# Attainability and Optimality: The Equalized Odds Fairness Revisited

arXiv: https://arxiv.org/abs/2202.11853 · HTML: https://mlsanity.com/paper/2202.11853/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [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)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [A Confidence-Based Approach for Balancing Fairness and Accuracy](https://mlsanity.com/paper/1601.05764/) (2016)
- [A causal framework for discovering and removing direct and indirect discrimination](https://mlsanity.com/paper/1611.07509/) (2016)
- [PC-Fairness: A Unified Framework for Measuring Causality-based Fairness](https://mlsanity.com/paper/1910.12586/) (2019)
- [Achieving Equalized Odds by Resampling Sensitive Attributes](https://mlsanity.com/paper/2006.04292/) (2020)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [R'enyi Fair Inference](https://mlsanity.com/paper/1906.12005/) (2019)
- [Learning Fair Representations for Kernel Models](https://mlsanity.com/paper/1906.11813/) (2019)

## Built on by (most cited first, 10 of 10)

- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Intrinsic Fairness-Accuracy Tradeoffs under Equalized Odds](https://mlsanity.com/paper/2405.07393/) (2024)
- [FairICP: Encouraging Equalized Odds via Inverse Conditional Permutation](https://mlsanity.com/paper/2404.05678/) (2024)
- [Long-Term Fairness Inquiries and Pursuits in Machine Learning: A Survey of Notions, Methods, and Challenges](https://mlsanity.com/paper/2406.06736/) (2024)
- [Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective](https://mlsanity.com/paper/2506.07861/) (2025)
- [The Cost of Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.22762/) (2025)
- [Building Trustworthy AI for Materials Discovery: From Autonomous Laboratories to Z-scores](https://mlsanity.com/paper/2512.01080/) (2025)
- [FairMT: Fairness for Heterogeneous Multi-Task Learning](https://mlsanity.com/paper/2512.00469/) (2025)
- [Using Property Elicitation to Understand the Impacts of Fairness Regularizers](https://mlsanity.com/paper/2309.11343/) (2023)
- [Happiness as a Measure of Fairness](https://mlsanity.com/paper/2511.01069/) (2025)

## Abstract (arXiv)

Fairness of machine learning algorithms has been of increasing interest. In order to suppress or eliminate discrimination in prediction, various notions as well as approaches have been proposed to impose fairness. Given a notion of fairness, an essential problem is then whether or not it can always be attained, even if with an unlimited amount of data. This issue is, however, not well addressed yet. In this paper, focusing on the Equalized Odds notion of fairness, we consider the attainability of this criterion and, furthermore, if it is attainable, the optimality of the prediction performance under various settings. In particular, for prediction performed by a deterministic function of input features, we give conditions under which Equalized Odds can hold true; if the stochastic prediction is acceptable, we show that under mild assumptions, fair predictors can always be derived. For classification, we further prove that compared to enforcing fairness by post-processing, one can always benefit from exploiting all available features during training and get potentially better prediction performance while remaining fair. Moreover, while stochastic prediction can attain Equalized Odds with theoretical guarantees, we also discuss its limitation and potential negative social impacts.