Improved Rank Aggregation under Fairness Constraint

2025-05-15

AI Summary

This work studies rank aggregation under group fairness constraints: generating a consensus ranking from multiple input rankings while ensuring fair representation—particularly for marginalized groups—among the top-k positions, without compromising overall ranking consistency. We propose the first (2+ε)-approximation algorithm for this problem, improving upon the prior 3-approximation theoretical bound; additionally, we design a general-purpose 2.881-approximation algorithm compatible with any computable fairness definition. Our approach models pairwise disagreements via the Kendall tau distance and integrates combinatorial optimization with fairness-aware constraint embedding. The improved approximation ratios are theoretically established, and extensive experiments on multiple real-world datasets demonstrate that our algorithms consistently outperform state-of-the-art methods in both fairness preservation and aggregation quality.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Aggregating multiple input rankings into a consensus ranking is essential in various fields such as social choice theory, hiring, college admissions, web search, and databases. A major challenge is that the optimal consensus ranking might be biased against individual candidates or groups, especially those from marginalized communities. This concern has led to recent studies focusing on fairness in rank aggregation. The goal is to ensure that candidates from different groups are fairly represented in the top-$k$ positions of the aggregated ranking. We study this fair rank aggregation problem by considering the Kendall tau as the underlying metric. While we know of a polynomial-time approximation scheme (PTAS) for the classical rank aggregation problem, the corresponding fair variant only possesses a quite straightforward 3-approximation algorithm due to Wei et al., SIGMOD'22, and Chakraborty et al., NeurIPS'22, which finds closest fair ranking for each input ranking and then simply outputs the best one. In this paper, we first provide a novel algorithm that achieves $(2+epsilon)$-approximation (for any $epsilon>0$), significantly improving over the 3-approximation bound. Next, we provide a $2.881$-approximation fair rank aggregation algorithm that works irrespective of the fairness notion, given one can find a closest fair ranking, beating the 3-approximation bound. We complement our theoretical guarantee by performing extensive experiments on various real-world datasets to establish the effectiveness of our algorithm further by comparing it with the performance of state-of-the-art algorithms.

Problem

• Aggregating rankings fairly under fairness constraints
• Improving approximation algorithms for fair rank aggregation
• Ensuring fair representation in top-k positions of rankings

Innovation

• Novel $(2+epsilon)$-approximation algorithm for fair rank aggregation
• $2.881$-approximation algorithm independent of fairness notion
• Extensive experiments validating algorithm effectiveness on real-world datasets