# Unravelling the (In)compatibility of Statistical-Parity and Equalized-Odds

arXiv: https://arxiv.org/abs/2601.19035 · HTML: https://mlsanity.com/paper/2601.19035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [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)
- [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)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Fairness Testing: Testing Software for Discrimination](https://mlsanity.com/paper/1709.03221/) (2017)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [On the relation between accuracy and fairness in binary classification](https://mlsanity.com/paper/1505.05723/) (2015)
- [Fairness Metrics: A Comparative Analysis](https://mlsanity.com/paper/2001.07864/) (2020)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Data Representativity for Machine Learning and AI Systems](https://mlsanity.com/paper/2203.04706/) (2022)
- [A Possibility in Algorithmic Fairness: Can Calibration and Equal Error Rates Be Reconciled?](https://mlsanity.com/paper/2002.07676/) (2020)

## Abstract (arXiv)

A key challenge in employing data, algorithms and data-driven systems is to adhere to the principle of fairness and justice. Statistical fairness measures belong to an important category of technical/formal mechanisms for detecting fairness issues in data and algorithms. In this contribution we study the relations between two types of statistical fairness measures namely Statistical-Parity and Equalized-Odds. The Statistical-Parity measure does not rely on having ground truth, i.e., (objectively) labeled target attributes. This makes Statistical-Parity a suitable measure in practice for assessing fairness in data and data classification algorithms. Therefore, Statistical-Parity is adopted in many legal and professional frameworks for assessing algorithmic fairness. The Equalized-Odds measure, on the contrary, relies on having (reliable) ground-truth, which is not always feasible in practice. Nevertheless, there are several situations where the Equalized-Odds definition should be satisfied to enforce false prediction parity among sensitive social groups. We present a novel analyze of the relation between Statistical-Parity and Equalized-Odds, depending on the base-rates of sensitive groups. The analysis intuitively shows how and when base-rate imbalance causes incompatibility between Statistical-Parity and Equalized-Odds measures. As such, our approach provides insight in (how to make design) trade-offs between these measures in practice. Further, based on our results, we plea for examining base-rate (im)balance and investigating the possibility of such an incompatibility before enforcing or relying on the Statistical-Parity criterion. The insights provided, we foresee, may trigger initiatives to improve or adjust the current practice and/or the existing legal frameworks.