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arxiv: 2604.25577 · v1 · submitted 2026-04-28 · 💻 cs.IR

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The Attention Market: Interpreting Online Fair Re-ranking as Manifold Optimization under Walrasian Equilibrium

Chen Xu , Wei Chu , Wenyu Hu , Fengran Mo , Jun Xu , Maarten de Rijke
Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:16 UTC · model grok-4.3

classification 💻 cs.IR
keywords fair re-rankingWalrasian equilibriummanifold optimizationattention marketonline fairnessgradient adjustmentinformation retrieval
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The pith

Fair re-ranking reduces to finding a Walrasian equilibrium in an attention market, which equates to gradient descent on a ranking manifold whose geometry varies by setting.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to explain why existing online fair re-ranking methods produce inconsistent results across different contexts by recasting the problem as an attentional market. In this market, fairness constraints act as taxation costs and the stable outcome is defined by Walrasian equilibrium. The key step is to couple this market formulation with manifold optimization, showing that locating the equilibrium is identical to descending the gradient of a ranking manifold built from the market's supply and demand. Different re-ranking scenarios create manifolds with distinct intrinsic geometries, which in turn shape the gradient landscape and the paths that optimization can follow. ManifoldRank implements this view by adding two explicit gradient corrections—one for fairness cost on the supply side and one predicted from ranking scores on the demand side—thereby producing balanced rankings without separate post-processing.

Core claim

The paper establishes that online fair re-ranking can be reformulated inside an attentional market governed by Walrasian equilibrium, with fairness modeled as a taxation cost. Under this market view, the search for equilibrium is mathematically equivalent to performing gradient descent on a ranking manifold whose geometry is determined by the market. Because each re-ranking setting induces its own manifold geometry, the gradient landscapes and reachable trajectories differ systematically; ManifoldRank therefore adjusts the gradient vector once for fairness requirements and once for predicted score effects, integrating both corrections to achieve both accuracy and fairness.

What carries the argument

The ranking manifold constructed by the market under Walrasian equilibrium; gradient descent on this manifold is shown to locate the equilibrium allocation.

If this is right

  • ManifoldRank produces a single online algorithm that works across multiple fairness requirements by changing only the supply-side gradient correction.
  • The demand-side correction can be pre-computed from ranking scores without solving the full market equilibrium at each step.
  • Performance disparities among prior fair re-ranking methods arise because they implicitly operate on different manifolds.
  • The same manifold view supplies a geometric explanation for why some fairness constraints are harder to satisfy than others.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework suggests that any ranking objective expressible as a market equilibrium can be attacked with manifold optimization once the corresponding manifold is identified.
  • Similar geometry-driven gradient adjustments could be tested in session-based or multi-objective recommendation settings where equilibrium concepts also appear.
  • If manifold curvature correlates with fairness-accuracy trade-off severity, curvature-aware optimizers might further improve the method.

Load-bearing premise

That fairness can be represented as a taxation cost while still guaranteeing existence of the equilibrium and that each re-ranking setting produces a manifold geometry whose intrinsic differences control the optimization trajectory.

What would settle it

An experiment in which gradient steps taken on the constructed manifold fail to converge to the same allocation as direct market-clearing computation, or in which the predicted performance gaps between methods disappear once the manifold geometry is ignored.

Figures

Figures reproduced from arXiv: 2604.25577 by Chen Xu, Fengran Mo, Jun Xu, Maarten de Rijke, Wei Chu, Wenyu Hu.

Figure 1
Figure 1. Figure 1: Performance rankings (lower is better) of fair on view at source ↗
Figure 2
Figure 2. Figure 2: Parallels between (a) an economic market, where view at source ↗
Figure 3
Figure 3. Figure 3: Pareto frontier with different size view at source ↗
Figure 5
Figure 5. Figure 5: NDCG@K and EF@K performance w.r.t. online step. −4 −3 −2 −1 0 1 Coefficient Estimate Value Skewness(mean) Skewness(var) Kurtosis(mean) Kurtosis(var) Entropy(mean) - Scaled by 1e-2 view at source ↗
Figure 6
Figure 6. Figure 6: Influence of the statistical properties of the demand view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that online fair re-ranking can be reformulated as an attentional market under Walrasian equilibrium, with fairness modeled as a taxation cost. It asserts that seeking this equilibrium is equivalent to gradient descent on a ranking manifold whose geometry is induced by the market parameters; different re-ranking settings (e.g., group fairness vs. long-tail promotion) produce distinct manifolds that dictate optimization trajectories. The authors introduce ManifoldRank, which performs supply-side gradient adjustment for fairness costs and demand-side empirical adjustment derived from ranking scores, and report improved balance of fairness and accuracy across multiple datasets and 20 settings.

Significance. If the equivalence is rigorously derived and the manifold construction preserves equilibrium existence, the work supplies a novel economic-geometric lens on fair re-ranking that could unify disparate prior methods and explain observed performance gaps. The explicit link between taxation costs, manifold geometry, and gradient trajectories offers a principled route to context-aware algorithms, with potential to influence both theoretical modeling and practical online ranking systems.

major comments (3)
  1. [Abstract] Abstract: the central claim that 'seeking this equilibrium is equivalent to performing gradient descent on a specific ranking manifold constructed by the market' is asserted without derivation steps, explicit excess-demand map, or verification that the fairness taxation cost keeps the feasible set a smooth manifold whose tangent space aligns with the projected Riemannian gradient. This equivalence is load-bearing for the entire ManifoldRank construction and the geometric interpretation of the 20 settings.
  2. [Abstract] Abstract: the demand-side term is described as 'empirically predicts an additional gradient adjustment term derived from the ranking scores.' If this term is constructed from the same scores that enter the manifold, the claimed equilibrium solution risks reducing to a post-hoc fitted adjustment rather than an independent market-clearing condition; the independence of the prediction and its alignment with Walrasian excess demand must be shown explicitly.
  3. [Experimental evaluation] Experimental section (referenced via the 20 settings): the assertion that 'different re-ranking settings induce distinct manifold geometries' whose 'intrinsic geometric differences dictate the gradient landscapes' requires verification that the taxation cost preserves convexity/differentiability conditions for Walrasian equilibrium existence and manifold smoothness across the evaluated settings; without this, the geometric explanation of performance disparities does not hold uniformly.
minor comments (2)
  1. [Abstract] The abstract mentions evaluation 'over 20 settings' and 'multiple datasets' without characterizing the settings or listing the datasets; a concise summary or pointer to the experimental section would improve readability.
  2. The free parameters (fairness taxation cost and demand-side gradient adjustment coefficient) are introduced without a dedicated sensitivity analysis or ablation; adding this would strengthen the empirical claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their constructive feedback, which has helped us identify areas for improvement in the manuscript. Below, we provide point-by-point responses to the major comments.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'seeking this equilibrium is equivalent to performing gradient descent on a specific ranking manifold constructed by the market' is asserted without derivation steps, explicit excess-demand map, or verification that the fairness taxation cost keeps the feasible set a smooth manifold whose tangent space aligns with the projected Riemannian gradient. This equivalence is load-bearing for the entire ManifoldRank construction and the geometric interpretation of the 20 settings.

    Authors: We acknowledge that the abstract presents the central claim at a high level. The full derivation including the excess-demand map is provided in Section 3. To address this, we will revise the abstract to include a brief outline of the derivation steps and a pointer to the detailed proof. Additionally, we will add a verification in the appendix confirming that the fairness taxation costs maintain the smoothness of the manifold and alignment of the tangent space with the Riemannian gradient for the settings considered. revision: partial

  2. Referee: [Abstract] Abstract: the demand-side term is described as 'empirically predicts an additional gradient adjustment term derived from the ranking scores.' If this term is constructed from the same scores that enter the manifold, the claimed equilibrium solution risks reducing to a post-hoc fitted adjustment rather than an independent market-clearing condition; the independence of the prediction and its alignment with Walrasian excess demand must be shown explicitly.

    Authors: The demand-side term is derived from ranking scores that independently model the demand in the attention market, separate from the manifold defined by supply-side costs. We will clarify this distinction in the revised manuscript by adding an explicit proof of alignment with the Walrasian excess demand in Section 4, demonstrating that the adjustment is not post-hoc but follows from the market equilibrium condition. revision: yes

  3. Referee: [Experimental evaluation] Experimental section (referenced via the 20 settings): the assertion that 'different re-ranking settings induce distinct manifold geometries' whose 'intrinsic geometric differences dictate the gradient landscapes' requires verification that the taxation cost preserves convexity/differentiability conditions for Walrasian equilibrium existence and manifold smoothness across the evaluated settings; without this, the geometric explanation of performance disparities does not hold uniformly.

    Authors: We agree on the importance of verifying the conditions. In the revised experimental section, we will include an analysis across the 20 settings showing that the taxation costs preserve the necessary convexity and differentiability, thereby supporting the manifold smoothness and the geometric interpretation of the results. revision: yes

Circularity Check

1 steps flagged

Demand-side gradient term in ManifoldRank is empirically predicted from ranking scores that define the manifold, reducing the claimed Walrasian-to-gradient-descent equivalence to a fitted adjustment by construction.

specific steps
  1. fitted input called prediction [Abstract]
    "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."

    The demand-side gradient adjustment is obtained by empirical prediction from the ranking scores. These are the same scores used to construct the ranking manifold in the claimed equivalence between seeking Walrasian equilibrium and performing gradient descent on that manifold. Consequently the 'prediction' is a fitted adjustment derived directly from the inputs rather than an independent derivation from market-clearing conditions.

full rationale

The paper's central derivation claims that Walrasian equilibrium seeking equals gradient descent on a market-constructed ranking manifold, with different re-ranking settings inducing distinct geometries. The algorithm description explicitly states that the demand-side adjustment is an empirical prediction derived from the ranking scores. This matches the fitted-input-called-prediction pattern: the term used to 'align' the trajectory is obtained from the same scores entering the manifold construction, so the optimization is not an independent equilibrium solution but a post-hoc adjustment forced by the inputs. The supply-side fairness taxation is presented as external, but the demand-side component makes the overall equivalence circular. No load-bearing self-citations or self-definitional loops are visible in the abstract; the circularity is localized to this prediction step, justifying a moderate score of 6 rather than 8-10.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim depends on the existence of a Walrasian equilibrium once fairness is cast as taxation and on the geometric distinctness of ranking manifolds induced by different fairness rules; both are introduced without independent derivation or external benchmark in the abstract.

free parameters (2)
  • fairness taxation cost
    Fairness requirement is treated as a cost parameter whose concrete scaling is not derived from first principles and must be set per setting.
  • demand-side gradient adjustment coefficient
    The additional term is empirically predicted from ranking scores; its scaling is therefore fitted rather than fixed by the equilibrium equations.
axioms (2)
  • domain assumption A Walrasian equilibrium exists in the modeled attention market once fairness is introduced as taxation
    Invoked to equate equilibrium search with manifold gradient descent.
  • domain assumption Ranking constraints plus fairness taxes define a smooth manifold whose geometry controls optimization trajectories
    Required for the claim that distinct settings produce distinct gradient landscapes.
invented entities (1)
  • Attention Market no independent evidence
    purpose: Economic framing that treats user attention allocation as supply-demand with fairness as tax
    Newly postulated to reinterpret re-ranking; no independent falsifiable prediction outside the ranking task is supplied.

pith-pipeline@v0.9.0 · 5532 in / 1644 out tokens · 51453 ms · 2026-05-07T15:16:05.777741+00:00 · methodology

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Reference graph

Works this paper leans on

49 extracted references · 4 canonical work pages · 2 internal anchors

  1. [1]

    Himan Abdollahpouri, Gediminas Adomavicius, Robin Burke, Ido Guy, Dietmar Jannach, Toshihiro Kamishima, Jan Krasnodebski, and Luiz Pizzato. 2020. Multi- stakeholder Recommendation: Survey and Research Directions.User Modeling and User-Adapted Interaction30, 1 (2020), 127–158

    2020

  2. [2]

    Himan Abdollahpouri and Robin Burke. 2019. Multi-stakeholder Recommenda- tion and its Connection to Multi-sided Fairness.arXiv preprint arXiv:1907.13158 (2019)

    work page arXiv 2019

  3. [3]

    Arrow and Gerard Debreu

    Kenneth J. Arrow and Gerard Debreu. 2024. Existence of an Equilibrium for a Competitive Economy. InThe Foundations of Price Theory Vol 5. Routledge, 289–316

    2024

  4. [4]

    Atkinson and Nicholas H

    Anthony B. Atkinson and Nicholas H. Stern. 1974. Pigou, Taxation and Public Goods.The Review of Economic Studies41, 1 (1974), 119–128

    1974

  5. [5]

    2009.The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium

    Yves Balasko. 2009.The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium. MIT Press

    2009

  6. [6]

    Santiago Balseiro, Haihao Lu, and Vahab Mirrokni. 2021. Regularized Online Allocation Problems: Fairness and Beyond. InInternational Conference on Machine Learning. PMLR, 630–639

    2021

  7. [7]

    Letchford

    Tolga Bektaş and Adam N. Letchford. 2020. Using ℓp-Norms for Fairness in Combinatorial Optimisation.Computers & Operations Research120 (2020), 104975

    2020

  8. [8]

    Farias, and Nikolaos Trichakis

    Dimitris Bertsimas, Vivek F. Farias, and Nikolaos Trichakis. 2011. The Price of Fairness.Operations Research59, 1 (2011), 17–31

    2011

  9. [9]

    Patro, Niloy Ganguly, Krishna P Gummadi, and Abhij- nan Chakraborty

    Arpita Biswas, Gourab K. Patro, Niloy Ganguly, Krishna P Gummadi, and Abhij- nan Chakraborty. 2021. Toward Fair Recommendation in Two-sided Platforms. ACM Transactions on the Web (TWEB)16, 2 (2021), 1–34

    2021

  10. [10]

    Virginie Do, Sam Corbett-Davies, Jamal Atif, and Nicolas Usunier. 2021. Two- sided Fairness in Rankings via Lorenz Dominance.Advances in Neural Information Processing Systems34 (2021), 8596–8608

    2021

  11. [11]

    Yi Fang, Ashudeep Singh, Zhiqiang Tao, et al. 2024. Fairness in Search Systems. Foundations and Trends in Information Retrieval18, 3 (2024), 262–416

    2024

  12. [12]

    Elizabeth Gómez, David Contreras, Ludovico Boratto, and Maria Salamó. 2025. Enhancing recommender systems with provider fairness through preference distribution awareness.International Journal of Information Management Data Insights5, 1 (2025), 100311

    2025

  13. [13]

    Ruining He and Julian McAuley. 2016. Ups and downs: Modeling the Visual Evolution of Fashion Trends with One-class Collaborative Filtering. InProceedings of the 25th International Conference on World Wide Web. 507–517

    2016

  14. [14]

    Balázs Hidasi, Alexandros Karatzoglou, Linas Baltrunas, and Domonkos Tikk

  15. [15]

    Session-based Recommendations with Recurrent Neural Networks.arXiv preprint arXiv:1511.06939(2015)

    work page internal anchor Pith review arXiv 2015

  16. [16]

    Zhihao Hu, Yiran Xu, and Xinmei Tian. 2023. Adaptive Priority Reweighing for Generalizing Fairness Improvement. In2023 International Joint Conference on Neural Networks (IJCNN). 01–08

    2023

  17. [17]

    Meng Jiang, Keqin Bao, Jizhi Zhang, Wenjie Wang, Zhengyi Yang, Fuli Feng, and Xiangnan He. 2024. Item-side Fairness of Large Language Model-based Recommendation System. InProceedings of the ACM Web Conference 2024. ACM, 4717–4726

    2024

  18. [18]

    Wang-Cheng Kang and Julian McAuley. 2018. Self-attentive Sequential Recom- mendation. In2018 IEEE international conference on data mining (ICDM). IEEE, 197–206

    2018

  19. [19]

    Gummadi, and Gerhard Weikum

    Preethi Lahoti, Krishna P. Gummadi, and Gerhard Weikum. 2019. iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making. In2019 IEEE 35th International Conference on Data Engineering (ICDE). IEEE, 1334–1345

    2019

  20. [20]

    Yunqi Li, Hanxiong Chen, Zuohui Fu, Yingqiang Ge, and Yongfeng Zhang. 2021. User-oriented Fairness in Recommendation. InProceedings of the Web Conference. 624–632

    2021

  21. [21]

    Yunqi Li, Hanxiong Chen, Shuyuan Xu, Yingqiang Ge, Juntao Tan, Shuchang Liu, and Yongfeng Zhang. 2023. Fairness in Recommendation: Foundations, Methods and Applications.ACM Transactions on Intelligent Systems and Technology14, 5 (2023), Article No.: 95

    2023

  22. [22]

    Yuanna Liu, Ming Li, Mohammad Aliannejadi, and Maarten de Rijke. 2025. Repeat- bias-aware Optimization of Beyond-accuracy Metrics for Next Basket Recom- mendation. InECIR 2025: 47th European Conference on Information Retrieval (Part I). Springer, Berlin, Heidelberg, 214–229

    2025

  23. [23]

    Lotov and Kaisa Miettinen

    Alexander V. Lotov and Kaisa Miettinen. 2008. Visualizing the Pareto frontier. In Multiobjective Optimization. Springer, 213–243

    2008

  24. [24]

    Andrew McLennan. 2002. Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem.Journal of Economic Theory105, 2 (2002), 435–449

    2002

  25. [25]

    Rahmani, and Yashar Deldjoo

    Mohammadmehdi Naghiaei, Hossein A. Rahmani, and Yashar Deldjoo. 2022. CP- Fair: Personalized Consumer and Producer Fairness Re-ranking for Recommender Systems.arXiv preprint arXiv:2204.08085(2022)

    work page arXiv 2022

  26. [26]

    1983.Welfare Economics

    Yew-Kwang Ng. 1983.Welfare Economics. Springer

    1983

  27. [27]

    Patro, Arpita Biswas, Niloy Ganguly, Krishna P

    Gourab K. Patro, Arpita Biswas, Niloy Ganguly, Krishna P. Gummadi, and Ab- hijnan Chakraborty. 2020. FairRec: Two-sided Fairness for Personalized Rec- ommendations in Two-sided Platforms. InProceedings of the Web Conference. 1194–1204

    2020

  28. [28]

    Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, and Lars Schmidt-Thieme

  29. [29]

    BPR: Bayesian Personalized Ranking from Implicit Feedback.arXiv preprint arXiv:1205.2618(2012)

    work page internal anchor Pith review arXiv 2012

  30. [30]

    Clara Rus, Maarten de Rijke, and Andrew Yates. 2023. Counterfactual Represen- tations for Intersectional Fair Ranking in Recruitment.. InHR@ RecSys

    2023

  31. [31]

    Clara Rus, Gabrielle Poerwawinata, Andrew Yates, and Maarten de Rijke. 2024. AnnoRank: A Comprehensive Web-Based Framework for Collecting Annotations and Assessing Rankings. InCIKM 2024: 33rd ACM International Conference on Information and Knowledge Management. ACM, 5400–5404

    2024

  32. [32]

    Yuta Saito and Thorsten Joachims. 2022. Fair Ranking as Fair Division: Impact- Based Individual Fairness in Ranking. InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1514–1524

    2022

  33. [33]

    Herbert A. Simon. 1971.Designing Organizations for an Information-rich World. Johns Hopkins University Press

    1971

  34. [34]

    Lequn Wang and Thorsten Joachims. 2021. User Fairness, Item Fairness, and Diversity for Rankings in Two-Sided Markets. InProceedings of the 2021 ACM SIGIR International Conference on Theory of Information Retrieval. 23–41

    2021

  35. [35]

    Yifan Wang, Weizhi Ma, Min Zhang, Yiqun Liu, and Shaoping Ma. 2023. A Survey on the Fairness of Recommender Systems.ACM Transactions on Information Systems41, 3 (2023), 1–43

    2023

  36. [36]

    Yao Wu, Jian Cao, and Guandong Xu. 2023. Fairness in Recommender Sys- tems: Evaluation Approaches and Assurance Strategies.ACM Transactions on Knowledge Discovery from Data18, 1 (2023), 1–37

    2023

  37. [37]

    Yao Wu, Jian Cao, Guandong Xu, and Yudong Tan. 2021. TFROM: A Two-Sided Fairness-Aware Recommendation Model for both Customers and Providers. In Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval. 1013–1022

    2021

  38. [38]

    Chen Xu, Sirui Chen, Jun Xu, Weiran Shen, Xiao Zhang, Gang Wang, and Zhenhua Dong. 2023. P-MMF: Provider Max-min Fairness Re-ranking in Recommender System. InProceedings of the ACM Web Conference 2023. 3701–3711

    2023

  39. [39]

    Chen Xu, Zhirui Deng, Clara Rus, Xiaopeng Ye, Yuanna Liu, Jun Xu, Zhicheng Dou, Ji-Rong Wen, and Maarten de Rijke. 2025. FairDiverse: A Comprehen- sive Toolkit for Fairness- and Diversity-aware Information Retrieval. InSIGIR 2025: 48th international ACM SIGIR Conference on Research and Development in Information Retrieval. ACM, 3540–3550

    2025

  40. [40]

    Chen Xu, Jun Xu, Yiming Ding, Xiao Zhang, and Qi Qi. 2024. FairSync: Ensuring Amortized Group Exposure in Distributed Recommendation Retrieval. InPro- ceedings of the ACM Web Conference 2024(Singapore, Singapore)(WWW ’24). 1092–1102

    2024

  41. [41]

    Chen Xu, Xiaopeng Ye, Wenjie Wang, Liang Pang, Jun Xu, and Tat-Seng Chua

  42. [42]

    InProceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’24)

    A Taxation Perspective for Fair Re-ranking. InProceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’24). 1494–1503

  43. [43]

    Chen Xu, Jujia Zhao, Wenjie Wang, Liang Pang, Jun Xu, Tat-Seng Chua, and Maarten de Rijke. 2025. Understanding Accuracy-Fairness Trade-offs in Re- ranking through Elasticity in Economics. InProceedings of the 48th International ACM SIGIR Conference on Research and Development in Information Retrieval. ACM, 539–548

    2025

  44. [44]

    Hong-Jian Xue, Xinyu Dai, Jianbing Zhang, Shujian Huang, and Jiajun Chen

  45. [45]

    InIJCAI, Vol

    Deep Matrix Factorization Models for Recommender Systems.. InIJCAI, Vol. 17. Melbourne, Australia, 3203–3209

  46. [46]

    Loftus, and Julia Stoyanovich

    Ke Yang, Joshua R. Loftus, and Julia Stoyanovich. 2020. Causal Intersectionality for Fair Ranking. InFORC 2021: 2nd Symposium on Foundations of Responsible Computing. Article No. 7

    2020

  47. [47]

    Tao Yang, Zhichao Xu, and Qingyao Ai. 2023. Vertical Allocation-based Fair Exposure Amortizing in Ranking. InProceedings of the Annual International ACM SIGIR Conference on Research and Development in Information Retrieval in the Asia Pacific Region(Beijing, China). ACM, 234–244

    2023

  48. [48]

    Sirui Yao and Bert Huang. 2017. Beyond Parity: Fairness Objectives for Collabo- rative Filtering.Advances in Neural Information Processing Systems30 (2017)

    2017

  49. [49]

    Xiao Zhang, Teng Shi, Jun Xu, Zhenhua Dong, and Ji-Rong Wen. 2024. Model- agnostic causal embedding learning for counterfactually group-fair recommen- dation.IEEE Transactions on Knowledge and Data Engineering36, 12 (2024), 8801–8813

    2024