The Seminar on Math, Stat, and AI is an interdisciplinary seminar series focusing on problems at the intersection of statistics, probability, artificial intelligence and related fields. The upcoming seminar takes place on Friday, April 10th at 10:30am in Maxwell-Dworkin G125. This week's speaker will be Hidenori Tanaka, Research Scientist, NTT Research at Harvard Associate, Center for Brain Science.
When Is Collective Intelligence a Lottery? Scaling Laws for Memetic Drift in LLM Populations
Abstract:
Large language model agents are increasingly deployed in settings where groups of AI systems exchange information and shape consequential decisions. A central question is whether the resulting consensus reflects genuine collective reasoning, systematic bias, or simply chance. In this talk, I will present a minimal model, Quantized Simplex Gossip (QSG), together with naming-game experiments in LLM populations, to show how mutual in-context learning can transform arbitrary early fluctuations into stable agreement. This yields a sampling-driven regime that I call memetic drift, by analogy with neutral evolution. The theory predicts a crossover between a drift-dominated regime, where consensus is effectively a lottery, and a selection regime, where even weak biases are amplified and determine the outcome. I will discuss scaling laws governing this transition in terms of population size, communication bandwidth, adaptation rate, and internal uncertainty, and the implications for collective decision-making in multi-agent AI systems.
This talk is based on the recent preprint, “When Is Collective Intelligence a Lottery? Multi-Agent Scaling Laws for Memetic Drift in LLMs”:
https://arxiv.org/abs/2603.24676