Emergence of Biased Consensus in Multi-Agent LLM Debates

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 $L\!\times\!L$ 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 $\mathbb{Z}_2$ symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-$L$ lattices yields effective exponents $γ/ν$ whose values are model-dependent, close to but incompatible with the 2D Ising universality class ($γ/ν=7/4$). Our method enables the extraction of effective $β$-weighted couplings $\tilde{J}(T)$ and fields $\tilde{h}(T)$, 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 ($\tilde{h}\gg\tilde{J}$) 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.

Large language models (LLMs) are increasingly deployed in applications involving interaction between agents, where their output plays a role in collective reasoning and decision-making processes. Despite significant research into the functioning of LLMs in such multi-agent systems, the processes of bias propagation in such systems are still a challenge. This work studies how biased opinions are propagated in the form of textual interaction in an environment of LLMs, in which a minority of agents maintain persistent extreme opinions, while the remaining agents iteratively update their beliefs through structured textual interactions. The findings show that even the presence of a small percentage of biased agents in such a system leads to significant shifts in the opinions of non-biased agents. It suggests that for the same percentage of biased agents, the shifts occur more quickly for the Llama~3.2 model when compared to a classical Friedkin-Johnsen (FJ) model. Further semantic analysis demonstrates that rhetorical consistency in textual explanations increases systematically with biased exposure and, importantly, is partially decoupled from numerical convergenumericalutral agents adopt the vocabulary employed by the biased agents even in configurations where their numerical opinion shifts remain moderate. The research helps explain how bias and language develop together in multi-agent language model ecosystems.

Multi-agent debate (MAD) is a promising strategy for improving LLM reasoning, but when agents converge on a shared answer, it is unclear whether that convergence reflects genuine deliberation or social compliance. We show that the conventional answer flip rate conflates three distinct mechanisms: spontaneous instability, stance-induced conformity, and reasoning-induced persuasion. Our three-source decomposition framework isolates each through controlled counterfactual conditions. In the primary MMLU-Pro setting, 37% of agent-question observations change under self-reflection alone, while robustness tests show substantial model-dependent instability across GPQA-Diamond and three model families; strict conformity is 29% in the primary setting and remains predominantly harmful across model replications (57-77% correct-to-wrong). A controlled information-gradient experiment reveals that even vacuous reasoning is associated with 20-39% error adoption among resistant agents, with reasoning-like presentation carrying substantial persuasive weight. Harmful conformity can be predicted from Round 0 features (AUC = 0.79), and risk-targeted intervention reduces it by 13.6 percentage points (p < 0.001). However, without correctness labels or self-reflection controls, reducing peer adoption does not improve accuracy, because harmful and beneficial influence cannot be distinguished.