When Is Collective Intelligence a Lottery? Toward a Physics of Bounded Agent Societies

Multi-agent LLM systems can reach agreement quickly, but agreement alone does not reveal whether a group has integrated evidence, amplified a bias, or merely locked in the luck of early samples. In this talk, I will develop a physics-style approach to this problem through two synthetic games. In reward-free naming games, populations form conventions through mutual in-context learning: agents treat one another's sampled outputs as evidence, so early fluctuations compound into consensus. A minimal model, Quantized Simplex Gossip (QSG), identifies this regime as memetic drift and predicts scaling laws and a crossover from lottery-like drift to bias-driven selection. I will then introduce the Flag Game, in which a hidden country flag provides verifiable ground truth but each agent sees only a private crop of it. Here, bounded agents must balance private evidence against social input. We find rich phenomenologies, where adding agents can help or hurt, large groups can polarize, and social-awareness prompting, model diversity, and organizational structure all reshape collective performance. Extending QSG with grounded evidence and model-specific update rules explains these effects. More broadly, these studies frame an LLM society as a network of networks, neural networks coupled through social interaction, and outline a route toward a multiscale physics of interacting AI agents, linking model-internal representations, agent-level decision mechanisms, and population-level social dynamics.