cs.AIOct 22, 2026
SaveWho Is the Influencer? Consensus Dynamics in Multi-Agent Systems
Organizations: The University of Tokyo
Abstract
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 candidate labels, listed in a random order that carries no meaning, and a memory of the last labels it has heard. In each interaction, a speaker and a listener are drawn uniformly from the 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 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 cells; the dashed line is chance ( ). 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 -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. , .
Figure 5: Two labels ( ). agents of a larger model and 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 ( 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) at and (b) at , 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 ’s output distribution is a point on the simplex , 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 (darker is lower), with each model’s assertion strength (its well has depth ); dots are the populations’ mean outputs at consensus, in the winner’s colour. (b) Energy along the 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 |
Table 1: Model identifiers of the seven main ladders.
| Family | Large | Medium | Small |
|---|---|---|---|
| Gemma 4 | |||
| Qwen 3.5 | |||
| Qwen 2.5 |
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 compositions of a -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 – and Spearman – across the models. The grey diagonal is 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 samples per memory.
Table 3: Fraction of trials won by the large model (31B) in the three-class Gemma 4 population, across population size and memory length ; chance is . Each cell has 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 (its well has depth ); 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 against the share of the trials its label wins; lines join the three classes of a family.
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