Who Is the Influencer? Consensus Dynamics in Multi-Agent Systems
Multi-agent LLM systems are becoming common, but it is hard to predict which model steers the group when agents disagree. This paper designs a minimalist naming game with meaningless labels to isolate consensus dynamics from pretrained knowledge or correctness. Across seven model families, the authors find that larger, more capable models dominate the final convention even when no answer is right, and they explain this with a simple energy landscape in which bigger models carry larger assertion weights.
The paper offers a clean experimental design and an intuitive physical analogy for heterogeneous multi-agent LLM consensus, but its theoretical claims are weakened by circular fitting and limited validation. The energy landscape and replicator dynamics explain the open-weight results well, yet because assertion strengths are fitted from the same trajectories they are supposed to predict, the framework amounts to a consistency test rather than an independent explanation. The model also fails to distinguish large and medium API models, undermining the claim that size universally determines influence.
The naming-game task is an elegant device: by using meaningless five-character labels, the authors strip out semantic correctness and ground truth, isolating pure consensus dynamics. The empirical finding that larger models win more often is robust across seven families and multiple hyperparameter sweeps, and the cross-family same-size experiment shows no dominant model, supporting the capability-gap hypothesis. The simplex visualizations and descent of the energy $E(\bar{\bm{x}})=-\frac{1}{2}\sum_k w_{c(k)}\bar{x}_k^2$ provide an accessible picture of how the population moves.
The central physical framework suffers from circularity and limited scope. The assertion strengths $w$ and the outputs $\bm{x}_i$ used to evaluate the energy are estimated from the same population runs whose outcomes they are compared with, making the agreement a test of consistency rather than out-of-sample prediction. Moreover, the regression-based separation of assertion strengths cannot distinguish large and medium API models, so the energy account is restricted to the three open-weight families. The closure approximations underlying the replicator equation are also heuristic: once a label spreads, agents of other classes assert it with their own strengths, which breaks the assumption that each label is pushed by the model that introduced it.
A second concern is the assumption that meaningless labels fully eliminate pretraining bias. While the authors randomize label order and content, LLMs may still carry inductive biases about social coordination or majority behavior that are not semantic yet still derived from pretraining. The paper does not test for this, so the claim that knowledge plays no role remains an untested premise.
The within-family evidence strongly supports the core claim. In every family, the population most often converges to the label of the most capable model, and the full ordering large > medium > small holds in every family. The cross-family same-size trial offers a useful control: when models of comparable size but different families are mixed, none dominates, which supports the idea that a substantial capability gap is necessary for influence to appear. Comparisons to related work are generally fair; the authors clearly delimit their contribution against homogeneous-population studies and two-agent attractor work. However, unlike classical models where social influence is measured independently, the assertion weights here are derived from the very dynamics they aim to explain.
The experimental protocol is documented in detail. The authors report exact prompts in Appendix B, list all model identifiers and benchmark scores in Appendix A, and specify hyperparameters $K=3$, $H=20$, $N=24$, and $T=60N$. The use of deterministic label generation and randomized label order in the prompt removes positional confounds. Yet independent reproduction faces serious barriers. The study relies on proprietary API models that may be updated, unavailable, or prohibitively expensive, and the paper does not state that code, interaction logs, or inference scripts have been released. Without these artifacts, reproducing the exact trajectories and fitted assertion strengths would require substantial reimplementation at high cost.
Multi-agent LLM systems are increasingly used in practice, but their behavior is complex and hard to understand. We design a simple task to ask which model has the most influence on the final consensus when several models are mixed in one system. Experimentally, across seven model families, we find that the opinions of the other models are absorbed into the opinion of the stronger model, the one with more parameters. This happens even though the task requires no pretraining knowledge and has no correct answer. To understand this phenomenon, we interpret the agents as weighted particles moving on a simplex. Larger models carry a larger weight and therefore occupy a deeper well in the energy landscape. A large weight means strong in-context learning: a model with a large weight amplifies the majority of its context. Larger models are generally better at in-context learning, and this is what makes the larger model the influencer. We hope that this work helps to interpret multi-agent systems, whose behavior is becoming too complex for humans to understand.
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