From Constraint to Control: Modeling Expected Fairness in Ranking Systems

Abstract

Modern learning to rank systems have achieved remarkable performance across a wide range of applications. However, they may also exhibit disparities in exposure, raising concerns about fairness, especially in sensitive domains such as healthcare, judicial decision-making, and recruitment, where biased rankings may have critical societal consequences. A common approach to mitigate such issues is to incorporate fairness constraints or regularization terms into the training objective. Yet, this provides limited insight into how these constraints influence the final level of bias, and consequently require costly hyperparameter tuning to reach a desired fairness outcome. In this work, we study fairness in ranking by leveraging threshold-based constraints on disparate exposure, which, under a distributional approximation, induce a predictable transformation of the exposure distribution. We derive a closed-form expression for the expected disparate exposure as a function of the threshold, and introduce an anchored formulation that accounts for practical optimization limits. This formulation enables practitioners to directly select a threshold that achieves a desired fairness target, eliminating the need for extensive hyperparameter tuning. An experimental evaluation on standard learning to rank benchmarks confirms that the proposed model closely matches empirical behavior. These results demonstrate that fairness can be explicitly modeled, predicted and controlled, providing novel and sound approach to tuning fairness in ranking systems. Finally, we disclose our source code1 for full reproducibility.