SCOPE: Selective Conformal Optimized Pairwise LLM Judging

Sher Badshah, Ali Emami, Hassan Sajjad
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:4894-4916, 2026.

Abstract

Large language models (LLMs) are increasingly used as scalable judges in pairwise evaluation, but they remain prone to miscalibration and biases. We propose 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 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 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, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-badshah26a, title = {{SCOPE}: Selective Conformal Optimized Pairwise {LLM} Judging}, author = {Badshah, Sher and Emami, Ali and Sajjad, Hassan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {4894--4916}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/badshah26a/badshah26a.pdf}, url = {https://proceedings.mlr.press/v306/badshah26a.html}, abstract = {Large language models (LLMs) are increasingly used as scalable judges in pairwise evaluation, but they remain prone to miscalibration and biases. We propose 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 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 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, 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.} }
Endnote
%0 Conference Paper %T SCOPE: Selective Conformal Optimized Pairwise LLM Judging %A Sher Badshah %A Ali Emami %A Hassan Sajjad %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-badshah26a %I PMLR %P 4894--4916 %U https://proceedings.mlr.press/v306/badshah26a.html %V 306 %X Large language models (LLMs) are increasingly used as scalable judges in pairwise evaluation, but they remain prone to miscalibration and biases. We propose 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 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 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, 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.
APA
Badshah, S., Emami, A. & Sajjad, H.. (2026). SCOPE: Selective Conformal Optimized Pairwise LLM Judging. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:4894-4916 Available from https://proceedings.mlr.press/v306/badshah26a.html.

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