Pooled conformal calibration incurs irreducible group-wise coverage distortion scaled by cross-group quantile heterogeneity, with Equalized Coverage and Equalized Set Size in fundamental tension.
The incompatibility follows from a Bayes coupling identity relating predictive values, base rates, and the likelihood ratio TPRg/FPRg
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On the Burden of Achieving Fairness in Conformal Prediction
Pooled conformal calibration incurs irreducible group-wise coverage distortion scaled by cross-group quantile heterogeneity, with Equalized Coverage and Equalized Set Size in fundamental tension.