Convergence of Opinion Diffusion is PSPACE-complete

TL;DR

This paper investigates the computational complexity of opinion convergence in social networks, proving that determining whether opinions stabilize is a PSPACE-complete problem, highlighting the inherent difficulty of predicting social opinion dynamics.

Contribution

It establishes the PSPACE-completeness of the problem of deciding opinion convergence in directed social networks, a novel complexity result for opinion diffusion models.

Findings

Opinion convergence problem is PSPACE-complete.

Stable opinions are computationally hard to determine.

Complexity results apply to directed social influence networks.

Abstract

We analyse opinion diffusion in social networks, where a finite set of individuals is connected in a directed graph and each simultaneously changes their opinion to that of the majority of their influencers. We study the algorithmic properties of the fixed-point behaviour of such networks, showing that the problem of establishing whether individuals converge to stable opinions is PSPACE-complete.