  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, as an alternative to traditional classification algorithms.
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, as it a) assigns the
desirable outcome to the most qualified individuals, and b) 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."
