[Paper] Comparative Separation: Evaluating Separation on Comparative Judgment Test Data

Source: arXiv - 2601.06761v1

Overview

The paper introduces comparative separation, a new fairness metric that lets developers evaluate whether a machine‑learning model treats different sensitive groups equally—without needing explicit class labels for every test instance. By leveraging comparative judgment data (e.g., “A is better than B”), the authors show that fairness can be assessed with less human effort while still meeting the rigorous separation criterion used in fairness research.

Key Contributions

• Novel fairness notion: Definition of comparative separation that works on pairwise comparative judgments instead of per‑instance labels.
• Metric suite: Concrete quantitative metrics (e.g., pairwise separation score, statistical tests) for measuring comparative separation.
• Theoretical equivalence: Proof that, for binary classification, comparative separation is mathematically equivalent to the classic separation criterion.
• Statistical power analysis: Derivation of how many data points and pairwise comparisons are needed to achieve the same confidence as traditional label‑based tests.
• Empirical validation: Experiments on real‑world datasets confirming the theory and demonstrating practical feasibility.

Methodology

1. Data Collection via Comparative Judgment – Human annotators are presented with pairs of test instances and asked which one the model performed better on (e.g., “Model’s prediction for A is more accurate than for B”). This reduces cognitive load compared with assigning absolute scores or class labels.
2. Formalizing Comparative Separation – The authors translate the classic separation condition (equal true‑positive rates across groups) into a pairwise setting: for any two groups, the probability that a randomly chosen pair from the same group is judged “more correct” should equal the probability for a pair from different groups.
3. Metric Design – They introduce a pairwise separation score computed from the proportion of cross‑group vs. within‑group judgments, and a hypothesis‑testing framework (e.g., chi‑square test) to decide if the model satisfies comparative separation.
4. Theoretical Proof – Using probability algebra, they demonstrate that when the underlying task is binary classification, the pairwise condition collapses to the standard separation condition.
5. Empirical Study – The team runs experiments on benchmark fairness datasets (e.g., Adult, COMPAS). They collect comparative judgments via crowdsourcing, compute the new metrics, and compare them against label‑based separation results. They also simulate varying numbers of instances and pairs to assess statistical power.

Results & Findings

• Equivalence confirmed: In all binary classification experiments, the comparative separation score matched the traditional separation metric within statistical noise.
• Reduced annotation effort: Obtaining reliable fairness assessments required roughly 30‑40 % fewer human judgments compared to full labeling, thanks to the lower cognitive burden of pairwise comparisons.
• Statistical power: To achieve the same confidence level (α = 0.05, power = 0.8), you need about 1.5× more pairs than individual labels, but because each pair can be generated from a relatively small pool of instances, the overall annotation cost is still lower.
• Robustness: The comparative approach remained stable even when annotators introduced modest noise (e.g., 10 % inconsistent judgments).

Practical Implications

• Faster fairness audits: Teams can run fairness checks on new models using cheap, quick pairwise surveys instead of expensive labeling pipelines.
• Lower barrier for small companies: Start‑ups and open‑source projects often lack resources for large labeled test sets; comparative judgment offers a scalable alternative.
• Integration with CI/CD: The pairwise evaluation can be automated as a lightweight step in continuous integration, flagging separation violations before deployment.
• Human‑in‑the‑loop monitoring: For high‑risk domains (loan underwriting, hiring), regulators could require periodic comparative fairness checks, which are less intrusive for users and faster to collect.

Limitations & Future Work

• Binary focus: The equivalence proof holds only for binary classification; extending comparative separation to multi‑class or regression tasks remains open.
• Assumption of consistent judgments: The method presumes annotators can reliably compare model performance; in domains where “better” is ambiguous, judgment quality may degrade.
• Sample complexity: While overall effort drops, the need for a quadratic number of pairs (O(n²)) can become costly for very large test sets; smarter pair selection strategies (active sampling) are a promising direction.
• Real‑world deployment studies: Future work should evaluate comparative separation in production pipelines, measuring impact on model updates and regulatory compliance.

Authors

• Xiaoyin Xi
• Neeku Capak
• Kate Stockwell
• Zhe Yu

Paper Information

• arXiv ID: 2601.06761v1
• Categories: cs.SE, cs.LG
• Published: January 11, 2026
• PDF: Download PDF