SCOPE: Selective Conformal Optimized Pairwise LLM Judging

Abstract:Large language models (LLMs) are increasingly used as scalable judges in pairwise evaluation, but they remain prone to miscalibration and biases. We propose \textsc{Scope} (Selective Conformal Optimized Pairwise Evaluation), a framework that calibrates an acceptance threshold so that, under exchangeability, the error rate among non-abstained judgments is at most a user-specified level $\alpha$. To supply \textsc{Scope} with a bias-neutral uncertainty signal, we introduce Bidirectional Preference Entropy (BPE), which queries the judge under both response positions and converts the order-averaged preference probability into an entropy-based score. Across various pairwise judging benchmarks, BPE outperforms standard confidence proxies in calibration and discrimination, while \textsc{Scope} consistently satisfies the target risk bound (empirical FDR $\approx 0.097$--$0.099$ at $\alpha=0.10$) and retains substantial coverage. Compared to vanilla baselines, \textsc{Scope} accepts up to $2.4\times$ more judgments under the same risk constraint, demonstrating that BPE enables reliable and high-coverage LLM-based evaluation.

Accepted at ICML 2026. 23 pages (9 main plus appendix), 7 figures, 11 tables

Computation and Language (cs.CL); Artificial Intelligence (cs.AI)

I.2.6; I.2.7; I.2.11; F.2.2

arXiv:2602.13110 [cs.CL]

(or arXiv:2602.13110v4 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2602.13110 Focus to learn more arXiv-issued DOI via DataCite

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