Imprecise Belief Fusion Improves Multi-agent Social Learning

Social Learning is a decentralized decision-making paradigm in which spatially dispersed agents collect streaming observations regulated by one of a finite number of models (the hypotheses). The agents are interested in assigning probability scores (the beliefs) to the possible hypotheses. To this end, the agents exchange their beliefs according to a certain communication graph. It has been shown that, under reasonable conditions on the identifiability of the decision model and the network connectivity, each agent ultimately places all the belief mass on the true hypothesis governing the data. However, several questions remain unanswered regarding the evaluation of the social learning performance. One recently adopted performance metric is the rejection rate, i.e., the rate at which the beliefs about the erroneous hypotheses vanish. One contribution of this work is to establish that the rejection rate leads to several paradoxes, which make it unsuitable as a valid performance measure. We then focus on studying the error probability measure. For a binary Gaussian problem, we derive an analytical formula characterizing the ratio between the individual agents' probabilities and the optimal Bayesian probability. The formula shows that this ratio is expressed by the product of two terms quantifying the effect of the network connectivity and the role of the prior information. As a result, an irreducible gap emerges between the decentralized and the centralized error probabilities, which is agent-dependent and does not disappear asymptotically.

Social learning is a powerful mechanism through which agents learn about the world from others. However, humans sometimes choose direct experience over social learning, which can carry time and cognitive resource costs. How do people balance social and non-social learning? We propose a Rational Mentalizing model of the decision to engage in social learning. This model estimates the utility of social learning by reasoning about another agent's goal and the informativeness of their future actions. It then weighs the utility of social learning against the utility of non-social learning. Using a novel game where players choose between observing other agents or exploring the environment, we show that the Rational Mentalizing model can quantitatively capture human trade-offs between these strategies. These findings suggest that selective social learning is guided by 'Theory of Mind' in the service of utility maximization.

Large language models (LLMs) are increasingly deployed in multi-agent environments. However, the processes by which beliefs form and propagate among interacting LLMs remain poorly understood. We introduce CoevolveSim, a framework for studying belief diffusion within networked LLM populations. CoevolveSim allows us to isolate and study three factors: domain specialization, social-role assignment, and social network structure. Within this framework, generalist and specialist LLM agents exchange and revise beliefs. In each round, an LLM agent observes a summary of its neighbors' beliefs before updating its own. We run 1,280 controlled simulations spanning four scenarios, two network structures, and 20 medical-indication statements. We find that persona-style role assignment and network structure reshape individual belief revision but have minimal effect on population-level consensus. In contrast, introducing (finetuned) specialist LLMs more than doubles the shift in consensus and gives rise to consistent asymmetries in exerted influence. We further show that simple persistence-based opinion-dynamics models reproduce collective outcomes in all-generalist LLM populations, whereas heterogeneous LLM populations require population-level belief composition to reproduce consensus and agent identity to predict individual belief transitions. Our results indicate that realistic simulation of belief diffusion in multi-agent LLM systems requires a diverse set of underlying LLMs, not persona prompting alone.