  Algorithmic decision systems are increasingly used in areas such as hiring,
school admission, or loan approval. Typically, these systems rely on labeled
data for training a classification model. However, in many scenarios,
ground-truth labels are unavailable, and instead we have only access to
imperfect labels as the result of (potentially biased) human-made decisions.
Despite being imperfect, historical decisions often contain some useful
information on the unobserved true labels. In this paper, we focus on scenarios
where only imperfect labels are available and propose a new fair ranking-based
decision system based on monotonic relationships between legitimate features
and the outcome. Our approach is both intuitive and easy to implement, and thus
particularly suitable for adoption in real-world settings. More in detail, we
introduce a distance-based decision criterion, which incorporates useful
information from historical decisions and accounts for unwanted correlation
between protected and legitimate features. Through extensive experiments on
synthetic and real-world data, we show that our method is fair in the sense
that a) it assigns the desirable outcome to the most qualified individuals, and
b) it removes the effect of stereotypes in decision-making, thereby
outperforming traditional classification algorithms. Additionally, we are able
to show theoretically that our method is consistent with a prominent concept of
individual fairness which states that "similar individuals should be treated
similarly."
