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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“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)
In the citing paper
“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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Dwork, C., Hardt, M., Pitassi, T., Reingold, O., & Zemel, R. (2012) · Proceedings of the 3rd Innovations in Theoretical Computer Science Conference · doi:10.1145/2090236.2090255 · Cited by 3,501 · cited 1×
“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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“Here too we can ask whether such decision-making is being applied uniformly across different groups of patients [16, 27], and in particular how medical tests may play a differential role for conditions that vary widely in frequency between these groups.”
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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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Hardt, M., Price, E., & Srebro, N. (2016) · arXiv · doi:10.48550/arxiv.1610.02413 · Cited by 2,536 · cited 1×
“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
Chouldechova, A. (2017) · Big Data · doi:10.1089/big.2016.0047 · Cited by 2,159 · cited 3×
“Also concurrent with our work and that of Hardt et al., Chouldechova [5] and Corbett-Davies et al. [6] (and see also [7]) consider binary prediction subject to these same analogues of the balance conditions for the negative and positive classes, together with a form of calibration adapted to binary prediction (requiri…”
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
Corbett-Davies, S., Pierson, E., Feller, A., Goel, S., & Huq, A. Z. (2017) · Knowledge Discovery and Data Mining · doi:10.1145/3097983.309809 · Cited by 1,464 · cited 1×
“[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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Calders, T., & Verwer, S. (2010) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-010-0190-x · Cited by 764 · cited 3×
“Work in these directions has developed learning algorithms that penalize violations of statistical parity [4, 22].”
BackgroundAutomated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination
Datta, A., Tschantz, M. C., & Datta, A. (2015) · Proceedings on Privacy Enhancing Technologies · doi:10.1515/popets-2015-0007 · Cited by 676 · 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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- [29][29] Richard S Zemel, Yu Wu, Kevin Swersky, Toniann Pitassi, and Cynthia Dwork. Learning Fair Representations. Proceedings of the 30th International Conference on Machine Learning , 28:325-333, 2013. -
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Nurhan, Y. I., & Short, M. B. (2026) · European Journal of Applied Mathematics · doi:10.1017/s0956792525100296
“Further, it is known [4, 11] that some fairness metrics are inherently incompatible with others, such that both cannot possibly be achieved simultaneously.”
Algorithmic fairness in context: liberty, opportunity, and well-being as ethical anchors
Perdana, A., Li, P., & Wangge, G. (2026) · AI and Ethics · doi:10.1007/s43681-025-00963-7
“Equalizing false positive and false negative rates (equalized odds) across groups with differing base rates of recidivism, whether defined by race, gender, or age, math - ematically requires departing from perfect calibration [ 24 , 61 ].”
InfluentialTalking to Our Students About Generative AI
Rebelsky, W. (2026) · ACM Technical Symposium on Computer Science Education (SIGCSE) · doi:10.1145/3770762.3772642
“Unfortunately, knowing about these biases is not enough to fix them due to the “unknown unknowns” [26] and the impossibility of balancing various definitions of fairness [36].”
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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