Beyond Exposure: Optimizing Ranking Fairness with Non-linear Time-Income Functions

Ranking systems in web search and recommendation allocate attention among items and providers, and therefore need to balance relevance-based effectiveness with provider fairness. Existing fair-ranking methods commonly focus on exposure fairness, where cumulative exposure is allocated in proportion to item merit. However, exposure is often only an intermediate signal: the actual utility received by a provider may depend on context-dependent conversion from exposure to income, such as clicks, purchases, or advertising value. This paper studies fair ranking under context-dependent provider utility, which we refer to as income. We formalize income fairness by requiring cumulative provider income to be proportional to relevance, and define an income-unfairness metric based on this proportionality condition. We then propose DIDRF, a Dynamic-Income-Derivative-aware Ranking Fairness algorithm for income-fair ranking. DIDRF uses the quadratic structure of income-fairness violations to derive a state-aware scoring rule that jointly considers ranking effectiveness and the marginal effect of each ranking decision on cumulative income fairness. Experiments on standard learning-to-rank datasets with log-calibrated semi-synthetic income environments based on advertising and e-commerce logs show that DIDRF consistently improves income fairness over representative fair-ranking baselines while preserving competitive ranking effectiveness.