Collective effects of the cost of opinion change

TL;DR

This paper investigates how the costs associated with changing opinions influence opinion dynamics, revealing complex phase transitions and effects on consensus and fragmentation in a heterogeneous bounded confidence model.

Contribution

It introduces a coupled model of opinion dynamics and resource investment, uncovering novel phase transition behaviors and effects of opinion change costs.

Findings

Identifies a second order phase transition with critical exponents.

Shows cost can paradoxically increase opinion cluster size.

Demonstrates different effects of cost depending on the confidence region.

Abstract

We study the dynamics of opinion formation in the situation where changing opinion involves a cost for the agents. To do so we couple the dynamics of a heterogeneous bounded confidence Hegselmann-Krause model with that of the resources that the agents invest on each opinion change. The outcomes of the dynamics are non-trivial and strongly depend on the different regions of the confidence parameter space. In particular, a second order phase transition, for which we determine the corresponding critical exponents, is found in the region where a re-entrant consensus phase is observed in the heterogeneous Hegselmann-Krause model. For regions where consensus always exist in the heterogeneous Hegselmann-Krause model, the introduction of cost does not lead to a phase transition but just to a continuous decrease of the size of the largest opinion cluster. Finally in the region where fragmentation is expected in the heterogeneous HK model, the introduction of a very small cost paradoxically increases the size of the largest opinion cluster.