A peer-reviewed paper by Giordano De Marzo, Claudio Castellano, and David Garcia quantifies majority-following behavior in AI agents across 10 different models. Published in Science Advances on August 14, 2026 (DOI: 10.1126/sciadv.aea6091), the study presents agents with a binary choice that has no correct answer, shows them only the choices of others around them, and examines when the group converges on one option.
The "1,000 agents" figure the study reports does not mean 1,000 agents achieved complex cooperation. For Claude 3.5 Sonnet, even the largest group actually measured—1,000 agents—still exceeded the theoretical consensus threshold. As a result, the critical group size could only be established as a lower bound of "more than 1,000." No humans were tested, so the results cannot be compared on the same scale as informal human groups.
What the paper measured is not agents' ability to arrive at correct answers, but conformity and convergence on a meaningless choice. In multi-agent design, which models amplify majority bias at which population sizes becomes a separate evaluation criterion from individual model performance.
The same majority-following pattern across 10 models
The subjects were not humans but the following 10 LLM versions.
| Developer | Models used in the experiment | Count |
|---|---|---|
| Anthropic | Claude 2.0, Claude 3 Haiku/Sonnet/Opus, Claude 3.5 Sonnet | 5 |
| OpenAI | GPT-3.5 Turbo, GPT-4, GPT-4o, GPT-4 Turbo | 4 |
| Meta | Llama 3 70B Instruct | 1 |
The comparison spans models from three companies, but each is a specific, fixed version. Each agent was given arbitrary labels of "k" and "z," with no instructions about correctness, rewards, or reaching consensus. The temperature for the main experiment was 0.2.
In the experiments, agents were placed in a fully connected group where everyone could see everyone else's current choice. However, there was no memory, and at each step only one randomly selected agent updated its choice. That agent could see all other agents' choices but not its own. The initial state was split evenly, and time t=1 corresponds to N updates (where N is the number of agents)—that is, the length of time during which each agent is selected on average once.
In measurements run with N=50 over 20 trials, continuing until each agent was updated an average of 10 times, Claude 3 Opus and GPT-4 Turbo reached complete consensus in all 20 trials. Claude 3 Haiku and GPT-3.5 Turbo reached consensus in zero trials, while Llama 3 70B moved toward consensus but did not achieve unanimous agreement within this time limit. Here, complete consensus is defined as C=|m|=1, not task accuracy.
The authors measured, across all 10 models, the probability of selecting an option as a function of the bias m within the group, using N=50. Nine of the models roughly fit P(m)=0.5[tanh(βm)+1], with β termed the "strength of majority influence." The core dataset of transition probabilities includes 200 responses for each of 15 collective opinion points. GPT-3.5 Turbo, however, was an exception to this approximation. For many models, β decreased as group size grew larger, but the explanation that this reflects perceived social pressure is offered by the authors only as a possibility.
In a comparison majority-vote count, accuracy did not decline as sharply with longer lists. The size-dependent curves include behavior distinct from whether vote-counting succeeded or failed. However, the experiment did not isolate what inside the LLM produces these responses.
1,000 agents was the upper limit tested
What was observed for Claude 3.5 Sonnet was β at N=1,000. The paper reports that this value still exceeded the theoretical threshold β_t(1,000), approximately 3.5, required for complete consensus, and set the critical group size N_c at "more than 1,000." The figure of 1,000 is not a number confirming this model's consensus-reaching population, but simply the largest population size tested.
According to the authors' estimates, N_c was approximately 30 for Llama 3 70B, approximately 80 for GPT-4o, and approximately 1,000 for GPT-4 Turbo. Even GPT-4 Turbo's value was not established by directly observing all population sizes to confirm the boundary—it was estimated from the intersection of β and the theoretical threshold as functions of group size. Furthermore, while cooperation-time measurements were typically averaged over 5 trials, N=500 used only 3 trials, and GPT-4 Turbo's N=1,000 case used just a single trial, with error bars indicating a range.
There is also a comparison with model benchmark scores. The correlation between MMLU and log(N_c), calculated using 8 model data points (excluding humans and the lower-bound value for Claude 3.5 Sonnet), yielded Pearson r=0.8178, P=0.013. The correlation between MMLU and β across all 10 models was r=0.7910, P=0.006. This is a cross-sectional comparison across model versions, not a measurement of a causal effect whereby improved capability produces larger consensus-reaching groups. Most other benchmarks had limited data ranges and did not yield significant N_c correlations.
Boundaries set using the mathematics of magnetism
The paper maps the experimentally obtained β values onto the Curie-Weiss model, which describes the collective behavior of ferromagnetic materials. Here, β_c=1 represents the theoretical boundary at which order begins to emerge, and β_t(N)≒0.5 log(N) serves as a theoretical benchmark for reaching complete consensus through ordinary fluctuations. The response curves measured from the LLMs and the predictions of the mathematical model are not the same kind of empirical measurement.
N_c is estimated by solving β(N_c)=β_t(N_c). The "approximately 30," "approximately 80," and "approximately 1,000" figures for each model are estimates derived by connecting measured response probabilities with the theoretical formula. A similar functional form does not prove that LLMs and magnets share the same underlying mechanism, nor does it prove that LLMs socialize the way humans do.
The research team separately ran five simulations of group splitting using Llama 3 70B, starting with groups of 150 agents, and obtained 54 splitting events across 10 splitting iterations. In this data, groups of fewer than roughly 15 agents almost never split, while groups larger than roughly 60 agents always split. 95% Wilson confidence intervals were also provided, but this is a simulation using binary-choice response measurements, not an observation of a real-world organization.
Consensus is not cooperative ability
Convergence on a meaningless binary choice does not measure task quality involving division of labor, understanding intent, or long-term memory. Even when the majority is wrong, this experiment cannot assess the ability to return to the correct answer. Regarding comparisons to the figure of 150–300 often cited as the scale of informal human relationships, the paper explicitly states that this is not directly equivalent, and notes that the estimate itself has been criticized.
The stability of the results varied by condition. Tests at temperatures of 0.2, 0.6, and 1.0 showed no major differences, but among five different prompts, two produced significantly different selection-probability curves for Llama 3 70B. Claude 3.5 Sonnet also showed a small deviation for one prompt. Whether the origin of majority-following behavior lies in training data, system prompts, RLHF, or the nature of computation itself cannot be determined from this experimental design.
The code and generated data are publicly available on GitHub and archived on Zenodo as well. While the materials needed for third-party replication are available, inspection of the labels, temperature, and prompts within the paper does not constitute independent replication. A team including overlapping authors has also released a follow-up preprint using 9 LLMs and 100 opinion pairs, suggesting that conformity can stabilize collective misalignment. This is a preprint, not yet peer-reviewed, and cannot be treated as independent replication of this study.
What needs to be verified in practice is whether the same relationship between β and N_c holds when tasks with correct answers, memory between agents, differentiated roles, and limited communication pathways are added. Only once such verification is complete can findings from binary-choice conformity experiments be connected to the safety design of real-world agent groups.