  Rankings on online platforms help their end-users find the relevant
information -- people, news, media, and products -- quickly. Fair ranking
tasks, which ask to rank a set of items to maximize utility subject to
satisfying group-fairness constraints, have gained significant interest in the
Algorithmic Fairness, Information Retrieval, and Machine Learning literature.
Recent works, however, identify uncertainty in the utilities of items as a
primary cause of unfairness and propose introducing randomness in the output.
This randomness is carefully chosen to guarantee an adequate representation of
each item (while accounting for the uncertainty). However, due to this
randomness, the output rankings may violate group fairness constraints. We give
an efficient algorithm that samples rankings from an individually-fair
distribution while ensuring that every output ranking is group fair. The
expected utility of the output ranking is at least $\alpha$ times the utility
of the optimal fair solution. Here, $\alpha$ depends on the utilities,
position-discounts, and constraints -- it approaches 1 as the range of
utilities or the position-discounts shrinks, or when utilities satisfy
distributional assumptions. Empirically, we observe that our algorithm achieves
individual and group fairness and that Pareto dominates the state-of-the-art
baselines.
