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

arXiv: https://arxiv.org/abs/2603.24676 · HTML: https://mlsanity.com/paper/2603.24676/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 20 of 20)

- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [Exploring Collaboration Mechanisms for LLM Agents: A Social Psychology View](https://mlsanity.com/paper/2310.02124/) (2023)
- [TradingAgents: Multi-Agents LLM Financial Trading Framework](https://mlsanity.com/paper/2412.20138/) (2024)
- [MDAgents: An Adaptive Collaboration of LLMs for Medical Decision-Making](https://mlsanity.com/paper/2404.15155/) (2024)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [Voting or Consensus? Decision-Making in Multi-Agent Debate](https://mlsanity.com/paper/2502.19130/) (2025)
- [Competition Dynamics Shape Algorithmic Phases of In-Context Learning](https://mlsanity.com/paper/2412.01003/) (2024)
- [ICLR: In-Context Learning of Representations](https://mlsanity.com/paper/2501.00070/) (2024)
- [Belief Dynamics Reveal the Dual Nature of In-Context Learning and Activation Steering](https://mlsanity.com/paper/2511.00617/) (2025)
- [Simulating Cooperative Prosocial Behavior with Multi-Agent LLMs: Evidence and Mechanisms for AI Agents to Inform Policy Decisions](https://mlsanity.com/paper/2502.12504/) (2025)
- [In-Context Learning Strategies Emerge Rationally](https://mlsanity.com/paper/2506.17859/) (2025)
- [Group size effects and collective misalignment in LLM multi-agent systems](https://mlsanity.com/paper/2510.22422/) (2025)
- [MALLM: Multi-Agent Large Language Models Framework](https://mlsanity.com/paper/2509.11656/) (2025)
- [An Electoral Approach to Diversify LLM-based Multi-Agent Collective Decision-Making](https://mlsanity.com/paper/2410.15168/) (2024)
- [LAW: Legal Agentic Workflows for Custody and Fund Services Contracts](https://mlsanity.com/paper/2412.11063/) (2024)
- [Disentangling Interaction and Bias Effects in Opinion Dynamics of Large Language Models](https://mlsanity.com/paper/2509.06858/) (2025)

## Built on by (most cited first, 6 of 6)

- [Physics of Agents: Statistical Mechanics Predicts Collective Behavior of AI Agents](https://mlsanity.com/paper/2608.16578/) (2026)
- [Flag Game: A Toy Model for Mechanistic Swarm Interpretability](https://mlsanity.com/paper/2609.19124/) (2026)
- [Candidate supply and answer selection shape the value of LLM judging in multi-agent systems](https://mlsanity.com/paper/2608.25937/) (2026)
- [A latent dimension of Condorcet's jury theorem for multiple AI advisers](https://mlsanity.com/paper/2609.14438/) (2026)
- [Xeno-Interpretability: Investigating the Alien Minds of LLMs](https://mlsanity.com/paper/2609.20408/) (2026)
- [Ecology of AI Agents: Collaboration Creates a Population Threshold for Takeoff](https://mlsanity.com/paper/2610.12436/) (2026)

## Abstract (arXiv)

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.