A Generalized Sznajd Model

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.

19 pages with 8 figures. Submitted to Physical Review E

References in corpus (5)

• Statistical physics of social dynamics
• Continuous Opinion Dynamics under Bounded Confidence: A Survey
• Scaling and universality in proportional elections
• Chaotic, staggered and polarized dynamics in opinion forming: the contrarian effect
• The Spread of Opinions and Proportional Voting

Cited by in corpus (4)

• Synchronization over $Z_2$ and community detection in multiplex signed networks with constraints
• Role of social environment and social clustering in spread of opinions in co-evolving networks
• Connections between the Sznajd Model with General Confidence Rules and graph theory
• Coexistence of Interacting Opinions in a Generalized Sznajd Model