# A Possibility in Algorithmic Fairness: Can Calibration and Equal Error Rates Be Reconciled?

arXiv: https://arxiv.org/abs/2002.07676 · HTML: https://mlsanity.com/paper/2002.07676/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

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

- [On (assessing) the fairness of risk score models](https://mlsanity.com/paper/2302.08851/) (2023)
- [Are demographically invariant models and representations in medical imaging fair?](https://mlsanity.com/paper/2305.01397/) (2023)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Beyond Impossibility: Balancing Sufficiency, Separation and Accuracy](https://mlsanity.com/paper/2205.12327/) (2022)
- [On the Burden of Achieving Fairness in Conformal Prediction](https://mlsanity.com/paper/2605.14260/) (2026)
- [Affirmative Action vs. Affirmative Information](https://mlsanity.com/paper/2102.10019/) (2021)
- [Unravelling the (In)compatibility of Statistical-Parity and Equalized-Odds](https://mlsanity.com/paper/2601.19035/) (2026)
- [An Accounting Identity for Algorithmic Fairness](https://mlsanity.com/paper/2601.20217/) (2026)
- [Revisiting Fairness Impossibility with Endogenous Behavior](https://mlsanity.com/paper/2604.06378/) (2026)
- [Is invariance all you need for algorithmic fairness? Removing demographic information can create new bias](https://mlsanity.com/paper/2609.32004/) (2026)

## Abstract (arXiv)

Decision makers increasingly rely on algorithmic risk scores to determine access to binary treatments including bail, loans, and medical interventions. In these settings, we reconcile two fairness criteria that were previously shown to be in conflict: calibration and error rate equality. In particular, we derive necessary and sufficient conditions for the existence of calibrated scores that yield classifications achieving equal error rates at any given group-blind threshold. We then present an algorithm that searches for the most accurate score subject to both calibration and minimal error rate disparity. Applied to the COMPAS criminal risk assessment tool, we show that our method can eliminate error disparities while maintaining calibration. In a separate application to credit lending, we compare our procedure to the omission of sensitive features and show that it raises both profit and the probability that creditworthy individuals receive loans.