  Ranking algorithms find extensive usage in diverse areas such as web search,
employment, college admission, voting, etc. The related rank aggregation
problem deals with combining multiple rankings into a single aggregate ranking.
However, algorithms for both these problems might be biased against some
individuals or groups due to implicit prejudice or marginalization in the
historical data. We study ranking and rank aggregation problems from a fairness
or diversity perspective, where the candidates (to be ranked) may belong to
different groups and each group should have a fair representation in the final
ranking. We allow the designer to set the parameters that define fair
representation. These parameters specify the allowed range of the number of
candidates from a particular group in the top-$k$ positions of the ranking.
Given any ranking, we provide a fast and exact algorithm for finding the
closest fair ranking for the Kendall tau metric under block-fairness. We also
provide an exact algorithm for finding the closest fair ranking for the Ulam
metric under strict-fairness, when there are only $O(1)$ number of groups. Our
algorithms are simple, fast, and might be extendable to other relevant metrics.
We also give a novel meta-algorithm for the general rank aggregation problem
under the fairness framework. Surprisingly, this meta-algorithm works for any
generalized mean objective (including center and median problems) and any
fairness criteria. As a byproduct, we obtain 3-approximation algorithms for
both center and median problems, under both Kendall tau and Ulam metrics.
Furthermore, using sophisticated techniques we obtain a
$(3-\varepsilon)$-approximation algorithm, for a constant $\varepsilon>0$, for
the Ulam metric under strong fairness.

Data Structures and Algorithms