# Counterfactual Fairness Is Basically Demographic Parity

arXiv: https://arxiv.org/abs/2208.03843 · HTML: https://mlsanity.com/paper/2208.03843/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 7 Aug 2022.

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

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [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)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [Reducing Sentiment Bias in Language Models via Counterfactual Evaluation](https://mlsanity.com/paper/1911.03064/) (2019)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [On Formalizing Fairness in Prediction with Machine Learning](https://mlsanity.com/paper/1710.03184/) (2017)
- [Counterfactual Risk Assessments, Evaluation, and Fairness](https://mlsanity.com/paper/1909.00066/) (2019)
- [The Use and Misuse of Counterfactuals in Ethical Machine Learning](https://mlsanity.com/paper/2102.05085/) (2021)
- [FlipTest: Fairness Testing via Optimal Transport](https://mlsanity.com/paper/1906.09218/) (2019)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder](https://mlsanity.com/paper/2011.11878/) (2020)
- [Causal Conceptions of Fairness and their Consequences](https://mlsanity.com/paper/2207.05302/) (2022)
- [The Sensitivity of Counterfactual Fairness to Unmeasured Confounding](https://mlsanity.com/paper/1907.01040/) (2019)
- [Counterfactual Reasoning for Fair Clinical Risk Prediction](https://mlsanity.com/paper/1907.06260/) (2019)
- [Selection, Ignorability and Challenges With Causal Fairness](https://mlsanity.com/paper/2202.13774/) (2022)
- [Causal Multi-Level Fairness](https://mlsanity.com/paper/2010.07343/) (2020)
- [Causal intersectionality for fair ranking](https://mlsanity.com/paper/2006.08688/) (2020)
- [Fairness Constraints: Mechanisms for Fair Classification](https://mlsanity.com/paper/1507.05259/) (2015)

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

- [The Capacity for Moral Self-Correction in Large Language Models](https://mlsanity.com/paper/2302.07459/) (2023)
- [The Possibility of Fairness: Revisiting the Impossibility Theorem in Practice](https://mlsanity.com/paper/2302.06347/) (2023)
- [AIM: Attributing, Interpreting, Mitigating Data Unfairness](https://mlsanity.com/paper/2406.08819/) (2024)
- [Counterfactual Fairness by Combining Factual and Counterfactual Predictions](https://mlsanity.com/paper/2409.01977/) (2024)
- [Navigating Fairness Measures and Trade-Offs](https://mlsanity.com/paper/2307.08484/) (2023)
- [Towards Standardizing AI Bias Exploration](https://mlsanity.com/paper/2405.19022/) (2024)
- [Consistent End-to-End Estimation for Counterfactual Fairness](https://mlsanity.com/paper/2310.17687/) (2023)
- [Counterfactual Fairness Is Not Demographic Parity, and Other Observations](https://mlsanity.com/paper/2402.02663/) (2024)
- [Fairness-enhancing mixed effects deep learning improves fairness on in- and out-of-distribution clustered (non-iid) data](https://mlsanity.com/paper/2310.03146/) (2023)
- [On the Maximal Local Disparity of Fairness-Aware Classifiers](https://mlsanity.com/paper/2406.03255/) (2024)
- [Test-Time Fairness and Robustness in Large Language Models](https://mlsanity.com/paper/2406.07685/) (2024)
- [Towards Large Language Models that Benefit for All: Benchmarking Group Fairness in Reward Models](https://mlsanity.com/paper/2503.07806/) (2025)
- [Do Counterfactually Fair Image Classifiers Satisfy Group Fairness? -- A Theoretical and Empirical Study](https://mlsanity.com/paper/2607.06603/) (2026)
- [Evaluating AI Group Fairness: a Fuzzy Logic Perspective](https://mlsanity.com/paper/2406.18939/) (2024)
- [Comparative assessment of fairness definitions and bias mitigation strategies in machine learning-based diagnosis of Alzheimer's disease from MR images](https://mlsanity.com/paper/2505.23528/) (2025)

## Abstract (arXiv)

Making fair decisions is crucial to ethically implementing machine learning algorithms in social settings. In this work, we consider the celebrated definition of counterfactual fairness [Kusner et al., NeurIPS, 2017]. We begin by showing that an algorithm which satisfies counterfactual fairness also satisfies demographic parity, a far simpler fairness constraint. Similarly, we show that all algorithms satisfying demographic parity can be trivially modified to satisfy counterfactual fairness. Together, our results indicate that counterfactual fairness is basically equivalent to demographic parity, which has important implications for the growing body of work on counterfactual fairness. We then validate our theoretical findings empirically, analyzing three existing algorithms for counterfactual fairness against three simple benchmarks. We find that two simple benchmark algorithms outperform all three existing algorithms -- in terms of fairness, accuracy, and efficiency -- on several data sets. Our analysis leads us to formalize a concrete fairness goal: to preserve the order of individuals within protected groups. We believe transparency around the ordering of individuals within protected groups makes fair algorithms more trustworthy. By design, the two simple benchmark algorithms satisfy this goal while the existing algorithms for counterfactual fairness do not.