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Beyond Procedure: Substantive Fairness in Conformal Prediction

Pengqi Liu, Zijun Yu, Mouloud Belbahri, Arthur Charpentier, Masoud Asgharian, Jesse C. Cresswell

TL;DR

An LLM-in-the-loop evaluator that approximates human assessment of substantive fairness across diverse modalities is introduced, and it is empirically show that equalized set sizes, rather than coverage, strongly correlate with improved substantive fairness, enabling practitioners to design more fair CP systems.

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.

Beyond Procedure: Substantive Fairness in Conformal Prediction

TL;DR

An LLM-in-the-loop evaluator that approximates human assessment of substantive fairness across diverse modalities is introduced, and it is empirically show that equalized set sizes, rather than coverage, strongly correlate with improved substantive fairness, enabling practitioners to design more fair CP systems.

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.
Paper Structure (53 sections, 1 theorem, 61 equations, 12 figures, 25 tables, 5 algorithms)

This paper contains 53 sections, 1 theorem, 61 equations, 12 figures, 25 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Conformal Set Predictors
  4. Fairness Notions for Set Predictors
  5. Advanced Conformal Prediction Variants
  6. Related Work
  7. Methodology
  8. Label-Clustered CP Reduces Set Size Disparity
  9. LLM-in-the-loop Substantive Fairness Evaluation
  10. Experimental Setup
  11. Experimental Design
  12. Tasks, Datasets, and Models
  13. Results
  14. RQ1: Validation of LLM-in-the-loop Evaluation
  15. RQ2: Substantive Fairness Benchmarking
  16. ...and 38 more sections

Key Result

Theorem 4.1

Fix any label-clustering map $h: \mathcal{Y} \to [K]$ and let $\mathcal{Y}_k := \{y \in \mathcal{Y}: h(y) = k \}$. Consider a label-clustered conformal set predictor $\mathcal{C}$ that uses cluster-specific thresholds. For any $y \in \mathcal{Y}, ~ k \in [K]$, and group $a \in \mathcal{A}$, define Then, for any two groups $a, b$,

Figures (12)

  • Figure 1: maxROR (%) of each CP method across four tasks. Lower is more substantively fair.
  • Figure 2: Accuracy improvement (%) relative to Control of each CP method, across four tasks. Higher is better.
  • Figure 3: Coverage gap (blue dots, left axis) and set size gap (red squares, right axis) across CP methods. The two procedural fairness metrics are in direct tension. Corresponding plots for FACET and ACSIncome are in \ref{['app:additional-plots']}.
  • Figure 4: maxROR (%) compared to the coverage gap (Left) and set size gap (Right) between groups, across CP methods and datasets. Regression lines are fitted for each dataset individually to show trends.
  • Figure 5: Average prediction set size gap between Female and Male on the BiosBias and RAVDESS datasets over 10 random splits. The maximum standard error of the average set size gap is .016 in (a) and .010 in (b).
  • ...and 7 more figures

Theorems & Definitions (1)

  • Theorem 4.1: Label-Clustered CP set size disparity bound