Opinion Consensus Formation Among Networked Large Language Models

TL;DR

This paper investigates how large language models (LLMs) reach consensus through multi-round interactions modeled by the DeGroot framework, revealing that consensus is influenced more by discussion topics and biases than initial opinions.

Contribution

It applies classical consensus models to LLM interactions, providing insights into opinion dynamics and convergence behavior in multi-agent LLM systems.

Findings

Agents typically reach consensus with exponential decay of disagreement.

The limiting opinion depends on discussion topics and biases, not initial conditions.

Convergence rate relates to the second-largest eigenvalue of the graph's matrix.

Abstract

Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse communication graphs. To track opinion evolution, we map each message to an opinion score via sentiment analysis. We find that agents typically reach consensus and the disagreement between the agents decays exponentially. However, the limiting opinion departs from DeGroot's network-centrality-weighted forecast. The consensus between LLM agents turns out to be largely insensitive to initial conditions and instead depends strongly on the discussion subject and inherent biases. Nevertheless, transient dynamics align with classical graph theory and the convergence rate of opinions is closely related to the second-largest eigenvalue of the graph's combination matrix. Together, these findings can be useful for LLM-driven social-network simulations and the design of resource-efficient multi-agent LLM applications.