Fair Rank Aggregation
Authors: Diptarka Chakraborty, Syamantak Das, Arindam Khan, Aditya Subramanian

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 {\em strong fairness}, i.e., when the final ranking is fair for all    values of $k$. We also provide an exact algorithm for finding the closest fair ranking for the    Ulam metric under strong 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.