Unfair Utilities and First Steps Towards Improving Them

Fairness in decision-making processes is often quantified using probabilistic metrics. However, these metrics need not reflect the consequences of decisions for the affected individuals and groups. We develop a utility-based framework that incorporates these consequences into the assessment of fairness. Our main result shows that a decision-making process can satisfy $\varepsilon$-fairness while nevertheless being maximally unfair once the utilities associated with its outcomes are taken into account. To address applications in which information on false negatives is unavailable, we also formulate a reduced setting that retains the essential elements of the utility-based fairness assessment. We illustrate the framework through two applications: college admissions and credit-risk assessment. In both cases, probabilistic metrics may classify a decision-making process as approximately fair even though the corresponding utility outcomes are highly unequal. In the college-admissions example, our analysis shows that improving completion rates is necessary to achieve equality of utility across groups, while in the mortgage example, mitigating unfairness requires not only adjusting approval rates but also reducing the adverse consequences of default. These findings demonstrate that fairness assessments should account not only for the probabilities of different decisions but also for the consequences of those decisions.

We study the Pareto frontier (optimal trade-off) between utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome. Through an information-theoretic lens, we prove a characterization of the utility-separation Pareto frontier, establish its concavity, and thereby prove the increasing marginal cost of separation in terms of utility. In addition, we characterize the conditions under which this trade-off becomes strict, providing a guide for trade-off selection in practice. Based on the theoretical characterization, we develop an empirical regularizer based on conditional mutual information (CMI) between predictions and sensitive attributes given the true outcome. The CMI regularizer is compatible with any deep model trained via gradient-based optimization and serves as a scalar monitor of residual separation violations, offering tractable guarantees during training. Finally, numerical experiments support our theoretical findings: across COMPAS, UCI Adult, UCI Bank, and CelebA, the proposed method substantially reduces separation violations while matching or exceeding the utility of established baseline methods. This study thus offers a provable, stable, and flexible approach to enforcing separation in deep learning.

Scoring functions are used to represent the relevance of individual documents. In modern information retrieval or recommendation systems, they are often learned from data and play a pivotal role in ranking sets of documents or items in a way that maximizes utility to a query or user. With the recent interest in algorithmic fairness, the success of scoring has naturally led to methods that learn scores that simultaneously trade off fairness and utility. In this work, we show that in stark contrast with utility-centric objectives, scoring is sub-optimal in achieving all utility-fairness trade-offs. We establish this with a series of counter-examples with a generic fairness formulation. We show that the issue persists whether we have a deterministic scoring function or a randomized one, or whether we measure fairness at the scope of a single query or across multiple queries. On the positive side, we empirically demonstrate that semi-greedy post-processing has the potential to achieve much better trade-offs, often approaching the ideal of exhaustive post-processing in a tractable way.