# On the Burden of Achieving Fairness in Conformal Prediction

arXiv: https://arxiv.org/abs/2605.14260 · HTML: https://mlsanity.com/paper/2605.14260/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 21 of 21)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [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)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [FACET: Fairness in Computer Vision Evaluation Benchmark](https://mlsanity.com/paper/2309.00035/) (2023)
- [Conformal Prediction Sets Improve Human Decision Making](https://mlsanity.com/paper/2401.13744/) (2024)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Equal Opportunity of Coverage in Fair Regression](https://mlsanity.com/paper/2311.02243/) (2023)
- [Conformal Prediction Sets Can Cause Disparate Impact](https://mlsanity.com/paper/2410.01888/) (2024)
- [A Possibility in Algorithmic Fairness: Can Calibration and Equal Error Rates Be Reconciled?](https://mlsanity.com/paper/2002.07676/) (2020)
- [Volume Optimality in Conformal Prediction with Structured Prediction Sets](https://mlsanity.com/paper/2502.16658/) (2025)
- [Conformal Classification with Equalized Coverage for Adaptively Selected Groups](https://mlsanity.com/paper/2405.15106/) (2024)
- [A Generic Framework for Conformal Fairness](https://mlsanity.com/paper/2505.16115/) (2025)
- [Counterfactually Fair Conformal Prediction](https://mlsanity.com/paper/2510.08724/) (2025)
- [A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage](https://mlsanity.com/paper/2512.19142/) (2025)
- [Beyond Procedure: Substantive Fairness in Conformal Prediction](https://mlsanity.com/paper/2602.16794/) (2026)

## Built on by (most cited first, 1 of 1)

- [Unifying Conformal Language Tasks with In-Context Ensembles](https://mlsanity.com/paper/2609.03005/) (2026)

## Abstract (arXiv)

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.