Theoretical Foundations of Algorithmic Fairness: A Unified Framework Through Pinsker’s Inequality

SUDJIANTO, A.

We establish a comprehensive theoretical framework connecting information theory and algorithmic fairness by systematically linking major fairness measures to Pinsker’s inequality. Our work provides the first unified theoretical foundation that relates statistical fairness metrics-including demographic parity, equalized opportunity, calibration, and individual fairness-to fundamental information-theoretic quantities through rigorous mathematical bounds. We prove that Pinsker’s inequality serves as a universal bridge between distributional differences (measured by KL divergence and mutual information) and fairness violations across all major fairness definitions. Our theoretical contributions include: (1) tight bounds relating each fairness metric to information-theoretic measures, (2) hierarchy theorems showing the relationships between different fairness criteria, (3) impossibility results that explain why certain fairness combinations cannot be simultaneously achieved, and (4) constructive proofs showing how to achieve any target fairness level through information theoretic constraints.

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