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

2026-03-25

AI Summary

This work addresses the unclear mechanisms underlying consensus formation in multi-agent large language model (LLM) systems—whether it arises from collective reasoning, systemic bias, or stochasticity. The authors propose the Quantized Simplex Gossip (QSG) model, revealing that consensus emerges through in-context learning as agents amplify arbitrary initial choices via sampled outputs. Introducing the novel concept of “meme drift,” analogously to neutral evolution, they identify a phase transition from randomness-dominated dynamics to weak-preference amplification. For the first time, they derive a scaling law that quantifies how group size and communication bandwidth jointly govern polarization. Through QSG simulations and LLM-based naming game experiments, the validity of this scaling law is empirically confirmed, offering a theoretical framework for understanding the emergence of social representations in multi-agent LLM systems.

Technology Category

• Multiagent Systems: Multiagent Learning
• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Multi-agent systems powered by large language models (LLMs) are increasingly deployed in settings that shape consequential decisions, both directly and indirectly. Yet it remains unclear whether their outcomes reflect collective reasoning, systematic bias, or mere chance. Recent work has sharpened this question with naming games, showing that even when no individual agent favors any label a priori, populations rapidly break symmetry and reach consensus. Here, we reveal the mechanism by introducing a minimal model, Quantized Simplex Gossip (QSG), and trace the microscopic origin of this agreement to mutual in-context learning. In QSG, agents maintain internal belief states but learn from one another's sampled outputs, so one agent's arbitrary choice becomes the next agent's evidence and can compound toward agreement. By analogy with neutral evolution, we call this sampling-driven regime memetic drift. QSG predicts a crossover from a drift-dominated regime, where consensus is effectively a lottery, to a selection regime, where weak biases are amplified and shape the outcome. We derive scaling laws for drift-induced polarization as a function of population size, communication bandwidth, in-context adaptation rate, and agents' internal uncertainty, and we validate them in both QSG simulations and naming-game experiments with LLM populations. Together, these results provide a framework for studying the collective mechanisms of social representation formation in multi-agent systems.

Problem

• collective intelligence
• memetic drift
• multi-agent systems
• LLMs
• consensus formation

Innovation

• memetic drift
• multi-agent systems
• in-context learning
• scaling laws
• collective intelligence