# Belief-Calibrated Multi-Agent Consensus Seeking for Complex NLP Tasks

arXiv: https://arxiv.org/abs/2510.06307 · HTML: https://mlsanity.com/paper/2510.06307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 58 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 30 of 49)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)
- [A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration](https://mlsanity.com/paper/2310.02170/) (2023)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration](https://mlsanity.com/paper/2307.05300/) (2023)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Theory of Mind for Multi-Agent Collaboration via Large Language Models](https://mlsanity.com/paper/2310.10701/) (2023)
- [Improving Multi-Agent Debate with Sparse Communication Topology](https://mlsanity.com/paper/2406.11776/) (2024)
- [Systematic Biases in LLM Simulations of Debates](https://mlsanity.com/paper/2402.04049/) (2024)
- [Exchange-of-Thought: Enhancing Large Language Model Capabilities through Cross-Model Communication](https://mlsanity.com/paper/2312.01823/) (2023)
- [On the Calibration of Large Language Models and Alignment](https://mlsanity.com/paper/2311.13240/) (2023)
- [GroupDebate: Enhancing the Efficiency of Multi-Agent Debate Using Group Discussion](https://mlsanity.com/paper/2409.14051/) (2024)
- [Voting or Consensus? Decision-Making in Multi-Agent Debate](https://mlsanity.com/paper/2502.19130/) (2025)
- [Do as We Do, Not as You Think: the Conformity of Large Language Models](https://mlsanity.com/paper/2501.13381/) (2025)
- [Multi-Agent Consensus Seeking via Large Language Models](https://mlsanity.com/paper/2310.20151/) (2023)
- [Learning to Break: Knowledge-Enhanced Reasoning in Multi-Agent Debate System](https://mlsanity.com/paper/2312.04854/) (2023)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Quantifying the Impact of Large Language Models on Collective Opinion Dynamics](https://mlsanity.com/paper/2308.03313/) (2023)
- [No Preference Left Behind: Group Distributional Preference Optimization](https://mlsanity.com/paper/2412.20299/) (2024)
- [Towards Effective GenAI Multi-Agent Collaboration: Design and Evaluation for Enterprise Applications](https://mlsanity.com/paper/2412.05449/) (2024)
- [A Survey of Distributed Consensus Protocols for Blockchain Networks](https://mlsanity.com/paper/1904.04098/) (2019)

## Built on by (most cited first, 2 of 2)

- [You Only Align Once: Propagating Cooperative Behaviors in Multi-Agent Systems through Seed Agents](https://mlsanity.com/paper/2605.27586/) (2026)
- [PFedMA: Who Should Join Next as Federated Multi-Agent Orchestration Evolves?](https://mlsanity.com/paper/2610.19458/) (2026)

## Abstract (arXiv)

A multi-agent system (MAS) enhances its capacity to solve complex natural language processing (NLP) tasks through collaboration among multiple agents, where consensus-seeking serves as a fundamental mechanism. However, existing consensus-seeking approaches typically rely on voting mechanisms to judge consensus, overlooking contradictions in system-internal beliefs that destabilize the consensus. Moreover, these methods often involve agents updating their results through indiscriminate collaboration with every other agent. Such uniform interaction fails to identify the optimal collaborators for each agent, hindering the emergence of a stable consensus. To address these challenges, we provide a theoretical framework for selecting optimal collaborators that maximize consensus stability. Based on the theorems, we propose the Belief-Calibrated Consensus Seeking (BCCS) framework to facilitate stable consensus via selecting optimal collaborators and calibrating the consensus judgment by system-internal beliefs. Experimental results on the MATH and MMLU benchmark datasets demonstrate that the proposed BCCS framework outperforms the best existing results by 2.23% and 3.95% of accuracy on challenging tasks, respectively. Our code and data are available at https://github.com/dengwentao99/BCCS.