A Statistical-Physics Look at How Multi-Agent LLM Systems Emerge Consensus
cephaloform · x · 2026-09-03
A blog post applies the statistical-physics Naming Game model to explain how populations of LLM agents spontaneously develop shared naming conventions without central coordination.
- Model background: The Naming Game, introduced by Steels and solved exactly by Baronchelli et al. in 2006, has two agents meet, one speaks a word from its private vocabulary, the other either accepts it or learns something new; repeated over a population this yields full consensus with convergence time N^(3/2) on a fully connected graph.
- Human evidence: A 2015 experiment by Centola and Baronchelli showed human groups playing an analogous game converge on shared conventions exactly as predicted.
- LLM agents: Recent work shows groups of LLMs playing minimal coordination games converge on shared conventions and can even develop collective biases no single agent exhibits in isolation.
The author argues this matters as multi-agent LLM systems move toward decentralized, self-organizing designs.
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