Critical phenomena in the spreading of opinion consensus and disagreement

TL;DR

This paper investigates how local consensus and disagreement influence opinion spreading, revealing critical phenomena and scaling behaviors in one- and two-dimensional models, highlighting nontrivial exponents and the importance of group interactions.

Contribution

It introduces a new class of opinion formation models emphasizing local consensus/disagreement dynamics, differing from traditional imitation-based models.

Findings

Full consensus probability scales with system size.

Two-dimensional models show nontrivial critical exponents.

Models highlight the role of small group interactions in opinion dynamics.

Abstract

We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement in one- and two-dimensional arrays. In both cases, the probability of reaching full consensus exhibits well-defined scaling properties as a function of the system size. Two-dimensional systems, in particular, possess nontrivial exponents and critical points. The dynamical rules of our models, which emphasize the interaction between small groups of agents, should be considered as complementary to the imitation mechanisms of traditional opinion dynamics.