Robust Conformal Consensus: Multi-Agent LLM-as-a-Judge Interval Evaluation with Conformal Prediction

Lihui Liu

cs.LGSep 6, 2026

Robust Conformal Consensus: Multi-Agent LLM-as-a-Judge Interval Evaluation with Conformal Prediction

Authors: Lihui Liu

Organizations: Wayne State University Detroit, Michigan, USA

Abstract

LLM-as-a-Judge has emerged as a promising paradigm for evaluating natural language generation. However, the uncertainty associated with such evaluations remains largely unexplored, which limits their reliability in real-world applications. Although conformal prediction offers a principled framework for uncertainty quantification, existing approaches typically apply it to a single LLM judge, overlooking the variability introduced by using different LLM evaluators. In this work, we propose a robust uncertainty estimation framework for multi-agent LLM-as-a-Judge evaluation. Our approach constructs conformal prediction intervals for LLM-based scores from multiple LLMs. By considering intervals from different LLM judges, we obtain more stable and reliable uncertainty estimates. Extensive experiments demonstrate that our method produces valid prediction intervals with coverage guarantees, and that interval-based aggregation across multiple judges leads to more stable evaluation outcomes.

Figures & tables

Figure 1: Overview of uncertainty quantification in rating-based multi-agent LLM-as-a-Judge evaluation. We apply conformal prediction to multiple LLM judges to construct prediction intervals for their ratings. These intervals are then aggregated, and the width of the resulting interval is used as a measure of evaluation uncertainty.

Method	SummEval Evaluated with G-Eval				ROSCOE Evaluated with SocREval
	Consistency	Coherence	Fluency	Relevance	CosmosQA	DROP	e-SNLI	GSM8K
GPT-4o mini
CQR	1.15 / 94.16%	2.87 / 93.15%	1.44 / 92.92%	2.09 / 90.92%	3.53 / 95.27%	3.82 / 96.70%	3.04 / 96.62%	3.53 / 95.67%
Asym CQR	1.25 / 94.97%	2.91 / 93.76%	1.60 / 93.75%	2.13 / 91.42%	3.90 / 98.71%	3.91 / 98.60%	2.87 / 96.67%	3.89 / 98.80%
CHR	0.67 / 88.99%	2.41 / 82.96%	0.94 / 88.86%	1.74 / 82.62%	2.54 / 73.06%	1.86 / 68.92%	1.36 / 72.24%	1.98 / 78.67%
LVD	1.01 / 92.35%	2.73 / 89.76%	1.11 / 90.59%	2.02 / 89.55%	3.10 / 83.95%	2.49 / 83.05%	2.17 / 86.18%	3.08 / 89.57%

Table 1: Interval width and coverage on SummEval evaluated by G-Eval and ROSCOE evaluated by SocREval before boundary adjustment. We mark coverage

<85\%

with gray text, coverage between

85\%-90\%

with underline and coverage with the smallest interval width

\geq 90\%

in bold.

Method	SummEval Evaluated with G-Eval				ROSCOE Evaluated with SocREval
	Consistency	Coherence	Fluency	Relevance	CosmosQA	DROP	e-SNLI	GSM8K
GPT-4o mini
CQR	1.15 / 95.45%	2.87 / 94.94%	1.44 / 93.80%	2.09 / 93.56%	3.53 / 95.34%	3.82 / 97.05%	3.04 / 96.89%	3.53 / 95.67%
Asym CQR	1.25 / 96.02%	2.90 / 95.41%	1.60 / 94.57%	2.14 / 94.14%	3.90 / 98.84%	3.91 / 98.73%	2.87 / 96.89%	3.89 / 98.80%
CHR	0.70 / 91.79%	2.41 / 87.78%	0.94 / 90.60%	1.74 / 88.10%	2.56 / 82.45%	1.87 / 78.86%	1.34 / 83.46%	1.94 / 83.23%
LVD	1.01 / 94.11%	2.73 / 93.72%	1.12 / 92.70%	2.03 / 93.82%	3.13 / 91.53%	2.52 / 90.22%	2.17 / 94.82%	3.09 / 93.37%

Table 2: Interval width and coverage on SummEval evaluated by G-Eval and ROSCOE evaluated by SocREval after boundary adjustment. We mark coverage

<85\%

with gray text , coverage between

85\%\textendash 90\%

with underline and coverage

\geq 90\%

with the smallest interval width in bold .

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LLM-as-a-judge ensembles are the standard paradigm for scalable evaluation, but their aggregation mechanisms suffer from a fundamental flaw: they implicitly assume that judges provide independent estimates of true quality. However, in practice, LLM judges exhibit correlated errors caused by shared latent confounders -- such as verbosity, stylistic preferences, or training artifacts -- causing standard aggregation rules like majority vote or averaging to provide little gain or even amplify systematic mistakes. To address this, we introduce CARE, a confounder-aware aggregation framework that explicitly models LLM judge scores as arising from both a latent true-quality signal and shared confounding factors. Rather than heuristically re-weighting judges, CARE separates quality from confounders without access to ground-truth labels. We provide theoretical guarantees for identifiability and finite-sample recovery under shared confounders, and we quantify the systematic bias incurred when aggregation models omit confounding latent factors. Across 12 public benchmarks spanning continuous scoring, binary classification, and pairwise preference settings, CARE improves aggregation accuracy, reducing error by up to 26.8%. Code is released in https://github.com/SprocketLab/CARE.

Abstract

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