Beyond Incompatibility: Trade-offs between Mutually Exclusive Fairness Criteria in Machine Learning and Law

Multiple fairness definitions cannot be simultaneously satisfied: The paper confirms that widely-used fairness measures like "calibration within groups" (where predictions are equally accurate across demographic groups) and "balance for the positive/negative class" (where outcomes are equally distributed across groups) are mathematically incompatible under realistic conditions, meaning decision-makers must choose which fairness goal to prioritize.

A new tool enables trade-offs between competing fairness goals: The researchers developed FAIM (FAir Interpolation Method), an algorithm that allows organizations to adjust the balance between different fairness criteria rather than choosing just one, tested successfully on real datasets including criminal justice (COMPAS) and e-commerce applications.

Legal compliance may require accepting partial fairness: The paper suggests that conflicting legal obligations—such as those in the EU's AI Act and Digital Markets Act—may be impossible to fully satisfy simultaneously, implying that organizations may need to operationalize a weighted combination of fairness criteria rather than achieve perfect fairness by any single definition.

Real-world applications demonstrate practical feasibility: The algorithm's effectiveness was demonstrated across synthetic data, the widely-studied COMPAS criminal risk assessment dataset, and a new real-world e-commerce dataset, suggesting the approach has practical applicability beyond theoretical scenarios.

Decision-makers need transparency about fairness trade-offs: The research implies that organizations using AI in high-stakes domains (criminal justice, credit scoring) should explicitly acknowledge and communicate which fairness criteria they are prioritizing, since achieving all fairness goals simultaneously is mathematically impossible.