# Pushing the limits of fairness impossibility: Who's the fairest of them all?

arXiv: https://arxiv.org/abs/2208.12606 · HTML: https://mlsanity.com/paper/2208.12606/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 24 Aug 2022.

## Builds on (most cited first, 18 of 18)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [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)
- [AI Fairness 360: An Extensible Toolkit for Detecting, Understanding, and Mitigating Unwanted Algorithmic Bias](https://mlsanity.com/paper/1810.01943/) (2018)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [A Confidence-Based Approach for Balancing Fairness and Accuracy](https://mlsanity.com/paper/1601.05764/) (2016)
- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [Empirical observation of negligible fairness-accuracy trade-offs in machine learning for public policy](https://mlsanity.com/paper/2012.02972/) (2020)
- [General Heuristics for Nonconvex Quadratically Constrained Quadratic Programming](https://mlsanity.com/paper/1703.07870/) (2017)
- [Achieving Fairness via Post-Processing in Web-Scale Recommender Systems](https://mlsanity.com/paper/2006.11350/) (2020)
- [The Impossibility Theorem of Machine Fairness -- A Causal Perspective](https://mlsanity.com/paper/2007.06024/) (2020)
- [The impossibility of "fairness": a generalized impossibility result for decisions](https://mlsanity.com/paper/1707.01195/) (2017)
- [Tightening McCormick Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning](https://mlsanity.com/paper/1606.05806/) (2016)

## Built on by (most cited first, 15 of 15)

- [FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods](https://mlsanity.com/paper/2306.09468/) (2023)
- [The Possibility of Fairness: Revisiting the Impossibility Theorem in Practice](https://mlsanity.com/paper/2302.06347/) (2023)
- [Causal Context Connects Counterfactual Fairness to Robust Prediction and Group Fairness](https://mlsanity.com/paper/2310.19691/) (2023)
- [Disentangling and Operationalizing AI Fairness at LinkedIn](https://mlsanity.com/paper/2306.00025/) (2023)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [Beyond Predictions: A Participatory Framework for Multi-Stakeholder Decision-Making](https://mlsanity.com/paper/2502.08542/) (2025)
- [Superhuman Fairness](https://mlsanity.com/paper/2301.13420/) (2023)
- [An Operational Perspective to Fairness Interventions: Where and How to Intervene](https://mlsanity.com/paper/2302.01574/) (2023)
- [A Canonical Data Transformation for Achieving Inter- and Within-group Fairness](https://mlsanity.com/paper/2310.15097/) (2023)
- [Balancing Fairness and Accuracy in Data-Restricted Binary Classification](https://mlsanity.com/paper/2403.07724/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [LiLAW: Lightweight Learnable Adaptive Weighting to Learn Sample Difficulty & Improve Noisy Training](https://mlsanity.com/paper/2509.20786/) (2025)
- [Fair Classification by Direct Intervention on Operating Characteristics](https://mlsanity.com/paper/2509.25481/) (2025)
- [Revisiting Fairness Impossibility with Endogenous Behavior](https://mlsanity.com/paper/2604.06378/) (2026)
- [FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data](https://mlsanity.com/paper/2606.23515/) (2026)

## Abstract (arXiv)

The impossibility theorem of fairness is a foundational result in the algorithmic fairness literature. It states that outside of special cases, one cannot exactly and simultaneously satisfy all three common and intuitive definitions of fairness - demographic parity, equalized odds, and predictive rate parity. This result has driven most works to focus on solutions for one or two of the metrics. Rather than follow suit, in this paper we present a framework that pushes the limits of the impossibility theorem in order to satisfy all three metrics to the best extent possible. We develop an integer-programming based approach that can yield a certifiably optimal post-processing method for simultaneously satisfying multiple fairness criteria under small violations. We show experiments demonstrating that our post-processor can improve fairness across the different definitions simultaneously with minimal model performance reduction. We also discuss applications of our framework for model selection and fairness explainability, thereby attempting to answer the question: who's the fairest of them all?