A Generalized Sznajd Model

TL;DR

This paper introduces a generalized Sznajd model incorporating a bounded confidence rule, enabling the coexistence of opinions and providing analytical and numerical insights into opinion dynamics on different network structures.

Contribution

It presents a new version of the Sznajd model with a generalized bounded confidence rule, applicable to multiple opinions, and analyzes its behavior through mean-field and network simulations.

Findings

The model allows opinion coexistence in stationary states.

Phase portraits for three and four opinions identify attractors and basins.

Discrepancies between mean-field and simulations are explained.

Abstract

In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule - a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabasi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.