Social contagion with degree-dependent thresholds

TL;DR

This paper studies how opinions spread in a network where individuals have different influence levels and thresholds for adopting new ideas, revealing complex behaviors beyond simple phase transitions.

Contribution

It introduces a threshold model with degree-dependent influence, showing how heterogeneity affects opinion dynamics and consensus formation.

Findings

High positive coupling leads to mixed opinions

Weak coupling results in consensus

Opinion dynamics are governed by multiple mechanisms

Abstract

We investigate opinion spreading by a threshold model in a situation where the influence of people is heterogeneously distributed. We focus on the response of the average opinion as a function between the trend between out-degree (number of neighbors)---effectively the strength of influence of a node---and the threshold for adopting a new product or opinion. We find that if the coupling is very positive, the final state of the system will be a mix of different opinions otherwise it will it converges to a consensus state. We find that this cannot be simply explained as a phase transition, but emerges from a combination of mechanisms and their relative dominance in different regions of parameter space.