2023/08/21 by Diptarka Chakraborty, Chakraborty, Diptarka, Syamantak Das +5 · 6 citations
Economics, Econometrics and Finance · Mathematics · #Aggregate (composite) #Algorithm #Combinatorics #Computer science #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Game Theory and Voting Systems #Learning to rank #Machine learning #Mathematics #Metric (unit) #Rank (graph theory) #Ranking (information retrieval) #Ranking SVM #Representation (politics) #Set (abstract data type) #Theoretical computer science #Voting
paper · doi:10.48550/arxiv.2308.10499
openalex publication_date 2023/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-ε)-approximation algorithm, for a constant ε>0, for the Ulam metric under strong fairness.