  This paper introduces a novel information-theoretic perspective on the
relationship between prominent group fairness notions in machine learning,
namely statistical parity, equalized odds, and predictive parity. It is well
known that simultaneous satisfiability of these three fairness notions is
usually impossible, motivating practitioners to resort to approximate fairness
solutions rather than stringent satisfiability of these definitions. However, a
comprehensive analysis of their interrelations, particularly when they are not
exactly satisfied, remains largely unexplored. Our main contribution lies in
elucidating an exact relationship between these three measures of (un)fairness
by leveraging a body of work in information theory called partial information
decomposition (PID). In this work, we leverage PID to identify the granular
regions where these three measures of (un)fairness overlap and where they
disagree with each other leading to potential tradeoffs. We also include
numerical simulations to complement our results.
