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On the Burden of Achieving Fairness in Conformal Prediction

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets · 0 citations (OpenAlex)

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Theoretical study showing pooled conformal calibration yields irreducible group-wise coverage distortion, and that Equalized Coverage and Equalized Set Size cannot be achieved simultaneously, with bounds on the cost of switching policies, validated on synthetic data, Bias in Bios, MultiNLI, and FACET.

Problem

Pooled split conformal calibration hides cross-group heterogeneity in score distributions, distorting group-wise coverage; group-conditional calibration shifts the disparity into set size. The paper asks how the two leading CP fairness notions (Equalized Coverage and Equalized Set Size) trade off.

Approach

Analyzes population score CDFs to derive a conservation law for pooled thresholds, a variance-type lower bound on group-wise coverage distortion scaled by an effective stiffness and cross-group quantile dispersion, and bidirectional impossibility results between exact group-wise coverage and equalized expected set size.

Key results

• On Bias in Bios at alpha=0.1, RMS distortions of the three policy-conversion quantities are 0.0015, 0.0051, and 0.0017.
• On MultiNLI with the simple score, pooled RMS genre-wise coverage distortion is 0.0150 and RMS set-size distortion after switching to group-wise thresholds is 0.0532.
• On FACET with RAPS, pooled RMS coverage distortion is 0.0083 and RMS set-size distortion after switching to group-wise thresholds is 0.1717.

Limitations

• Results rely on local regularity assumptions (density lower bounds, monotone set-size curves) and population-level analysis.
• Groups are prespecified and discrete; no adaptive subgroup validity.
• Set-size curves are proxied by linear functions in the synthetic experiments; finite-sample theory is not developed.

Experimental setup

Datasets: Bias in Bios MultiNLI FACET

Benchmarks: Bias in Bios MultiNLI FACET

Metrics: RMS group-wise coverage distortion RMS set-size distortion expected set size

Baselines: pooled split conformal prediction group-conditional conformal prediction

Builds on: split conformal prediction RAPS Equalized Odds

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