# On the (im)possibility of fairness

arXiv: https://arxiv.org/abs/1609.07236 · HTML: https://mlsanity.com/paper/1609.07236/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2016.

## Built on by (most cited first, 11 of 11)

- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [Emergent Unfairness in Algorithmic Fairness-Accuracy Trade-Off Research](https://mlsanity.com/paper/2102.01203/) (2021)
- [Marrying Fairness and Explainability in Supervised Learning](https://mlsanity.com/paper/2204.02947/) (2022)
- [Conformity Assessments and Post-market Monitoring: A Guide to the Role of Auditing in the Proposed European AI Regulation](https://mlsanity.com/paper/2111.05071/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [`It is currently hodgepodge'': Examining AI/ML Practitioners' Challenges during Co-production of Responsible AI Values](https://mlsanity.com/paper/2307.10221/) (2023)
- [Locating disparities in machine learning](https://mlsanity.com/paper/2208.06680/) (2022)
- [Bias Discovery in Machine Learning Models for Mental Health](https://mlsanity.com/paper/2205.12093/) (2022)
- [Beyond traditional assumptions in fair machine learning](https://mlsanity.com/paper/2101.12476/) (2021)
- [Assessing Phenotype Definitions for Algorithmic Fairness](https://mlsanity.com/paper/2203.05174/) (2022)
- [The Flawed Foundations of Fair Machine Learning](https://mlsanity.com/paper/2306.01417/) (2023)

## Abstract (arXiv)

What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which the distinctions in previous papers can be made formal. In addition to characterizing the spaces of inputs (the "observed" space) and outputs (the "decision" space), we introduce the notion of a construct space: a space that captures unobservable, but meaningful variables for the prediction. We show that in order to prove desirable properties of the entire decision-making process, different mechanisms for fairness require different assumptions about the nature of the mapping from construct space to decision space. The results in this paper imply that future treatments of algorithmic fairness should more explicitly state assumptions about the relationship between constructs and observations.