pith. sign in

arxiv: 2606.26369 · v1 · pith:OZ3UK6M2new · submitted 2026-06-24 · 💻 cs.IR · cs.CY· cs.LG

Scoring Is Not Enough: Addressing Gaps in Utility-fairness Trade-offs for Ranking

Shubham Singh , Ian A. Kash , Mesrob I. Ohannessian This is my paper

Pith reviewed 2026-06-26 00:51 UTC · model grok-4.3

classification 💻 cs.IR cs.CYcs.LG
keywords rankingfairnessutility trade-offsscoring functionspost-processinginformation retrievalcounterexamples
0
0 comments X

The pith

Scoring functions cannot achieve every utility-fairness trade-off in ranking.

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

The paper shows that even when scores are learned or chosen to balance utility and fairness, they leave some achievable trade-offs on the table. This limitation appears in counterexamples built from a generic fairness formulation and holds for both deterministic and randomized scores as well as for fairness measured per query or across queries. A reader would care because modern ranking and recommendation systems rely on scoring to encode relevance and fairness constraints. The work also reports that semi-greedy post-processing can reach better points on the trade-off curve than scoring alone.

Core claim

Scoring is sub-optimal in achieving all utility-fairness trade-offs. We establish this with a series of counter-examples with a generic fairness formulation. We show that the issue persists whether we have a deterministic scoring function or a randomized one, or whether we measure fairness at the scope of a single query or across multiple queries. On the positive side, we empirically demonstrate that semi-greedy post-processing has the potential to achieve much better trade-offs, often approaching the ideal of exhaustive post-processing in a tractable way.

What carries the argument

Counter-examples built on a generic fairness formulation that prove scoring functions are sub-optimal for the full set of utility-fairness trade-offs.

If this is right

  • Deterministic scoring functions leave some utility-fairness pairs unreachable.
  • Randomized scoring functions exhibit the same gaps.
  • The gaps appear both when fairness is enforced on individual queries and when it is enforced across multiple queries.
  • Semi-greedy post-processing can reach trade-off points that scoring cannot.
  • Exhaustive post-processing sets an upper bound that semi-greedy methods often approach.

Where Pith is reading between the lines

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

  • Ranking pipelines may need to move beyond score-based selection toward direct selection or re-ranking steps when fairness constraints are active.
  • If many practical fairness definitions turn out to have extra structure, the reported gaps might shrink or disappear.
  • Developers could test whether their current fairness metric admits scoring-based solutions before investing in post-processing layers.

Load-bearing premise

The generic fairness formulation used to build the counterexamples captures the fairness notions that actually appear in deployed ranking systems.

What would settle it

A concrete fairness definition drawn from a production ranking system for which every utility-fairness point can be realized by some scoring function would refute the claim of sub-optimality.

Figures

Figures reproduced from arXiv: 2606.26369 by Ian A. Kash, Mesrob I. Ohannessian, Shubham Singh.

Figure 1
Figure 1. Figure 1: Overview of the paper, highlighting key ideas about the limitations of scoring for utility-fairness trade-offs [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Utility and unfairness values for α = {0, . . . , 1} achieved by beam search (orange), greedy (green) and the randomized scoring-based trained PL model (purple) on these datasets. Unlike the real-world COMPAS dataset, the synthetic data is tractable, and we also include the brute-force optimal ex-post (blue) and best deterministic scorer (pink). 5 Alternatives to Scoring Having seen the theoretical shortco… view at source ↗
Figure 3
Figure 3. Figure 3: Tradeoff gap between the optimal ranker and the best scorer in the example of Corollary 1, as a function of [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: AI-Generated Illustration of Beam Trade-off Search (Algorithm 1) [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Utility and unfairness values for α = {0, . . . , 1} achieved by the beam search (orange), greedy (green), and the trained PL model (purple) on the German Credit dataset. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Utility and unfairness values for α = {0, . . . , 1} achieved by beam search (orange), greedy (green) and the trained PL model (purple) on the Movielens 100K dataset. E.2 MovieLens 100K Dataset Data Preprocessing. MovieLens 100K is a popular dataset used for learning-to-rank tasks Harper and Konstan [2016]. As the name suggests, the dataset contains 100,000 movie ratings for 1,682 movies from 943 users. A … view at source ↗
read the original abstract

Scoring functions are used to represent the relevance of individual documents. In modern information retrieval or recommendation systems, they are often learned from data and play a pivotal role in ranking sets of documents or items in a way that maximizes utility to a query or user. With the recent interest in algorithmic fairness, the success of scoring has naturally led to methods that learn scores that simultaneously trade off fairness and utility. In this work, we show that in stark contrast with utility-centric objectives, scoring is sub-optimal in achieving all utility-fairness trade-offs. We establish this with a series of counter-examples with a generic fairness formulation. We show that the issue persists whether we have a deterministic scoring function or a randomized one, or whether we measure fairness at the scope of a single query or across multiple queries. On the positive side, we empirically demonstrate that semi-greedy post-processing has the potential to achieve much better trade-offs, often approaching the ideal of exhaustive post-processing in a tractable way.

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

2 major / 2 minor

Summary. The paper claims that scoring functions (deterministic or randomized) are sub-optimal for achieving the complete set of utility-fairness trade-offs in ranking. This is established via counterexamples under a generic fairness formulation, shown to hold for both single-query and multi-query settings. The authors additionally report that semi-greedy post-processing can achieve trade-offs approaching those of exhaustive search in a tractable manner.

Significance. If the result holds under fairness notions used in practice, the work identifies a structural limitation of score-based ranking that would require shifting from learned scores to direct optimization or post-processing for Pareto-optimal fairness-utility frontiers. The explicit counterexample approach (rather than parameter fitting) provides a clean, falsifiable demonstration of sub-optimality.

major comments (2)
  1. [Counterexample construction and generic fairness formulation] The central claim rests on counterexamples constructed with a generic fairness formulation that permits arbitrary mappings from ranked lists to fairness values. Practical fairness notions (e.g., exposure disparity, demographic parity on protected groups, or listwise KL-divergence) typically impose additional structure such as monotonicity or dependence only on group proportions. It is not shown whether the constructed counterexamples remain feasible or the sub-optimality persists once these constraints are imposed; a concrete test would be to specialize the generic formulation to one of these deployed metrics and re-run the counterexamples.
  2. [Multi-query extension] The multi-query setting is addressed, but the paper does not specify how the generic fairness function aggregates across queries (e.g., whether it is a sum, average, or more complex set function). This aggregation choice directly affects whether the single-query counterexamples lift to the multi-query case without additional assumptions.
minor comments (2)
  1. [Preliminaries] Notation for the fairness function and utility should be introduced with an explicit definition before the counterexamples are presented.
  2. [Empirical evaluation] The empirical section on semi-greedy post-processing would benefit from reporting the exact computational complexity relative to exhaustive search.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript accordingly to clarify the scope and strengthen the empirical grounding of the results.

read point-by-point responses

  1. Referee: [Counterexample construction and generic fairness formulation] The central claim rests on counterexamples constructed with a generic fairness formulation that permits arbitrary mappings from ranked lists to fairness values. Practical fairness notions (e.g., exposure disparity, demographic parity on protected groups, or listwise KL-divergence) typically impose additional structure such as monotonicity or dependence only on group proportions. It is not shown whether the constructed counterexamples remain feasible or the sub-optimality persists once these constraints are imposed; a concrete test would be to specialize the generic formulation to one of these deployed metrics and re-run the counterexamples.

    Authors: The generic formulation establishes that scoring is structurally sub-optimal for achieving the full utility-fairness frontier even in the absence of metric-specific constraints. We agree that demonstrating persistence under practical metrics would increase relevance. We will revise the manuscript to specialize one counterexample to exposure disparity (a monotonic, group-proportion-based metric) and verify that the same scoring sub-optimality holds. revision: yes

  2. Referee: [Multi-query extension] The multi-query setting is addressed, but the paper does not specify how the generic fairness function aggregates across queries (e.g., whether it is a sum, average, or more complex set function). This aggregation choice directly affects whether the single-query counterexamples lift to the multi-query case without additional assumptions.

    Authors: We will add an explicit definition in the revised manuscript: multi-query fairness is the average of the per-query fairness values under the generic function. Under this aggregation the single-query counterexamples extend directly by replication across queries, without requiring further assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity; claim established by explicit counterexamples

full rationale

The paper's central claim—that scoring functions are sub-optimal for achieving all utility-fairness trade-offs—is established via a series of constructed counter-examples under a generic fairness formulation. This is a direct theoretical argument by counterexample rather than any reduction to fitted parameters, self-definitional loops, or load-bearing self-citations. No equations or steps in the provided abstract reduce the result to its own inputs by construction. The approach is self-contained against external benchmarks (the counterexamples themselves) and does not invoke uniqueness theorems or ansatzes from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides insufficient detail for exhaustive ledger; the paper invokes a generic fairness formulation whose precise axioms are not stated here.

axioms (1)
  • domain assumption A generic fairness formulation exists that captures the relevant trade-offs for the counterexamples
    The abstract states the result holds for a generic fairness formulation without specifying its exact properties.

pith-pipeline@v0.9.1-grok · 5714 in / 1202 out tokens · 24890 ms · 2026-06-26T00:51:47.436261+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 42 canonical work pages

  1. [1]

    Equity and Access in Algorithms, Mechanisms, and Optimization , location =

    Fair Decision-Making for Food Inspections , author =. Equity and Access in Algorithms, Mechanisms, and Optimization , location =. doi:10.1145/3551624.3555289 , isbn = 9781450394772, url =

    work page doi:10.1145/3551624.3555289

  2. [2]

    1994 , howpublished =

    Hofmann, Hans , title =. 1994 , howpublished =

    1994

  3. [3]

    Addressing

    Agarwal, Aman and Wang, Xuanhui and Li, Cheng and Bendersky, Michael and Najork, Marc , year =. Addressing. The. doi:10.1145/3308558.3313697 , urldate =

    work page doi:10.1145/3308558.3313697

  4. [4]

    Bruce , year =

    Ai, Qingyao and Bi, Keping and Guo, Jiafeng and Croft, W. Bruce , year =. Learning a. The 41st. doi:10.1145/3209978.3209985 , urldate =

    work page doi:10.1145/3209978.3209985

  5. [5]

    Learning

    Ai, Qingyao and Wang, Xuanhui and Bruch, Sebastian and Golbandi, Nadav and Bendersky, Michael and Najork, Marc , year =. Learning. Proceedings of the 2019. doi:10.1145/3341981.3344218 , urldate =

    work page doi:10.1145/3341981.3344218 2019

  6. [6]

    Asudeh, Abolfazl and Jagadish, H. V. and Stoyanovich, Julia and Das, Gautam , year =. Designing. Proceedings of the 2019. doi:10.1145/3299869.3300079 , urldate =

    work page doi:10.1145/3299869.3300079 2019

  7. [7]

    Asudeh, Abolfazl and Jagadish, H. V. , year =. Responsible. arXiv , langid =:1911.10073 , primaryclass =

    arXiv 1911

  8. [8]

    Bapat, R. B. and Beg, M. I. , year =. Order. Sankhy. 25050725 , eprinttype =

  9. [9]

    Benjaminson, Emma , urldate =. The

  10. [10]

    and Goodrow, Cristos , year =

    Beutel, Alex and Chen, Jilin and Doshi, Tulsee and Qian, Hai and Wei, Li and Wu, Yi and Heldt, Lukasz and Zhao, Zhe and Hong, Lichan and Chi, Ed H. and Goodrow, Cristos , year =. Fairness in. Proceedings of the 25th. doi:10.1145/3292500.3330745 , urldate =

    work page doi:10.1145/3292500.3330745

  11. [11]

    and Gummadi, Krishna P

    Biega, Asia J. and Gummadi, Krishna P. and Weikum, Gerhard , year =. Equity of. The 41st. doi:10.1145/3209978.3210063 , urldate =

    work page doi:10.1145/3209978.3210063

  12. [12]

    Individually

    Bower, Amanda and Eftekhari, Hamid and Yurochkin, Mikhail and Sun, Yuekai , year =. Individually. International

  13. [13]

    2024 , month = jan, journal =

    Bradley--. 2024 , month = jan, journal =

    2024

  14. [14]

    Bruch, Sebastian and Han, Shuguang and Bendersky, Michael and Najork, Marc , year =. A. Proceedings of the 13th. doi:10.1145/3336191.3371844 , urldate =

    work page doi:10.1145/3336191.3371844

  15. [15]

    Learning to

    Burges, Christopher and Ragno, Robert and Le, Quoc , year =. Learning to. Advances in

  16. [16]

    Learning to

    Burges, Chris and Shaked, Tal and Renshaw, Erin and Lazier, Ari and Deeds, Matt and Hamilton, Nicole and Hullender, Greg , year =. Learning to. Proceedings of the 22nd International Conference on. doi:10.1145/1102351.1102363 , urldate =

    work page doi:10.1145/1102351.1102363

  17. [17]

    Learning to Rank: From Pairwise Approach to Listwise Approach , shorttitle =

    Cao, Zhe and Qin, Tao and Liu, Tie-Yan and Tsai, Ming-Feng and Li, Hang , year =. Learning to Rank: From Pairwise Approach to Listwise Approach , shorttitle =. Proceedings of the 24th International Conference on. doi:10.1145/1273496.1273513 , urldate =

    work page doi:10.1145/1273496.1273513

  18. [18]

    Learn to Be

    Chen, Fumian and Fang, Hui , year =. Learn to Be. Proceedings of the 2023. doi:10.1145/3578337.3605132 , urldate =

    work page doi:10.1145/3578337.3605132 2023

  19. [19]

    and Fligner, Michael A

    Critchlow, Douglas E. and Fligner, Michael A. , year =. Paired Comparison, Triple Comparison, and Ranking Experiments as Generalized Linear Models, and Their Implementation on. Psychometrika , volume =. doi:10.1007/BF02294488 , urldate =

    work page doi:10.1007/bf02294488

  20. [20]

    Low-Variance

    Gadetsky, Artyom and Struminsky, Kirill and Robinson, Christopher and Quadrianto, Novi and Vetrov, Dmitry , year =. Low-Variance. doi:10.48550/arXiv.1911.10036 , urldate =. arXiv , keywords =:1911.10036 , primaryclass =

    work page doi:10.48550/arxiv.1911.10036 1911

  21. [21]

    , year =

    Gey, Fredric C. , year =. Inferring Probability of Relevance Using the Method of Logistic Regression , booktitle =

  22. [22]

    Optimizing

    Gorantla, Sruthi and Bhansali, Eshaan and Deshpande, Amit and Louis, Anand , year =. Optimizing. doi:10.48550/arXiv.2308.13242 , urldate =. arXiv , keywords =:2308.13242 , primaryclass =

    work page doi:10.48550/arxiv.2308.13242

  23. [23]

    Sampling

    Gorantla, Sruthi and Deshpande, Amit and Louis, Anand , year =. Sampling. Thirty-. doi:10.24963/ijcai.2023/46 , urldate =

    work page doi:10.24963/ijcai.2023/46 2023

  24. [24]

    Sampling

    Gorantla, Sruthi and Deshpande, Amit and Louis, Anand , year =. Sampling. arXiv , langid =:2203.00887 , primaryclass =

    arXiv

  25. [25]

    Backpropagation through the

    Grathwohl, Will and Choi, Dami and Wu, Yuhuai and Roeder, Geoff and Duvenaud, David , year =. Backpropagation through the. International

  26. [26]

    2019 , month = sep, urldate =

    The. 2019 , month = sep, urldate =

    2019

  27. [27]

    Huijben, Iris A. M. and Kool, Wouter and Paulus, Max B. and. A. 2022 , month = mar, number =. doi:10.48550/arXiv.2110.01515 , urldate =. arXiv , keywords =:2110.01515 , primaryclass =

    work page doi:10.48550/arxiv.2110.01515 2022

  28. [28]

    Javed, Syed Ashar , urldate =

  29. [29]

    Optimizing Search Engines Using Clickthrough Data , booktitle =

    Joachims, Thorsten , year =. Optimizing Search Engines Using Clickthrough Data , booktitle =. doi:10.1145/775047.775067 , urldate =

    work page doi:10.1145/775047.775067

  30. [30]

    Estimation of

    K. Estimation of. Proceedings of the. 2021 , month = apr, series =. doi:10.1145/3442381.3450080 , urldate =

    work page doi:10.1145/3442381.3450080 2021

  31. [31]

    Estimating

    Kool, Wouter and. Estimating. 2020 , journal =

    2020

  32. [32]

    Derivative of the

    Kurbiel, Thomas , year =. Derivative of the. Medium , urldate =

  33. [33]

    and Garg, Nikhil and Borgs, Christian , year =

    Liu, Lydia T. and Garg, Nikhil and Borgs, Christian , year =. Strategic. arXiv:2109.08240 [cs] , eprint =

    arXiv

  34. [34]

    1959 , series =

    Individual Choice Behavior , author =. 1959 , series =

    1959

  35. [35]

    Carnegie Mellon University , langid =

    Lowerre, Bruce T , year =. Carnegie Mellon University , langid =

  36. [36]

    Learning-to-

    Ma, Jiaqi and Yi, Xinyang and Tang, Weijing and Zhao, Zhe and Hong, Lichan and Chi, Ed and Mei, Qiaozhu , year =. Learning-to-. Proceedings of

  37. [37]

    Fairness for

    Memarrast, Omid and Rezaei, Ashkan and Fathony, Rizal and Ziebart, Brian , year =. Fairness for. doi:10.48550/arXiv.2112.06288 , urldate =. arXiv , keywords =:2112.06288 , primaryclass =

    work page doi:10.48550/arxiv.2112.06288

  38. [38]

    Mnih, Andriy and Gregor, Karol , year =. Neural. Proceedings of the 31st

  39. [39]

    Computationally

    Oosterhuis, Harrie , year =. Computationally. doi:10.48550/arXiv.2105.00855 , urldate =. arXiv , keywords =:2105.00855 , primaryclass =

    work page doi:10.48550/arxiv.2105.00855

  40. [40]

    Learning-to-

    Oosterhuis, Harrie , year =. Learning-to-. Proceedings of the 45th. doi:10.1145/3477495.3531842 , urldate =. arXiv , keywords =:2204.10872 , primaryclass =

    work page doi:10.1145/3477495.3531842

  41. [41]

    Fairness of

    Ovaisi, Zohreh and Saadatpanah, Parsa and Sefati, Shahin and Ohannessian, Mesrob and Zheleva, Elena , year =. Fairness of. ACM Transactions on Recommender Systems , doi =

  42. [42]

    Proceedings of the 43rd

    Pang, Liang and Xu, Jun and Ai, Qingyao and Lan, Yanyan and Cheng, Xueqi and Wen, Jirong , year =. Proceedings of the 43rd. doi:10.1145/3397271.3401104 , urldate =

    work page doi:10.1145/3397271.3401104

  43. [43]

    Plackett, R. L. , year =. The. Applied Statistics , volume =. doi:10.2307/2346567 , urldate =. 2346567 , eprinttype =

    work page doi:10.2307/2346567

  44. [44]

    Rastogi, Richa and Joachims, Thorsten , year =. Fair. doi:10.48550/arXiv.2309.01610 , urldate =. arXiv , keywords =:2309.01610 , primaryclass =

    work page doi:10.48550/arxiv.2309.01610

  45. [45]

    Saito, Yuta and Joachims, Thorsten , year =. Fair. Proceedings of the 28th. doi:10.1145/3534678.3539353 , urldate =

    work page doi:10.1145/3534678.3539353

  46. [46]

    Gradient Estimation Using Stochastic Computation Graphs , booktitle =

    Schulman, John and Heess, Nicolas and Weber, Theophane and Abbeel, Pieter , year =. Gradient Estimation Using Stochastic Computation Graphs , booktitle =

  47. [47]

    Shafer, Glenn and Vovk, Vladimir , abstract =. A

  48. [48]

    Fairness of

    Singh, Ashudeep and Joachims, Thorsten , year =. Fairness of. Proceedings of the 24th. doi:10.1145/3219819.3220088 , urldate =

    work page doi:10.1145/3219819.3220088

  49. [49]

    Singh, Ashudeep and Joachims, Thorsten , pages =. Policy. 2019 , journal =

    2019

  50. [50]

    Systems, Laboratory for Intelligent Probabilistic , year =. The. Laboratory for Intelligent Probabilistic Systems , urldate =

  51. [51]

    Markov-Based Ranking Methods , author =

  52. [52]

    Simple Statistical Gradient-Following Algorithms for Connectionist Rein- forcement Learning.Machine Learning, 1992

    Simple Statistical Gradient-Following Algorithms for Connectionist Reinforcement Learning , author =. 1992 , month = may, journal =. doi:10.1007/BF00992696 , urldate =

    work page doi:10.1007/bf00992696 1992

  53. [53]

    Plackett-

    Xia, Tian and Zhai, Shaodan and Wang, Shaojun , year =. Plackett-. doi:10.48550/arXiv.1909.06722 , urldate =. arXiv , keywords =:1909.06722 , primaryclass =

    work page doi:10.48550/arxiv.1909.06722 1909

  54. [54]

    Conformal

    Xu, Yunpeng and Guo, Wenge and Wei, Zhi , year =. Conformal. doi:10.48550/arXiv.2404.17769 , urldate =. arXiv , keywords =:2404.17769 , primaryclass =

    work page doi:10.48550/arxiv.2404.17769

  55. [55]

    Measuring

    Yang, Ke and Stoyanovich, Julia , year =. Measuring. Proceedings of the 29th. doi:10.1145/3085504.3085526 , urldate =

    work page doi:10.1145/3085504.3085526

  56. [56]

    Fairness in

    Zehlike, Meike and Yang, Ke and Stoyanovich, Julia , year =. Fairness in. ACM Computing Surveys , volume =. doi:10.1145/3533379 , urldate =

    work page doi:10.1145/3533379

  57. [57]

    Fairness in

    Zehlike, Meike and Yang, Ke and Stoyanovich, Julia , year =. Fairness in. ACM Computing Surveys , volume =. doi:10.1145/3533380 , urldate =

    work page doi:10.1145/3533380

  58. [58]

    Zhang, Junzi and Kim, Jongho and O'Donoghue, Brendan and Boyd, Stephen , year =. Sample. Proceedings of the AAAI Conference on Artificial Intelligence , volume =. doi:10.1609/aaai.v35i12.17300 , urldate =

    work page doi:10.1609/aaai.v35i12.17300

  59. [59]

    arXiv preprint arXiv:2412.04466 , year=

    User-item fairness tradeoffs in recommendations , author=. arXiv preprint arXiv:2412.04466 , year=

    arXiv

  60. [60]

    Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval , pages=

    Probabilistic Permutation Graph Search: Black-Box Optimization for Fairness in Ranking , author=. Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval , pages=

  61. [61]

    Bekta. Using. 2020 , month = aug, journal =. doi:10.1016/j.cor.2020.104975 , urldate =

    work page doi:10.1016/j.cor.2020.104975 2020

  62. [62]

    Freitag, Markus and. Beam. Proceedings of the. 2017 , month = aug, pages =. doi:10.18653/v1/W17-3207 , urldate =

    work page doi:10.18653/v1/w17-3207 2017

  63. [63]

    Proceedings of the fifteenth ACM international conference on web search and data mining , pages=

    Toward Pareto efficient fairness-utility trade-off in recommendation through reinforcement learning , author=. Proceedings of the fifteenth ACM international conference on web search and data mining , pages=

  64. [64]

    Angwin, Julia and Larson, Jeff and Mattu, Surya and Kirchner, Lauren , year =. Machine

  65. [65]

    Fairness-aware ranking in search & recommendation systems with application to

    Geyik, Sahin Cem and Ambler, Stuart and Kenthapadi, Krishnaram , booktitle=. Fairness-aware ranking in search & recommendation systems with application to

  66. [66]

    Proceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval , pages=

    Measuring and mitigating item under-recommendation bias in personalized ranking systems , author=. Proceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval , pages=

  67. [67]

    Information Processing & Management , volume=

    Toward creating a fairer ranking in search engine results , author=. Information Processing & Management , volume=. 2020 , publisher=

    2020

  68. [68]

    Maxwell and Konstan, Joseph A

    Harper, F. Maxwell and Konstan, Joseph A. , year = 2016, month = jan, journal =. The. doi:10.1145/2827872 , urldate =

    work page doi:10.1145/2827872 2016

  69. [69]

    and Deldjoo, Yashar , year = 2022, month = jul, series =

    Naghiaei, Mohammadmehdi and Rahmani, Hossein A. and Deldjoo, Yashar , year = 2022, month = jul, series =. Proceedings of the 45th. doi:10.1145/3477495.3531959 , urldate =

    work page doi:10.1145/3477495.3531959 2022

  70. [70]

    and Trichakis, Nikolaos , year = 2013, month = feb, journal =

    Bertsimas, Dimitris and Farias, Vivek F. and Trichakis, Nikolaos , year = 2013, month = feb, journal =. Fairness,. doi:10.1287/opre.1120.1138 , urldate =

    work page doi:10.1287/opre.1120.1138 2013

  71. [71]

    Algorithm-

    Cheng, Lingwei and Drayton, Cameron and Chouldechova, Alexandra and Vaithianathan, Rhema , editor =. Algorithm-. Proceedings of the. doi:10.1609/AIES.V7I1.31636 , urldate =

    work page doi:10.1609/aies.v7i1.31636

  72. [72]

    Proceedings of the 2017

    From. Proceedings of the 2017. doi:10.1145/3132847.3132869 , urldate =

    work page doi:10.1145/3132847.3132869 2017

  73. [73]

    Behzad, Tina and Devic, Siddartha and Sharan, Vatsal and Korolova, Aleksandra and Kempe, David , year = 2025, publisher =. An. doi:10.48550/ARXIV.2511.10752 , urldate =

    work page doi:10.48550/arxiv.2511.10752 2025

  74. [74]

    Real-Time

    Grbovic, Mihajlo and Cheng, Haibin , year = 2018, month = jul, series =. Real-Time. Proceedings of the 24th. doi:10.1145/3219819.3219885 , urldate =

    work page doi:10.1145/3219819.3219885 2018