  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.
