  The fair-ranking problem, which asks to rank a given set of items to maximize
utility subject to group fairness constraints, has received attention in the
fairness, information retrieval, and machine learning literature. Recent works,
however, observe that errors in socially-salient (including protected)
attributes of items can significantly undermine fairness guarantees of existing
fair-ranking algorithms and raise the problem of mitigating the effect of such
errors. We study the fair-ranking problem under a model where socially-salient
attributes of items are randomly and independently perturbed. We present a
fair-ranking framework that incorporates group fairness requirements along with
probabilistic information about perturbations in socially-salient attributes.
We provide provable guarantees on the fairness and utility attainable by our
framework and show that it is information-theoretically impossible to
significantly beat these guarantees. Our framework works for multiple
non-disjoint attributes and a general class of fairness constraints that
includes proportional and equal representation. Empirically, we observe that,
compared to baselines, our algorithm outputs rankings with higher fairness, and
has a similar or better fairness-utility trade-off compared to baselines.
