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

TL;DR

The paper tackles fairness in data-driven decisions by comparing Statistical-Parity (SP) and Equalized-Odds (EO) under base-rate imbalance across sensitive groups. It develops a binary-channel, graph-based analytical framework using per-group base-rates $p_s$, posterior $q_s$, and per-group $FPR_s$, $TPR_s$, to characterize when SP and EO are compatible. The main finding is that SP and EO cannot be simultaneously satisfied unless $p_0=p_1$ (base-rate balance) or the classifier is random; otherwise enforcing one metric induces trade-offs in the other, as illustrated in the $FPR$-$TPR$ plane with an intersection at $(FPR_*,TPR_*)=(q_*,q_*)$. These results inform policy and practice by recommending assessment of base-rate balance and, when both SP and EO are required in imbalanced settings, the use of randomization to satisfy both metrics. The work provides a practical visualization tool for designers and policymakers to understand fairness trade-offs and to motivate updates to legal frameworks on selective labelling and preselection.

Abstract

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.

Figures (5)

• Figure 1: A binary channel model of binary classification.
• Figure 2: An illustration of the main parameters of the binary channel model.
• Figure 3: An illustration of the generic form of the binary classification performance lines, with an arbitrary $p_s$ and a varying $q_{\ast}$.
• Figure 4: Case I: Choosing the operation point on $TPR=FPR$ (i.e., on the ROC chance line).
• Figure 5: An illustration of choosing the operation points on a good ROC curve.

Theorems & Definitions (16)

• Example 1
• Example 2
• Example 3
• Definition 1
• Lemma 1
• proof
• Example 4
• Theorem 1
• proof
• Corollary 1