Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking

2026-05-22

AI Summary

This work addresses the tendency of standard rank aggregation methods to exacerbate underrepresentation of disadvantaged groups in applications such as hiring and recommendation. Focusing on fairness-aware rank aggregation under the Spearman footrule (i.e., L1 distance), the paper presents the first optimal algorithm for fair Top-$k$ ranking and improves the approximation ratio for fair full-ranking aggregation from 3 to 2. Through careful design of combinatorial optimization and approximation algorithms, the authors theoretically establish the optimality of their Top-$k$ solution and an improved approximation guarantee for the full-ranking setting. Extensive experiments on multiple real-world datasets demonstrate that the proposed methods significantly outperform existing baselines, effectively narrowing the performance gap between fair constrained rankings and their unconstrained counterparts.

Abstract

Ensuring fairness in algorithmic ranking systems is a critical challenge with significant societal implications for hiring, recommendations, web search, and data management. Standard methods for aggregating multiple preference orders into a consensus ranking may perpetuate and even amplify the lack of representation of underrepresented groups. To address this, recent research has focused on incorporating fairness constraints to ensure the presence of different groups in the top-$k$ positions of the final aggregate ranking. We study two fairness-aware variants under the well-known Spearman footrule, which corresponds to the $L_1$ distance between rankings. First, we address the practically salient task of computing a fair aggregate top-$k$ ranking -- crucial in settings like recommendations and hiring where selection is primarily based on the top-$k$ results -- and present the first optimal algorithm for this problem. Second, we consider fair (full) rank aggregation over all candidates (not specifically on top-$k$). We already know of a $3$-approximation for this fair rank aggregation variant (Wei et al., SIGMOD'22; Chakraborty et al., NeurIPS'22), whereas an exact algorithm exists for the corresponding unconstrained (unfair) version (Dwork et al., WWW'01). Closing the computational gap between fair and unconstrained rank aggregation has remained a tantalizing open problem. We make significant progress by giving a $2$-approximation algorithm for fair (full) rank aggregation, improving substantially over the previous $3$-approximation. Further, we complement our theoretical contributions with experiments on different real-world datasets, which corroborate our theoretical results and demonstrate strong empirical performance relative to state-of-the-art baselines.

Problem

• fairness
• rank aggregation
• top-k ranking
• Spearman footrule
• algorithmic bias

Innovation

• fair ranking
• top-k aggregation
• Spearman footrule
• approximation algorithm
• rank aggregation