The DOI matches its DataCite record; 21 of the 35 references it cites were found in a registry or an index.
Inherent Trade-Offs in the Fair Determination of Risk Scores
Open accessAbstract
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness conditions that lie at the heart of these debates, and we prove that except in highly constrained special cases, there is no method that can satisfy these three conditions simultaneously. Moreover, even satisfying all three conditions approximately requires that the data lie in an approximate version of one of the constrained special cases identified by our theorem. These results suggest some of the ways in which key notions of fairness are incompatible with each other, and hence provide a framework for thinking about the trade-offs between them.
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“each technical definition carry strong values assumptions which can often be in tension with each other (Friedler et al., 2016; Kleinberg et al., 2017).”
From Social Data: Biases, Methodological Pitfalls, and Ethical Boundaries (2019) · cites this paper as Kleinberg et al., 2017
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“Existing literature often treats fairness and performance as a trade-off problem”
From The Impact of Structured Validation and Audit Frameworks on the Fairness and Efficiency of AI-Driven Hiring Systems (2025) · cites this paper as Kleinberg et al., 2017
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“Many fairness metrics have been proposed, and the most widely used criteria were shown to be incompatible ([20], [41]), and to present risks for the populations they were meant to protect ([24]).”
From Fairness and explainability in automatic decision-making systems. A challenge for computer science and law (2023) · cites this paper as [41]
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“commonly used statistical fairness criteria can be mutually incompatible except under restrictive conditions”
From The Impact of Structured Validation and Audit Frameworks on the Fairness and Efficiency of AI-Driven Hiring Systems (2025) · cites this paper as Kleinberg et al., 2017
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“Kleinberg, Mullainathan and Raghavan (2017) shows theoretically that these notions of fairness are usually incompatible.”
From An algorithm for removing sensitive information: Application to race-independent recidivism prediction (2019) · cites this paper as Kleinberg, Mullainathan and Raghavan (2017)
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“These two notions of fairness are indeed distinct.”
From An algorithm for removing sensitive information: Application to race-independent recidivism prediction (2019) · cites this paper as Kleinberg, Mullainathan and Raghavan (2017)
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“propose a framework based on a task-specific externally defined similarity metric between individuals, seeking to achieve fairness through the goal that “similar people [be] treated similarly” [11].”
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“Barocas and Selbst survey a range of ways in which data-analysis algorithms can lead to discriminatory outcomes [3], and review articles by Romei and Ruggieri [25] and Zliobaite [30] survey data-analytic and algorithmic methods for measuring discrimination.”
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“consider the natural analogues of our conditions (B) and (C), balance for the negative and positive classes, in the case of classifiers that output binary “yes/no” predictions rather than real-valued scores as in our case [19].”
Fair prediction with disparate impact: a study of bias in recidivism prediction instruments
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Certifying and Removing Disparate Impact
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“This latter global requirement is a version of statistical parity [12, 4, 21, 22].”
BackgroundAlgorithmic Decision Making and the Cost of Fairness
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“[7] (and see also [6]) consider binary prediction subject to analogues of the balance conditions for the negative and positive classes, together with a form of calibration adapted to binary prediction.”
BackgroundDiscrimination in online ad delivery
Sweeney, L. (2013) · Communications of the ACM · doi:10.1145/2447976.2447990 · Cited by 783 · cited 1×
“Second, in a very different domain, researchers have begun to analyze the ways in which different genders and racial groups experience advertising and commercial content on the Internet differently [9, 26].”
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Flagged first, then by citations
14 of the 35 references couldn’t be matched to a known paper.
Research works printed but not linked: 3
- [9][9] Amit Datta, Michael Carl Tschantz, and Anupam Datta. Automated experiments on ad privacy settings. Proceedings on Privacy Enhancing Technologies , 2015(1):92-112, 2015. -
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“In a related line of work, Kleinberg et al. [17] explore the inherent trade-offs between different notions of fairness, emphasizing again the difficulty of achieving unbiased cloud-based machine learning models.”
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“3) Calibration: Another important fairness criterion, especially relevant in risk prediction tasks common in healthcare, is calibration [8].”
Fitzpatrick Thresholding for Skin Image Segmentation
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“…Applying stratified thresholds to binary classification is not trivial: raising sensitivity for an under-served group often worsens its false-positive rate, and—by impossibility results—one cannot simultaneously satisfy perfect calibration and equalized odds once prevalence differs [14, 18].”
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“Furthermore, research indicates that different definitions of group fairness can sometimes be contradictory [3, 27].”
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“In addition to these tradeoffs, we believe that students at this level should be introduced to the lack of a singular “Fairness” metric, as well as the inherent tradeoffs between accuracy and fairness [10, 21].”
Dual erosion of equality and remedy in algorithmic decision systems
Johari, B. (2026) · Discover Artificial Intelligence · doi:10.1007/s44163-026-01040-6 · Cited by 3
Wegner, L., Mirsch, M., & Leicht-Scholten, C. (2026) · AI and Ethics · doi:10.1007/s43681-026-01036-z · Cited by 2
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Kaul, S. (2018) · Proceedings of the AAAI/ACM Conference on AI Ethics and Society · doi:10.1145/3278721.3278748 · Cited by 1
“(Kleinberg, Mullainathan, and Raghavan 2016; Chouldechova 2017) initiated the study of such tradeoffs, proving that TPRs and TNRs typically cannot be equated for calibrated scores.”
BackgroundDEFINING AND DETECTING FAIRNESS BIAS FOR BINARY CLASSIFICATION PROBLEM IN FINANCIAL ANALYSIS
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(2022) · Philosophical studies series · doi:10.1007/978-3-030-75267-5 · Cited by 1
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“Recently, evidence has emerged that enhancing accuracy comes at the cost of equity [11]–[18]; models end up discriminating against people due to their age, gender, or race, since accuracy could work in opposition to equity [19]–[21].”
BackgroundTowards Fairness and Interpretability: Clinical Decision Support for Acute Coronary Syndrome
Sahoo, H. S., Ingraham, N. E., Silverman, G., & Sartori, J. (2022) · International Conference on Machine Learning and Applications · doi:10.1109/icmla55696.2022.00146 · Cited by 2
“…for demographic parity is however not practical for devising CDS models for ACS prediction because it may restrict the model from capturing critical clinical attributes associated to the sensitive attribute and the outcome, hence decreasing the model’s performance for all demographics groups [18].”
MethodActive feature elicitation: An unified framework
Das, S., Ramanan, N., Kunapuli, G., Predrag Radivojac, A., & Natarajan, S. (2023) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2023.1029943 · Cited by 1
“While our work has been motivated as improving a specific performance metric such as accuracy, the framework is general enough to incorporate any metric including more recently addressed fairness metrics (Dwork et al., 2012; Kleinberg et al., 2017; Gillen et al., 2018).”
MethodSoft Ethics and the Governance of AI
Floridi, L. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780198883098.003.0006 · Cited by 1
DNBP: Differentiable Nonparametric Belief Propagation
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“More broadly, the past decade has seen a transformative proliferation of discriminative neural networks [10, 34, 62] as well as extraordinary growth in the body of research focused on algorithmic fairness [15, 33].”
BackgroundMindSet: A Bias-Detection Interface Using a Visual Human-in-the-Loop Workflow
Kalananthan, S., Kichutkin, A., Shang, Z., Strausz, A., Bautiste, F. J. S., & El‐Assady, M. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-50485-3_8 · Cited by 1
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“This principle is distinct from the “right to be forgotten” (Biega et al. 2020), which enables individuals to submit requests to have their data deleted.”
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BackgroundBig data and the risk of misguided responsibilization
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“…certain phenomena happen with different likelihoods among mem - bers of different subgroups, this leads to complex statistical challenges and can mean that members of minorities have greater error intervals than members of the majority (see e.g., Kleinberg et al., 2017 ; Schmidt & Stephens, 2019).”
BackgroundCross-Cultural Fairness of the PCL: SV: A New Zealand Analysis
Botha, R., Nichols, T., & Polaschek, D. L. L. (2024) · Criminal Justice and Behavior · doi:10.1177/00938548241297649 · Cited by 1
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MethodTransparency, Statistics, and Justice System Knowledge Is Essential for Science of Risk Assessment
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An Exploratory Study on Fairness-Aware Design Decision-Making
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BackgroundL’équité de l’apprentissage machine en assurance
Arthur Charpentier, A., & Barry, L. (2022) · Statistique et société · doi:10.4000/statsoc.550 · Cited by 3
“Apprentissage”
Practical bias correction in neural networks: a credit default prediction case study
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“Forexample, Kleinbergetal. showthatamodelcannotintegratemultiplefairnessmet-rics simultaneously, except in highly constrained special cases [24].”
BackgroundMeasurement invariance, selection invariance, and fair selection revisited.
Heesen, R., & Romeijn, J. (2022) · Psychological Methods · doi:10.1037/met0000491 · Cited by 2
“Interestingly, the problem of implicit discrimination in Borsboom et al. (2008) was rediscovered, presumably independently, by Kleinberg et al. (2017) and Chouldechova (2017) in the context of the discussion on fairness in Artificial Intelligence (AI): a machine learner that fairly judges…”
BackgroundResultInfluentialA New Framework to Assess the Individual Fairness of Probabilistic Classifiers
Khan, M. F. A., & Karimi, H. R. (2022) · International Conference on Machine Learning and Applications · doi:10.1109/icmla55696.2022.00145 · Cited by 1
“Moreover, different definitions of group fairness often contradict each other [12], [13], [14].”
BackgroundPhase Transitions of Diversity in Stochastic Block Model Dynamics
Brânzei, S., Kumar, N., & Ranade, G. V. (2023) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton58177.2023.10313364 · Cited by 1
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“(For example, a thriving line of work in Machine Learning (ML) addresses the unfairness that arises when ML predictions inform high-stakes decisions [18, 22, 31, 8, 1, 16, 11] by defining it as a form of predictive disparity, e.”
BackgroundOn the Fairness of Machine-Assisted Human DecisionsPreprint
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“Because fairness criteria are mutually incompatible in general (Barocas, Hardt, & Narayanan, 2023; Kleinberg, Mullainathan, & Raghavan, 2017), applying a criterion from the ML literature without first verifying that it aligns with the specific regulatory standard being enforced can produce findings…”
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“Our proposed method addresses the problem of balancing error rates in classification, which is explored in [31], [32] and addressed by methods in [10], [13], [29].”
MethodGuest Editors’ Comments: Risk Assessment and Judicial Decision Making
Salisbury, E. J., Sundt, J. L., & Boppre, B. (2019) · Criminal Justice and Behavior · doi:10.1177/0093854818821958
Access to Population-Level Signaling as a Source of InequalityPreprint
Immorlica, N., Ligett, K., & Ziani, J. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1809.04224 · Cited by 1
“At a high level, these objectives tend to focus either on ensuring grouplevel fairness [8, 17, 19, 23, 24, 29, 31, 32, 40] or individual-level fairness [15, 27, 30].”
BackgroundTowards Effective Data Augmentations via Unbiased GAN Utilization
Verma, S., Wang, C., Zhu, L., & Liu, W. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-29894-4_45 · Cited by 1
Designing Interfaces to Help Stakeholders Comprehend, Navigate, and Manage Algorithmic Trade-Offs.Preprint
Yu, B., Yuan, Y., Terveen, L., Wu, Z. S., & Zhu, H. (2019) · arXiv (Cornell University)
Framework for developing algorithmic fairness
Kristiadi, D. P., Sunarya, P. A., Ismanto, M., Dylan, J., Santoso, I. R., & Warnars, H. L. H. S. (2020) · Bulletin of Electrical Engineering and Informatics · doi:10.11591/eei.v9i4.2028 · Cited by 1
“Kleinberg et al. specify their three desired property of fairness as [9] a. Calibration within groups: For every group, a score of x should mean an x fraction of people in category b is positive, independent of each group’s protected attribute. b. Balancing for the positive class is when the…”
BackgroundAbstraction and Prediction Algorithms: A Harm-reduction Framework
Desilvestro, A. (2020) · Tuwhera (Auckland University of Technology)
Predição do Risco de Reprovação no Ensino Superior Usando Algoritmos de Machine Le-arning
da Silva, A. F., de Almeida, A. T. C., & Ramalho, H. M. D. B. (2020) · Teoria e Prática em Administração · doi:10.21714/2238-104x2020v10i2-51124
Legally grounded fairness objectivesPreprint
Holden-Sim, D., Leech, G., & Aitchison, L. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2009.11677
“But we can prove that some sets of commonsensical definitions are incompatible, outside trivial cases (Kleinberg et al., 2016; A.Chouldechova, 2017).”
BackgroundAlgorithmic Suspicion and Big Data Searches
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0007
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0008
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0006
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0002
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0001
Brayne, S. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780190684099.003.0005
Fair Learning: an optimal transport based approach
Gordaliza, P. (2020) · UVaDOC UVaDOC University of Valladolid Documentary Repository (University of Valladolid) · doi:10.35376/10324/43392
State-Visitation Fairness in Average-Reward MDPs.Preprint
Ghalme, G. S., Nair, V., Patil, V., & Zhou, Y. (2021) · arXiv (Cornell University)
Conclusion: Toward Technical Culture
Rieder, B. (2020) · Amsterdam University Press eBooks · doi:10.5117/9789462986190_concl
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0008
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0011
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0004
The Epistemology of Prejudice Acquisition
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0005
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0010
The Epistemology of Prejudice Maintenance
Begby, E. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780198852834.003.0006
Predictive Power at What Cost? Economic and Racial Justice of Data-Driven AlgorithmsPreprint
Jabri, R. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3422535
Non-Comparative Fairness for Human-Auditing and Its Relation to Traditional Fairness NotionsPreprint
Telukunta, M., & Nadendla, V. S. S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.01277
“Another example for group-conditional metric is calibration [12], [13] which ensures positive predictive value across different groups.”
BackgroundInfluentialTowards Reducing Biases in Combining Multiple Experts Online
Sun, Y., Díaz, I. R., Infante, A. C., & Veeramachaneni, K. K. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/416
“However, recent work shows that it is impossible to achieve equalized odds [Chouldechova, 2017; Kleinberg et al. , 2017] simultaneously with other notions of fairness such as calibration, which requires that outcomes are independent of protected attributes conditional on the estimates from…”
BackgroundFARF: A Fair and Adaptive Random Forests ClassifierPreprint
Zhang, W., Bifet, A., Zhang, X., Weiss, J. C., & Nejdl, W. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.07403
“Current methods also lack a mechanism for easily adjusting the trade-off that exists between accuracy and fairness [27,28].”
MethodEnhancing Fairness in Supervised Machine Learning
Omidi, B. (2021) · uO Research (University of Ottawa) · doi:10.20381/ruor-26258
Metadata
- Authors
- Kleinberg, J., Mullainathan, S., & Raghavan, M.
- Affiliations
- Cornell University (US)
- Harvard University (US)
- University of California, Berkeley (US)
- Venue
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Publisher
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Published
- 2017
- ISSN
- 2331-8422 (ISSN-L)
- OpenAlex
- W2962922665
- Cited by
- 943
- References
- 35
- Citations by year
- 2026: 49 · 2025: 74 · 2024: 112 · 2023: 139 · 2022: 102 · 2021: 153 · 2020: 129 · 2019: 107 · 2018: 54 · 2017: 21
- Type
- posted content
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- arXiv (Cornell University) (submittedVersion)
- DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Leibniz international proceedings in informatics (cc-by)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Ethics and Social Impacts of AI
- Physical Sciences › Computer Science › Artificial Intelligence › Explainable Artificial Intelligence (XAI)
- Physical Sciences › Computer Science › Artificial Intelligence › Privacy-Preserving Technologies in Data
- Keywords
- algorithmic fairness, risk score, probabilistic classification, fairness conditions, impossibility results
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