Unravelling the (In)compatibility of Statistical-Parity and Equalized-Odds

A key challenge in employing data, algorithms and data-driven systems is to adhere to the principle of fairness and justice. Statistical fairness measures belong to an important category of technical/formal mechanisms for detecting fairness issues in data and algorithms. In this contribution we study the relations between two types of statistical fairness measures namely Statistical-Parity and Equalized-Odds. The Statistical-Parity measure does not rely on having ground truth, i.e., (objectively) labeled target attributes. This makes Statistical-Parity a suitable measure in practice for assessing fairness in data and data classification algorithms. Therefore, Statistical-Parity is adopted in many legal and professional frameworks for assessing algorithmic fairness. The Equalized-Odds measure, on the contrary, relies on having (reliable) ground-truth, which is not always feasible in practice. Nevertheless, there are several situations where the Equalized-Odds definition should be satisfied to enforce false prediction parity among sensitive social groups. We present a novel analyze of the relation between Statistical-Parity and Equalized-Odds, depending on the base-rates of sensitive groups. The analysis intuitively shows how and when base-rate imbalance causes incompatibility between Statistical-Parity and Equalized-Odds measures. As such, our approach provides insight in (how to make design) trade-offs between these measures in practice. Further, based on our results, we plea for examining base-rate (im)balance and investigating the possibility of such an incompatibility before enforcing or relying on the Statistical-Parity criterion. The insights provided, we foresee, may trigger initiatives to improve or adjust the current practice and/or the existing legal frameworks.