A Generalized Sznajd Model

Instituto de Física, Universidade de São Paulo Caixa Postal 66318, 05314-970 São Paulo São Paulo Brazil (Dated: May 4, 2009) Abstract In the last decade the Sznajd Model has been successfully emp loyed in modeling some properties and scale features of both proportional and majority elections . We propose a new version of the Sznajd model with a generalizedbounded confidence rule a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationar y 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 Barabási -Albert network (for three and four opinions), studying the transient and the possible stationary states. W built the phase portrait for the special cases of three and four opinions, defining the attractors and their ba sins of attraction. Through this analysis, we were able to understand and explain discrepancies between meanfield and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and t hree opinions. Both the dynamical system approach and our generalized bounded confidence rule are qui te general and we think it can be useful to the understanding of other similar models.