Coexistence of Interacting Opinions in a Generalized Sznajd Model

TL;DR

This paper extends the Sznajd opinion model to complex networks, demonstrating the coexistence of interacting opinions and ongoing opinion dynamics in stationary states, contrasting with mean-field predictions.

Contribution

It introduces network structures that enable coexistence of interacting opinions and persistent opinion changes, advancing understanding of opinion dynamics beyond mean-field models.

Findings

Networks can support coexistence of interacting opinions.

Opinions continue to evolve even in stationary states.

Behavior approaches mean-field predictions as network structure changes.

Abstract

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favour groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, that has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviours we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model, by generalizing the bounded confidence rule that is common to many continuous opinion models. In that work we have found that the mean-field version of this model (corresponding to a complete network) allows for stationary states where non-interacting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions. Moreover, we show that the model does not become inactive, that is, the opinions keep changing, even in the stationary regime. We also provide results that give some insights on how this behaviour approaches the mean-field behaviour, as the networks are changed.