Beyond Procedure: Substantive Fairness in Conformal Prediction

TL;DR

This paper investigates how conformal prediction can be made fairer in real-world decision-making by analyzing its impact on downstream outcomes, providing theoretical bounds, empirical tools, and practical insights.

Contribution

It introduces a theoretical decomposition of fairness disparities, an LLM-based evaluator for empirical analysis, and demonstrates that label-clustered CP improves substantive fairness.

Findings

Label-clustered CP variants enhance fairness in outcomes.

Equalized set sizes correlate with better substantive fairness.

Theoretical bounds clarify sources of unfairness in CP.

Abstract

Conformal prediction (CP) offers distribution-free uncertainty quantification for machine learning models, yet its interplay with fairness in downstream decision-making remains underexplored. Moving beyond CP as a standalone operation (procedural fairness), we analyze the holistic decision-making pipeline to evaluate substantive fairness-the equity of downstream outcomes. Theoretically, we derive an upper bound that decomposes prediction-set size disparity into interpretable components, clarifying how label-clustered CP helps control method-driven contributions to unfairness. To facilitate scalable empirical analysis, we introduce an LLM-in-the-loop evaluator that approximates human assessment of substantive fairness across diverse modalities. Our experiments reveal that label-clustered CP variants consistently deliver superior substantive fairness. Finally, we empirically show that equalized set sizes, rather than coverage, strongly correlate with improved substantive fairness, enabling practitioners to design more fair CP systems. Our code is available at https://github.com/layer6ai-labs/llm-in-the-loop-conformal-fairness.