# Confidence Calibration and Rationalization for LLMs via Multi-Agent Deliberation

arXiv: https://arxiv.org/abs/2404.09127 · HTML: https://mlsanity.com/paper/2404.09127/

## Key facts

- Cited by 26 papers in the map (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 42 of its 52 references that are in the map.
- First posted on arXiv 14 Apr 2024.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 42)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [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)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [AmbigQA: Answering Ambiguous Open-domain Questions](https://mlsanity.com/paper/2004.10645/) (2020)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)

## Built on by (most cited first, 26 of 26)

- [MediQ: Question-Asking LLMs and a Benchmark for Reliable Interactive Clinical Reasoning](https://mlsanity.com/paper/2406.00922/) (2024)
- [Internet of Agents: Fundamentals, Applications, and Challenges](https://mlsanity.com/paper/2505.07176/) (2025)
- [ACC-Collab: An Actor-Critic Approach to Multi-Agent LLM Collaboration](https://mlsanity.com/paper/2411.00053/) (2024)
- [Uncertainty Quantification in LLM Agents: Foundations, Emerging Challenges, and Opportunities](https://mlsanity.com/paper/2602.05073/) (2026)
- [Overconfidence in LLM-as-a-Judge: Diagnosis and Confidence-Driven Solution](https://mlsanity.com/paper/2508.06225/) (2025)
- [Counterfactual Debating with Preset Stances for Hallucination Elimination of LLMs](https://mlsanity.com/paper/2406.11514/) (2024)
- [From Code Foundation Models to Agents and Applications: A Comprehensive Survey and Practical Guide to Code Intelligence](https://mlsanity.com/paper/2511.18538/) (2025)
- [Robustness in Large Language Models: A Survey of Mitigation Strategies and Evaluation Metrics](https://mlsanity.com/paper/2505.18658/) (2025)
- [MARS: Benchmarking the Metaphysical Reasoning Abilities of Language Models with a Multi-task Evaluation Dataset](https://mlsanity.com/paper/2406.02106/) (2024)
- [iMAD: Intelligent Multi-Agent Debate for Efficient and Accurate LLM Inference](https://mlsanity.com/paper/2511.11306/) (2025)
- [Multi-Agent Debate Strategies to Enhance Requirements Engineering with Large Language Models](https://mlsanity.com/paper/2507.05981/) (2025)
- [Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignment](https://mlsanity.com/paper/2510.14008/) (2025)
- [Counterfactual Graph for Multi-Agent LLM Calibration](https://mlsanity.com/paper/2605.30653/) (2026)
- [Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning](https://mlsanity.com/paper/2603.01221/) (2026)
- [Refine and Align: Confidence Calibration through Multi-Agent Interaction in VQA](https://mlsanity.com/paper/2511.11169/) (2025)
- [BELLE: A Bi-Level Multi-Agent Reasoning Framework for Multi-Hop Question Answering](https://mlsanity.com/paper/2505.11811/) (2025)
- [Calibration Is Not Enough: Evaluating Confidence Estimation Under Language Variations](https://mlsanity.com/paper/2601.08064/) (2026)
- [Uncertainty Decomposition for Clarification Seeking in LLM Agents](https://mlsanity.com/paper/2606.19559/) (2026)
- [Multi-Agent Debate Strategies: Survey, Taxonomy, and Challenges](https://mlsanity.com/paper/2607.26212/) (2026)
- [Beware of Reasoning Overconfidence: Pitfalls in the Reasoning Process for Multi-solution Tasks](https://mlsanity.com/paper/2512.01725/) (2025)
- [Believe Your Model: Distribution-Guided Confidence Calibration](https://mlsanity.com/paper/2603.03872/) (2026)
- [A Systematic Evaluation of Black-Box Uncertainty Estimation Methods for Large Language Models](https://mlsanity.com/paper/2606.19868/) (2026)
- [Confidence Composition for Multiagent Language Model Systems](https://mlsanity.com/paper/2606.13591/) (2026)
- [Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate](https://mlsanity.com/paper/2608.03648/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [From Process Loss to Assembly Bonus: Human-Grounded Diagnosis of Multi-Agent LLM Collaboration](https://mlsanity.com/paper/2609.13261/) (2026)

## Abstract (arXiv)

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose decisions and confidences not only stem from intrinsic beliefs but can also be adjusted through daily observations, existing calibration methods for LLMs focus on estimating or eliciting individual confidence without taking full advantage of the "Collective Wisdom": the interaction among multiple LLMs that can collectively improve both accuracy and calibration. In this work, we propose Collaborative Calibration, a post-hoc training-free calibration strategy that leverages the collaborative and expressive capabilities of multiple tool-augmented LLM agents in a simulated group deliberation process. We demonstrate the effectiveness of Collaborative Calibration on generative QA tasks across various domains, showing its potential in harnessing the rationalization of collectively calibrated confidence assessments and improving the reliability of model predictions.