When Is Collective Intelligence a Lottery? Multi-Agent Scaling Laws for Memetic Drift in LLMs

A new research paper by Hidenori Tanaka, titled 'When Is Collective Intelligence a Lottery? Multi-Agent Scaling Laws for Memetic Drift in LLMs,' provides a critical framework for understanding how groups of AI agents reach consensus. The study introduces a minimal model called Quantized Simplex Gossip (QSG) to trace how agents, through mutual in-context learning, can amplify each other's arbitrary choices. This process, termed 'memetic drift' by analogy to neutral evolution in biology, reveals that populations of LLM agents can rapidly break symmetry and agree on a label even when no individual agent has a prior preference for it.

Tanaka's model predicts a fundamental crossover between two regimes. In the 'drift-dominated' regime, the final consensus is effectively random—a lottery determined by initial sampling noise. In the 'selection' regime, even weak inherent biases in the agents are amplified and reliably shape the collective outcome. The paper's key contribution is deriving mathematical scaling laws that predict the polarization and consensus time based on concrete parameters: population size, communication bandwidth, the agents' in-context adaptation rate, and their internal uncertainty.

These findings were validated through both QSG simulations and real naming-game experiments with populations of LLMs. The work moves beyond observing that multi-agent systems can reach consensus and instead provides a predictive, mechanistic understanding of *how* and *when* that consensus is meaningful versus arbitrary. This is a significant step toward a physics-like theory of collective behavior in AI systems.