# The Possibility of Fairness: Revisiting the Impossibility Theorem in Practice

arXiv: https://arxiv.org/abs/2302.06347 · HTML: https://mlsanity.com/paper/2302.06347/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 68 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 23 of 23)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [A comparative study of fairness-enhancing interventions in machine learning](https://mlsanity.com/paper/1802.04422/) (2018)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Aequitas: A Bias and Fairness Audit Toolkit](https://mlsanity.com/paper/1811.05577/) (2018)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Empirical observation of negligible fairness-accuracy trade-offs in machine learning for public policy](https://mlsanity.com/paper/2012.02972/) (2020)
- [Towards the Right Kind of Fairness in AI](https://mlsanity.com/paper/2102.08453/) (2021)
- [Counterfactual Fairness Is Basically Demographic Parity](https://mlsanity.com/paper/2208.03843/) (2022)
- [Pushing the limits of fairness impossibility: Who's the fairest of them all?](https://mlsanity.com/paper/2208.12606/) (2022)
- [Case Study: Predictive Fairness to Reduce Misdemeanor Recidivism Through Social Service Interventions](https://mlsanity.com/paper/2001.09233/) (2020)
- [Achieving Fairness via Post-Processing in Web-Scale Recommender Systems](https://mlsanity.com/paper/2006.11350/) (2020)
- [Towards Substantive Conceptions of Algorithmic Fairness: Normative Guidance from Equal Opportunity Doctrines](https://mlsanity.com/paper/2207.02912/) (2022)
- [Fairness as Equality of Opportunity: Normative Guidance from Political Philosophy](https://mlsanity.com/paper/2106.08259/) (2021)
- [A Recommendation and Risk Classification System for Connecting Rough Sleepers to Essential Outreach Services](https://mlsanity.com/paper/2007.15326/) (2020)

## Built on by (most cited first, 18 of 18)

- [Causal Context Connects Counterfactual Fairness to Robust Prediction and Group Fairness](https://mlsanity.com/paper/2310.19691/) (2023)
- [Fairness in Algorithmic Recourse Through the Lens of Substantive Equality of Opportunity](https://mlsanity.com/paper/2401.16088/) (2024)
- [Understanding Fairness Surrogate Functions in Algorithmic Fairness](https://mlsanity.com/paper/2310.11211/) (2023)
- [Embracing Contradiction: Theoretical Inconsistency Will Not Impede the Road of Building Responsible AI Systems](https://mlsanity.com/paper/2505.18139/) (2025)
- [What is Fair? Defining Fairness in Machine Learning for Health](https://mlsanity.com/paper/2406.09307/) (2024)
- [Overcoming Fairness Trade-offs via Pre-processing: A Causal Perspective](https://mlsanity.com/paper/2501.14710/) (2025)
- [Addressing Both Statistical and Causal Gender Fairness in NLP Models](https://mlsanity.com/paper/2404.00463/) (2024)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [Fair Enough? A map of the current limitations of the requirements to have fair algorithms](https://mlsanity.com/paper/2311.12435/) (2023)
- [Cherry on the Cake: Fairness is NOT an Optimization Problem](https://mlsanity.com/paper/2406.16606/) (2024)
- [FairlyUncertain: A Comprehensive Benchmark of Uncertainty in Algorithmic Fairness](https://mlsanity.com/paper/2410.02005/) (2024)
- [Beyond Predictions: A Participatory Framework for Multi-Stakeholder Decision-Making](https://mlsanity.com/paper/2502.08542/) (2025)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [FAIRTOPIA: Envisioning Multi-Agent Guardianship for Disrupting Unfair AI Pipelines](https://mlsanity.com/paper/2506.09107/) (2025)
- [Fair Classification by Direct Intervention on Operating Characteristics](https://mlsanity.com/paper/2509.25481/) (2025)
- [An Accounting Identity for Algorithmic Fairness](https://mlsanity.com/paper/2601.20217/) (2026)
- [How Supply Chain Dependencies Complicate Bias Measurement and Accountability Attribution in AI Hiring Applications](https://mlsanity.com/paper/2604.22679/) (2026)
- [The Pok'emon Theorem and other Fairness Impossibility Results](https://mlsanity.com/paper/2605.09221/) (2026)

## Abstract (arXiv)

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two special cases: when the prevalence of the outcome being predicted is equal across groups, or when a perfectly accurate predictor is used. However, theory does not always translate to practice. In this work, we challenge the implications of the impossibility theorem in practical settings. First, we show analytically that, by slightly relaxing the impossibility theorem (to accommodate a textitpractitioner's perspective of fairness), it becomes possible to identify a large set of models that satisfy seemingly incompatible fairness constraints. Second, we demonstrate the existence of these models through extensive experiments on five real-world datasets. We conclude by offering tools and guidance for practitioners to understand when -- and to what degree -- fairness along multiple criteria can be achieved. For example, if one allows only a small margin-of-error between metrics, there exists a large set of models simultaneously satisfying False Negative Rate Parity, False Positive Rate Parity, and Positive Predictive Value Parity, even when there is a moderate prevalence difference between groups. This work has an important implication for the community: achieving fairness along multiple metrics for multiple groups (and their intersections) is much more possible than was previously believed.