On the Burden of Achieving Fairness in Conformal Prediction

TL;DR

This paper investigates the inherent fairness trade-offs in conformal prediction calibration, revealing fundamental tensions and costs associated with pooled versus group-specific calibration strategies.

Contribution

It derives a conservation law and lower bounds for coverage distortion, and analyzes the trade-offs between fairness definitions and calibration policies.

Findings

Pooled calibration causes irreducible group-wise coverage distortion.

Equalized Coverage and Equalized Set Size are fundamentally in tension.

Calibration policy choice determines whether distortion appears in coverage or size.

Abstract

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.