In settings such as e-recruitment and online dating, recommendation involves distributing limited opportunities, calling for novel approaches to quantify and enforce fairness.We introduce inferiority, a novel (un)fairness measure quantifying a user's competitive disadvantage for their recommended items.Inferiority complements envy, a fairness notion measuring preference for others' recommendations.We combine inferiority and envy with utility, an accuracy-related measure of aggregated relevancy scores.Since these measures are non-differentiable, we reformulate them using a probabilistic interpretation of recommender systems, yielding differentiable versions.We combine these loss functions in a multi-objective optimization problem called FEIR (Fairness through Envy and Inferiority Reduction), applied as post-processing for standard recommender systems.Experiments on synthetic and real-world data demonstrate that our approach improves trade-offs between inferiority, envy, and utility compared to naive recommendations and the baseline methods.

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