# The Value of Variance: Mitigating Debate Collapse in Multi-Agent Systems via Uncertainty-Driven Policy Optimization

arXiv: https://arxiv.org/abs/2602.07186 · HTML: https://mlsanity.com/paper/2602.07186/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 26 of 26)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [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)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [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)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Emergent Multi-Agent Communication in the Deep Learning Era](https://mlsanity.com/paper/2006.02419/) (2020)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [On the Resilience of LLM-Based Multi-Agent Collaboration with Faulty Agents](https://mlsanity.com/paper/2408.00989/) (2024)
- [Uncertainty-Based Abstention in LLMs Improves Safety and Reduces Hallucinations](https://mlsanity.com/paper/2404.10960/) (2024)
- [An Introduction to Centralized Training for Decentralized Execution in Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2409.03052/) (2024)
- [Robust Multi-Agent Reinforcement Learning with State Uncertainty](https://mlsanity.com/paper/2307.16212/) (2023)
- [Open Source Language Models Can Provide Feedback: Evaluating LLMs' Ability to Help Students Using GPT-4-As-A-Judge](https://mlsanity.com/paper/2405.05253/) (2024)

## Built on by (most cited first, 8 of 8)

- [Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning](https://mlsanity.com/paper/2603.01221/) (2026)
- [EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibrium](https://mlsanity.com/paper/2605.09278/) (2026)
- [The Trap of Trajectory: Towards Understanding and Mitigating Spurious Correlations in Agentic Memory](https://mlsanity.com/paper/2605.09330/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Social Circuits behind Multi-agent Echo Chambers](https://mlsanity.com/paper/2609.34444/) (2026)
- [Measuring Collapse and Correction in Homogeneous-Panel LLM Debate](https://mlsanity.com/paper/2609.35279/) (2026)
- [Understanding and Mitigating Inference-Time Overreliance Using Agentic Memory](https://mlsanity.com/paper/2610.07311/) (2026)
- [Sequential Probabilistic Uncertainty Estimation for Parallel Multi-Agent Reasoning Systems](https://mlsanity.com/paper/2610.08901/) (2026)

## Abstract (arXiv)

Multi-agent debate (MAD) systems improve LLM reasoning through iterative deliberation, but remain vulnerable to debate collapse, a failure type where final agent decisions are compromised on erroneous reasoning. Existing methods lack principled mechanisms to detect or prevent such failures. To address this gap, we first propose a hierarchical metric that quantifies behavioral uncertainty at three levels: intra-agent (individual reasoning uncertainty), inter-agent (interactive uncertainty), and system-level (output uncertainty). Empirical analysis across several benchmarks reveals that our proposed uncertainty quantification reliably indicates system failures, which demonstrates the validity of using them as diagnostic metrics to indicate the system failure. Subsequently, we propose a mitigation strategy by formulating an uncertainty-driven policy optimization to penalize self-contradiction, peer conflict, and low-confidence outputs in a dynamic debating environment. Experiments demonstrate that our proposed uncertainty-driven mitigation reliably calibrates the multi-agent system by consistently improving decision accuracy while reducing system disagreement.