# Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics

arXiv: https://arxiv.org/abs/2605.10528 · HTML: https://mlsanity.com/paper/2605.10528/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- 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, 20 of 20)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Cooperate or Collapse: Emergence of Sustainable Cooperation in a Society of LLM Agents](https://mlsanity.com/paper/2404.16698/) (2024)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [CalibraEval: Calibrating Prediction Distribution to Mitigate Selection Bias in LLMs-as-Judges](https://mlsanity.com/paper/2410.15393/) (2024)
- [When LLMs Play the Telephone Game: Cultural Attractors as Conceptual Tools to Evaluate LLMs in Multi-turn Settings](https://mlsanity.com/paper/2407.04503/) (2024)
- [The Bias is in the Details: An Assessment of Cognitive Bias in LLMs](https://mlsanity.com/paper/2509.22856/) (2025)
- [Cooperative AI via Decentralized Commitment Devices](https://mlsanity.com/paper/2311.07815/) (2023)
- [Detailed balance in large language model-driven agents](https://mlsanity.com/paper/2512.10047/) (2025)
- [Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks](https://mlsanity.com/paper/2505.21426/) (2025)
- [Reaching Agreement Among Reasoning LLM Agents](https://mlsanity.com/paper/2512.20184/) (2025)
- [Bias Beyond Borders: Political Ideology Evaluation and Steering in Multilingual LLMs](https://mlsanity.com/paper/2601.23001/) (2026)
- [Source framing triggers systematic evaluation bias in Large Language Models](https://mlsanity.com/paper/2505.13488/) (2025)
- [Increasing intelligence in AI agents can worsen collective outcomes](https://mlsanity.com/paper/2603.12129/) (2026)
- [More is More: Addition Bias in Large Language Models](https://mlsanity.com/paper/2409.02569/) (2024)
- [Profit is the Red Team: Stress-Testing Agents in Strategic Economic Interactions](https://mlsanity.com/paper/2603.20925/) (2026)
- [Karma Mechanisms for Decentralised, Cooperative Multi Agent Path Finding](https://mlsanity.com/paper/2604.07970/) (2026)

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

- [Microscopic dynamics of consensus formation in multi-agent LLM Naming Games](https://mlsanity.com/paper/2608.02178/) (2026)
- [Multi-agent discussion gains less when dissent is withheld](https://mlsanity.com/paper/2609.38324/) (2026)

## Abstract (arXiv)

We investigate the emergent collective dynamics of LLM-based multi-agent systems on a 2D square lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-agent systems. In our framework, each node of an L!×!L lattice hosts an identical LLM agent holding a binary state (+1/-1, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature T serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe mathbbZ2 symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-L lattices yields effective exponents γ/nu whose values are model-dependent, close to but incompatible with the 2D Ising universality class (γ/nu=7/4). Our method enables the extraction of effective β-weighted couplings tildeJ(T) and fields tildeh(T), which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective alignment is dominated by an intrinsic bias (tildehggtildeJ) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM agents and a quantitative diagnostic for the reliability of multi-agent consensus and collective alignment.