incompatible. This work focuses on group fairness.
Most group fairness metrics desire a parity between selected statistics
computed from confusion matrices belonging to different sensitive groups.
Generalizing this intuition, this paper proposes a new equal confusion fairness
test to check an automated decision system for fairness and a new confusion
parity error to quantify the extent of any unfairness. To further analyze the
source of potential unfairness, an appropriate post hoc analysis methodology is
also presented. The usefulness of the test, metric, and post hoc analysis is
demonstrated via a case study on the controversial case of COMPAS, an automated
decision system employed in the US to assist judges with assessing recidivism
risks. Overall, the methods and metrics provided here may assess automated
decision systems' fairness as part of a more extensive accountability
assessment, such as those based on the system accountability benchmark.
