🤖 AI Summary
This study investigates the systematic trade-offs between model performance and group fairness in algorithmic decision-making. Framing binary prediction as a multi-objective optimization problem that jointly maximizes decision-maker utility and fairness, the work reveals that Pareto-optimal solutions are characterized by group-specific threshold rules with both upper and lower bounds—extending beyond prior approaches that consider only lower-bound thresholds. The proposed framework accommodates arbitrary utility functions, data distributions, and generalized fairness metrics, unifying preprocessing, in-processing, and post-processing fairness interventions within a single theoretical structure. Theoretically, the Pareto frontier depends solely on population characteristics, the utility function, and the fairness measure, independent of any specific learning algorithm, thereby establishing a foundational basis for evaluating and comparing fair decision systems.
📝 Abstract
Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is still poorly understood. We investigate fairness in binary prediction-based decision problems by conceptualizing decision making as a multi-objective optimization problem that simultaneously considers decision-maker utility and group fairness. We investigate the set of Pareto-optimal decision rules for arbitrary utility functions for decision maker, arbitrary population distributions, and a wide range of group fairness metrics.
We find that the Pareto frontier consists of deterministic, group-specific threshold rules applied to individuals' success probability. This complements existing optimality theorems from literature which, for specific fairness constraints, posit lower-bound threshold rules only. However we also show that, depending on the used fairness metric, the Pareto frontier may include upper-bound threshold rules, thus preferring individuals with lower success probabilities. We show that the location of the Pareto frontier depends only on population characteristics, utility functions and fairness score, but not on the technical design of the algorithm - our findings hold for pre-, in-, and post-processing approaches alike.
Our results generalize existing optimality theorems for fairness-constrained classification and extend them to generalized fairness metrics and fairness principles, and to partial fairness regimes. This paper connects formal fairness research with legal and ethical requirements to search for less discriminatory alternatives, offering a principled foundation for evaluating and comparing algorithmic decision systems.