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.
Figures & tables
Figure 1: The naming game and our research question we ask. Left: each agent holds K candidate labels, listed in a random order that carries no meaning, and a memory of the last H labels it has heard. In each interaction, a speaker and a listener are drawn uniformly from the N agents; the speaker emits one label, and only the listener appends it to its memory. Right: when the population mixes models of one family (here Opus, Sonnet, and Haiku), each seeded with its own label, whose label does the population adopt? In our experiments it is most often the strongest model’s.
Figure 2: A population of one model, reproducing the setting of Tanaka (2026) . All agents are Claude Haiku 4.5, and every memory starts empty. Left: share of each label in the agents’ answers, for one trial won by each label; the dashed line marks consensus. The difference between the plots is due to the difference in random seeds. Right: the same shares on the simplex, for every trial (faint) and averaged over the trials won by each label (bold).
Figure 3: Who wins. Fraction of the 108 trials per family in which each class’s label becomes the population’s convention. Whiskers are one standard error from a cluster bootstrap over the 18 cells; the dashed line is chance ( 1/3 ). The Gemini ladder is ordered by model generation.
Figure 4: One representative trial per family. Each point is an agent, placed on the simplex by the composition of its 20 -slot memory; the large class starts at the top vertex and the medium and small classes at the bottom. Lines trace each agent’s path. In each of these trials the cloud contracts, drifts, and is absorbed at the large model’s vertex. N=24 , H=20 .
Figure 5: Two labels ( K=2 ). 12 agents of a larger model and 12 of a smaller one from the same family. (a) Fraction of trials won by each model’s label. (b) One trial per family: each line is one agent’s share of the larger model’s label in memory, by round ( N=24 interactions). Dark lines are the larger model’s agents.
Figure 6: Cross model family results
Figure 7: Time to consensus. Median number of interactions to consensus against (a) N at H=20 and (b) H at N=24 , on log–log axes; bars are interquartile ranges over the trials of a cell. Slopes are least-squares exponents per family.
Figure 8: Agents as particles. Agent i ’s output distribution xi is a point on the simplex ΔK−1 , whose vertices are the labels; each interaction moves it.
Figure 9: The consensus energy for Gemma 4. (a) The energy of Equation 2 as a function of the mean output xˉ (darker is lower), with each model’s assertion strength w (its well has depth −w/2 ); dots are the populations’ mean outputs at consensus, in the winner’s colour. (b) Energy along the 108 trials, scaled by its value at the start, against the number of interactions; mean and one standard deviation, with a trial that has reached consensus kept at its final value. (c) One round’s change in the mean output, predicted by the flow of Equation 3 against measured, both scaled by their 99th percentile; the dashed line is perfect agreement. Results for Qwen 3.5 and Qwen 2.5 are in Appendix I .
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Family
Large
Medium
Small
GPT-5
gpt-5
gpt-5-mini
gpt-5-nano
GPT-4.1
gpt-4.1
gpt-4.1-mini
gpt-4.1-nano
Claude 5
claude-opus-5
claude-sonnet-5
claude-haiku-4.5
Gemini
gemini-3.8-flash
gemini-3.5-flash
gemini-2.5-flash
Gemma 4
gemma-4-31B-it
gemma-4-26B-A4B-it
gemma-4-E4B-it
Qwen 3.5
Qwen3.5-122B-A10B
Qwen3.5-35B-A3B
Qwen3.5-9B
Appendix
Table 1: Model identifiers of the seven main ladders.
Family
Large
Medium
Small
Gemma 4
85.2
82.6
69.4
Qwen 3.5
86.7
85.3
82.5
Qwen 2.5
69.0
63.7
56.3
Appendix
Table 2: MMLU-Pro accuracy (%) reported by the developers for the open-weight ladders ( Gemma Team, 2026 ; Qwen Team, 2026 ; Yang et al., 2024a ) .
Figure 10: Memory share and output probability. Each point is one of the 66 compositions of a 20 -slot memory over three labels (in steps of two slots) and one label: its share of the memory against the probability that the model, queried in isolation, says it. Pearson r=0.83 – 0.93 and Spearman 0.82 – 0.96 across the 18 models. The grey diagonal is w=0 in Equation 4 (saying exactly what is remembered); the sigmoidal departure from it is the assertion of the majority. Open-weight values are read from log-probabilities; GPT-5, Claude, and Gemini values are estimated from 20 samples per memory.
N\H
6
10
20
40
3
0.50
0.64
0.69
0.72
6
0.53
0.50
0.50
0.56
12
0.39
0.61
0.53
0.67
24
0.42
0.72
0.83
0.78
Appendix
Table 3: Fraction of trials won by the large model (31B) in the three-class Gemma 4 population, across population size N and memory length H ; chance is 1/3 . Each cell has 36 trials (six label sets, three cyclic assignments, two seeds), all of which fixated.
Figure 11: Energy landscapes of the three open-weight families , with each model’s assertion strength w (its well has depth −w/2 ); dots are the mean outputs at consensus of every trial, in the winner’s colour.
Figure 12: Local agreement in all three families. One round’s change of the mean output, predicted by the flow against measured, both scaled by their 99th percentile; each point is one trial, round, and label.
Figure 13: Energy descent in all three families. Left: energy along the trials, scaled by its start value (mean and one standard deviation). Right: fraction of rounds in which the energy falls, by the class that wins the trial; the dashed line is chance.
Figure 14: Assertion strength and outcome. Each class’s w against the share of the 108 trials its label wins; lines join the three classes of a family.
The effectiveness of multi-agent LLM deliberation depends not only on the agents' individual predictions, but also on how they communicate and collaborate. We study this mechanism through the lens of Friedkin-Johnsen (FJ) opinion dynamics, a tractable model for analyzing stubbornness, influence, and opinion change in multi-agent systems that captures empirically observed deliberation patterns. We show that the FJ parameters are input-dependent, turning multi-agent deliberation into a mixture of experts. This perspective implies that multi-agent systems can outperform single agents and static ensembles when routing reflects agent competence. Since competence is latent in practice, we analyze how influence is established through observable proxies: agents' self-assessed confidence, their perceived confidence, and initial alignment with other agents' views.
Franka Bause, Jonas Niederle, Martin Pawelczyk +1
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany · Faculty of Computer Science, University of Vienna, Vienna, Austria.
When two AI agents disagree, who persuades whom? As multi-agent systems increasingly combine language models of different families and sizes, the answer can determine which judgments survive interaction. Measuring persuasion as the probabilistic shift in an agent's decision after a single exchange with a dissenting peer, we test seven open-weight models across three language understanding tasks. We find that persuasion is strong: when models disagree, receivers often abandon their initial judgment after seeing a peer's answer and explanation. Surprisingly, however, neither standalone certainty nor model scale reliably predicts persuasion dynamics. Models producing almost perfectly consistent decisions in isolation can be among the most susceptible to persuasion, and small models can match larger ones as persuaders and resist their influence just as effectively. Furthermore, we show that the size of the shift depends more on the susceptibility of the listener than on the persuasiveness of the speaker. Persuasion patterns are therefore specific to each model pairing, with heterogeneity amplifying persuasion in some combinations and suppressing it in others, allowing a dissenting agent running a small model to overturn the judgments of a much larger one. These findings show that the behavior of interacting models cannot be inferred from their individual properties but must be evaluated in the combinations in which they will operate.
Frida Nøhr Laustsen, Marie Haahr Petersen, Victoria Popa +4
IT University of Copenhagen, Denmark · University of Pisa, Italy · City St. George’s, University of London, United Kingdom +1
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.
Omran Berjawi, Giuseppe Fenza, Rida Khatoun
Institut Polytechnique de Paris, Télécom Paris, Palaiseau, France · University of Salerno, Fisciano, Italy