# Confidence Composition for Multiagent Language Model Systems

arXiv: https://arxiv.org/abs/2606.13591 · HTML: https://mlsanity.com/paper/2606.13591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 28 of 28)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (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)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Zero-Shot Stance Detection: A Dataset and Model using Generalized Topic Representations](https://mlsanity.com/paper/2010.03640/) (2020)
- [Calibrating Large Language Models with Sample Consistency](https://mlsanity.com/paper/2402.13904/) (2024)
- [Talk Isn't Always Cheap: Understanding Failure Modes in Multi-Agent Debate](https://mlsanity.com/paper/2509.05396/) (2025)
- [Factual Confidence of LLMs: on Reliability and Robustness of Current Estimators](https://mlsanity.com/paper/2406.13415/) (2024)
- [MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2402.11756/) (2024)
- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [Confidence v.s. Critique: A Decomposition of Self-Correction Capability for LLMs](https://mlsanity.com/paper/2412.19513/) (2024)
- [Can LLM Agents Really Debate? A Controlled Study of Multi-Agent Debate in Logical Reasoning](https://mlsanity.com/paper/2511.07784/) (2025)
- [Debate Only When Necessary: Adaptive Multiagent Collaboration for Efficient LLM Reasoning](https://mlsanity.com/paper/2504.05047/) (2025)
- [Confidence Calibration and Rationalization for LLMs via Multi-Agent Deliberation](https://mlsanity.com/paper/2404.09127/) (2024)
- [Enhancing Multi-Agent Debate System Performance via Confidence Expression](https://mlsanity.com/paper/2509.14034/) (2025)
- [CER: Confidence Enhanced Reasoning in LLMs](https://mlsanity.com/paper/2502.14634/) (2025)
- [DebUnc: Improving Large Language Model Agent Communication With Uncertainty Metrics](https://mlsanity.com/paper/2407.06426/) (2024)
- [iMAD: Intelligent Multi-Agent Debate for Efficient and Accurate LLM Inference](https://mlsanity.com/paper/2511.11306/) (2025)
- [UTFPR at SemEval-2019 Task 5: Hate Speech Identification with Recurrent Neural Networks](https://mlsanity.com/paper/1904.07839/) (2019)
- [Refine and Align: Confidence Calibration through Multi-Agent Interaction in VQA](https://mlsanity.com/paper/2511.11169/) (2025)

## Abstract (arXiv)

Multiagent language model systems, such as collaborative reasoning and debate, produce multiple correlated candidate answers and confidence signals. However, these signals are usually calibrated only at the individual agent level, and provide no principled confidence estimate for the system's final answer. We formulate this as a confidence composition problem where combining confidence across agents and reasoning stages while preserving both selective utility and probabilistic reliability. We study confidence-aware routing and log-odds pooling protocols that select among candidate answers and output a system-level confidence. Across five benchmarks, 30 heterogeneous and homogeneous model pairs, and two confidence estimators, our gated-fusion methods improve AUARC and reduce Brier score over single agent, standard debate, and selective debate baselines, while retaining competitive weighted F1-score as a correctness metric. We further show that our log-odds fusion is overconfident due to correlated intermediate signals. We propose a shared dependence discount that substantially improves reliability while preserving predictions.