The Attention Market: Interpreting Online Fair Re-ranking as Manifold Optimization under Walrasian Equilibrium
sigir26-090 · Full research paper · Chen Xu, Wei Chu, Wenyu Hu, Fengran Mo, Jun Xu, Maarten de Rijke
Fairness Metrics and Evaluation · 50% Evaluation Metrics and User Models · 50%
Abstract
Fair re-ranking aims to promote long-tail items and enhance diversity within groups in information retrieval. While previous research on online fairness-aware re-ranking has shown promising outcomes, our comprehensive evaluation of online fair re-ranking methods over 20 settings reveals significant performance disparities among existing methods. To uncover the root causes of these inconsistencies, we reformulate fair re-ranking within an attentional market framework governed by a Walrasian Equilibrium, where the fairness is treated as a taxation cost. This market-based formulation is then coupled with manifold optimization, demonstrating that seeking this equilibrium is equivalent to performing gradient descent on a specific ranking manifold constructed by the market. Different re-ranking settings induce distinct manifold geometries, and these intrinsic geometric differences dictate the gradient landscapes and optimization trajectories. We propose ManifoldRank, an efficient online fair re-ranking algorithm. ManifoldRank adjusts gradients to align with the ranking manifold, considering various contextual settings. On the supply side, it incorporates a gradient adjustment based on different fairness requirements, accounting for associated costs. On the demand side, it empirically predicts an additional gradient adjustment term derived from the ranking scores. By integrating these two gradient adjustments, ManifoldRank effectively balances fairness and accuracy. Experimental results across multiple datasets confirm ManifoldRank's effectiveness.
Assigned reviewers
| # | Reviewer | Match | Why (closest evidence publications in the taxonomy) | |
|---|---|---|---|---|
| 1 | Theresia Veronika Rampisela | 70 | 70 Evaluation Measures of Individual Item Fairness for Recommender Systems: A Critical Study (2025) Fairness Metrics and Evaluation 70 Joint Evaluation of Fairness and Relevance in Recommender Systems with Pareto Frontier (2025) Fairness Metrics and Evaluation 70 Can We Trust Recommender System Fairness Evaluation? The Role of Fairness and Relevance (2024) Fairness Metrics and Evaluation |
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| 2 | Sruthi Gorantla | 62 | 70 Sampling Individually-Fair Rankings that are Always Group Fair (2023) Fairness Metrics and Evaluation 70 Optimizing Learning-to-Rank Models for Ex-Post Fair Relevance (2024) Fairness Metrics and Evaluation 70 On the Problem of Underranking in Group-Fair Ranking (2021) Fairness Metrics and Evaluation |
Area chair
| Area chair | Match | |
|---|---|---|
| Zhijing Wu 0001 | 35 |
Area-chair candidates (3)
| Fernando Diaz 0001 COI: co-author | 45 | 12 papers | |
| Xiaoxue Zang COI: co-author | 37 | 4 papers | |
| Jun Xu 0001 COI: author | 36 | 2 papers |
Candidates from the panel ranked by match score
| # | Reviewer | Match | Load | Why | |
|---|---|---|---|---|---|
| 1 | Theresia Veronika Rampisela assigned | 70 | 3 | 70 Evaluation Measures of Individual Item Fairness for Recommender Systems: A Critical Study (2025) Fairness Metrics and Evaluation 70 Joint Evaluation of Fairness and Relevance in Recommender Systems with Pareto Frontier (2025) Fairness Metrics and Evaluation |
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| 2 | Tetsuya Sakai COI: co-author | 64 | 3 | 70 Diversification as Risk Minimization (2026) Evaluation Metrics and User Models 70 Summaries, ranked retrieval and sessions: a unified framework for information access evaluation (2013) Evaluation Metrics and User Models |
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| 3 | Sruthi Gorantla assigned | 62 | 3 | 70 Sampling Individually-Fair Rankings that are Always Group Fair (2023) Fairness Metrics and Evaluation 70 Optimizing Learning-to-Rank Models for Ex-Post Fair Relevance (2024) Fairness Metrics and Evaluation |
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| 4 | Mark D. Smucker | 51 | 3 | 70 Offline Evaluation by Maximum Similarity to an Ideal Ranking (2020) Evaluation Metrics and User Models 70 Assessing Top- Preferences (2021) Evaluation Metrics and User Models |
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| 5 | Leif Azzopardi COI: co-author | 50 | 3 | 100 Measuring Bias in a Ranked List Using Term-Based Representations (2024) Evaluation Metrics and User Models 100 Efficiently Estimating Retrievability Bias (2014) Evaluation Metrics and User Models |
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| 6 | Zechun Niu | 47 | 3 | 55 Addressing Personalized Bias for Unbiased Learning to Rank (2025) Unbiased Learning to Rank 45 Investigating the Robustness of Counterfactual Learning to Rank Models: A Reproducibility Study (2025) Unbiased Learning to Rank |
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| 7 | Yimeng Bai | 45 | 3 | 62 Recommendation Unlearning via Influence Function (2025) Efficient Training and Data Optimization 43 LabelCraft: Empowering Short Video Recommendations with Automated Label Crafting (2024) Recommendation Systems and Evaluation |
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| 9 | Paul Thomas 0001 | 44 | 3 | 73 On the Use of LLMs for Relevance Labelling (2026) LLM-Based Relevance Assessment 62 User Models, Metrics and Measures of Search: A Tutorial on the C/W/L Evaluation Framework (2021) User Behavior and Search Interaction |
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| 10 | Andrew Parry | 43 | 3 | 73 Large Language Model Relevance Assessors Agree With One Another More Than With Human Assessors (2025) LLM-Based Relevance Assessment 45 [inline-graphic not available: see fulltext] SuiteEval: Simplifying Retrieval Benchmarks (2026) Retrieval Toolkits and Reproducibility |
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| 11 | Negar Arabzadeh COI: co-author | 40 | 3 | 44 A Reproducibility Study of LLM-Based Query Reformulation (2026) Query Reformulation and Expansion 44 Matches Made in Heaven: Toolkit and Large-Scale Datasets for Supervised Query Reformulation (2021) Query Reformulation and Expansion |
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| 12 | Yifan Wang 0017 | 40 | 3 | 62 A Survey on the Fairness of Recommender Systems (2023) Popularity Bias and Long-Tail Debiasing 39 Improving Long-tail User CTR Prediction via Hierarchical Distribution Alignment (2025) Bias Mitigation Methods |
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| 13 | Haritz Puerto | 40 | 3 | 70 Leaky Thoughts: Large Reasoning Models Are Not Private Thinkers (2025) Fairness Metrics and Evaluation 31 C-SEO Bench: Does Conversational SEO Work? (2025) Reasoning Evaluation and Benchmarks |
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| 14 | Xiao Wang 0043 | 39 | 3 | 45 Retrieve, Rerank, Answer, Experiment: Hands-On IR Research with PyTerrier (2026) Retrieval Toolkits and Reproducibility 39 Neural Pseudo-Relevance Feedback Models for Sparse and Dense Retrieval (2022) Query Reformulation and Expansion |
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| 15 | Xuanhui Wang COI: co-author | 39 | 3 | 43 TF-Ranking: Scalable TensorFlow Library for Learning-to-Rank (2019) Retrieval Toolkits and Reproducibility 43 Rax: Composable Learning-to-Rank Using JAX (2022) Retrieval Toolkits and Reproducibility |
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| 16 | Jizhi Zhang | 39 | 3 | 54 Is ChatGPT Fair for Recommendation? Evaluating Fairness in Large Language Model Recommendation (2023) Preference Alignment and Optimization 42 On the Theories Behind Hard Negative Sampling for Recommendation (2023) Recommendation Systems and Evaluation |
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| 17 | Min Hou 0004 | 39 | 3 | 70 Fair Personalized Learner Modeling Without Sensitive Attributes (2025) Fairness Metrics and Evaluation 39 RecCocktail: A Generalizable and Efficient Framework for LLM-Based Recommendation (2026) Preference Alignment and Optimization |
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| 18 | Chongming Gao COI: co-author | 39 | 3 | 43 KuaiRec: A Fully-observed Dataset and Insights for Evaluating Recommender Systems (2022) Recommendation Systems and Evaluation 42 On the Theories Behind Hard Negative Sampling for Recommendation (2023) Recommendation Systems and Evaluation |
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| 19 | Xialong Liu | 38 | 3 | 70 Fairness-Aware Design for Contextual Experiments: Guaranteeing Reliability and Equity in Heterogeneous Subgroups (2026) Fairness Metrics and Evaluation 42 CROLoss: Towards a Customizable Loss for Retrieval Models in Recommender Systems (2022) Recommendation with Search and Ranking |
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| 20 | Jaime Arguello | 38 | 3 | 44 Tip of the Tongue Query Elicitation for Simulated Evaluation (2025) User Simulation for Interactive Systems 44 Multilingual and Domain-Agnostic Tip-of-the-Tongue Query Generation for Simulated Evaluation (2026) User Simulation for Interactive Systems |
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| 21 | Yang Zhang 0072 | 38 | 3 | 69 Exact and Efficient Unlearning for Large Language Model-Based Recommendation (2025) Efficiency and Deployment 40 Preliminary Study on Incremental Learning for Large Language Model-based Recommender Systems (2024) Efficiency and Deployment |
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| 22 | Zhen Qin 0001 | 38 | 3 | 43 Improving Recommendation Quality in Google Drive (2020) Recommendation Systems and Evaluation 43 Bootstrapping Recommendations at Chrome Web Store (2021) Recommendation Systems and Evaluation |
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| 23 | Fan Zhang 0053 | 38 | 3 | 62 Evaluating Mobile Search with Height-Biased Gain (2017) User Behavior and Search Interaction 49 Incorporating Query Reformulating Behavior into Web Search Evaluation (2021) User Behavior and Search Interaction |
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| 24 | Rolf Jagerman COI: co-author | 38 | 3 | 43 Bootstrapping Recommendations at Chrome Web Store (2021) Recommendation Systems and Evaluation 43 Rax: Composable Learning-to-Rank Using JAX (2022) Retrieval Toolkits and Reproducibility |
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| 25 | Falk Scholer | 38 | 3 | 42 Can Generative LLMs Create Query Variants for Test Collections? An Exploratory Study (2023) Query Reformulation and Expansion 42 sMARE: a new paradigm to evaluate and understand query performance prediction methods (2022) Query Performance Prediction |
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| 26 | Daiting Shi | 38 | 3 | 70 MA4DIV: Multi-Agent Reinforcement Learning for Search Result Diversification (2025) Evaluation Metrics and User Models 42 Population-Guided Intent-Aware Query Rewriting for Web Search (2026) Query Reformulation and Expansion |
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| 27 | Jiqun Liu | 37 | 3 | 70 Toward A Two-Sided Fairness Framework in Search and Recommendation (2023) Fairness Metrics and Evaluation 41 TRUE: A Reproducible Framework for LLM-Driven Relevance Judgment in Information Retrieval (2026) LLM-Based Relevance Assessment |
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| 28 | Gustavo Penha | 37 | 3 | 43 Contextualizing Spotify's Audiobook List Recommendations with Descriptive Shelves (2025) Recommendation Systems and Evaluation 42 Evaluating the Robustness of Retrieval Pipelines with Query Variation Generators (2022) Query Reformulation and Expansion |
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| 29 | Yuchen Li 0006 COI: co-author | 37 | 3 | 44 FULTR: A Large-Scale Fusion Learning to Rank Dataset and Its Application for Satisfaction-Oriented Ranking (2025) Web-Scale Learning to Rank 42 RankExpert: A Mixture of Textual-and-Behavioral Experts for Multi-Objective Learning-to-Rank in Web Search (2025) Unbiased Learning to Rank |
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| 30 | Sunhao Dai COI: co-author | 37 | 3 | 42 Bias and Unfairness in Information Retrieval Systems: New Challenges in the LLM Era (2024) Bias Mitigation Methods 42 Unifying Bias and Unfairness in Information Retrieval: New Challenges in the LLM Era (2025) Bias Mitigation Methods |
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| 31 | Sara Allawati COI: co-author | 37 | 3 | 42 VulGen: Workshop on Vulnerabilities in Generative Systems for Information Retrieval (2026) Bias Mitigation Methods 36 A Comparative Analysis of Linguistic and Retrieval Diversity in LLM-Generated Search Queries (2025) User Behavior and Search Interaction |