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

arXiv: https://arxiv.org/abs/2609.06367 · HTML: https://mlsanity.com/paper/2609.06367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 35 of its 64 references that are in the map.
- First posted on arXiv 6 Sep 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 35)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [Cosmos QA: Machine Reading Comprehension with Contextual Commonsense Reasoning](https://mlsanity.com/paper/1909.00277/) (2019)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement](https://mlsanity.com/paper/2407.18370/) (2024)
- [Can Large Language Models Faithfully Express Their Intrinsic Uncertainty in Words?](https://mlsanity.com/paper/2405.16908/) (2024)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [MR-GSM8K: A Meta-Reasoning Benchmark for Large Language Model Evaluation](https://mlsanity.com/paper/2312.17080/) (2023)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Abstractive Dialogue Summarization with Sentence-Gated Modeling Optimized by Dialogue Acts](https://mlsanity.com/paper/1809.05715/) (2018)
- [Improving Trustworthiness of AI Disease Severity Rating in Medical Imaging with Ordinal Conformal Prediction Sets](https://mlsanity.com/paper/2207.02238/) (2022)
- [Cautious Deep Learning](https://mlsanity.com/paper/1805.09460/) (2018)
- [SocREval: Large Language Models with the Socratic Method for Reference-Free Reasoning Evaluation](https://mlsanity.com/paper/2310.00074/) (2023)
- [Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Prediction](https://mlsanity.com/paper/2509.18658/) (2025)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [KompaRe: A Knowledge Graph Comparative Reasoning System](https://mlsanity.com/paper/2011.03189/) (2020)
- [Logic Query of Thoughts: Guiding Large Language Models to Answer Complex Logic Queries with Knowledge Graphs](https://mlsanity.com/paper/2404.04264/) (2024)
- [Neural-Symbolic Reasoning over Knowledge Graphs: A Survey from a Query Perspective](https://mlsanity.com/paper/2412.10390/) (2024)
- [An Empirical Analysis of Uncertainty in Large Language Model Evaluations](https://mlsanity.com/paper/2502.10709/) (2025)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Black-box Uncertainty Quantification Method for LLM-as-a-Judge](https://mlsanity.com/paper/2410.11594/) (2024)

## Abstract (arXiv)

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.