FEIR: Quantifying and Reducing Envy and Inferiority for Fair Recommendation of Limited Resources

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 \emph{inferiority}, a novel (un)fairness measure quantifying a user's competitive disadvantage for their recommended items. Inferiority complements \emph{envy}, a fairness notion measuring preference for others' recommendations. We combine inferiority and envy with \emph{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 \texttt{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.