Effects of inhomogeneous influence of individuals on an order-disorder transition in opinion dynamics

TL;DR

This paper analytically examines how inhomogeneous influence among individuals affects the order-disorder transition in opinion dynamics, revealing that influence heterogeneity shifts the transition point and impacts collective opinion formation.

Contribution

It introduces a model with two types of individuals with different influence levels and analyzes how their inhomogeneous influence alters the critical transition in opinion dynamics.

Findings

Inhomogeneous influence shifts the order-disorder transition point.

The distribution of influence affects collective opinion formation.

Heterogeneity in influence is crucial for understanding opinion dynamics.

Abstract

We study the effects of inhomogeneous influence of individuals on collective phenomena. We focus analytically on a typical model of the majority rule, applied to the completely connected agents. Two types of individuals $A$ and $B$ with different influence activity are introduced. The individuals $A$ and $B$ are distributed randomly with concentrations $\nu$ and $1-\nu$ at the beginning and fixed further on. Our main result is that the location of the order-disorder transition is affected due to the introduction of the inhomogeneous influence. This result highlights the importance of inhomogeneous influence between different types of individuals during the process of opinion updating.