Can memory & higher-order neighbors improve LLM agent consensus?
FJ-MM: The Friedkin-Johnsen Opinion Dynamics Model with Memory and Higher-Order Neighbors
This paper introduces FJ-MM, an extension of the Friedkin-Johnsen (FJ) model for opinion dynamics. FJ-MM incorporates memory and multi-hop influence, allowing agents to consider past opinions and indirect influence from non-adjacent neighbors. This reduces opinion polarization and alters the equilibrium. Importantly for LLM-based multi-agent systems, FJ-MM highlights that considering past interactions and indirect influences (analogous to message history and multi-agent communication pathways) can significantly reshape the outcome landscape, even in simple linear models. While improving realism, these additions also slow down convergence. Further, the paper analyses the convergence rate and stability of FJ-MM, demonstrating its dependence on network topology and agent susceptibility to influence. This is directly applicable to multi-agent systems where the communication network and agents' responsiveness to others' messages are key design parameters.