THE SZNAJD CONSENSUS MODEL WITH CONTINUOUS OPINIONS

Abstract

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighboring agents with the same opinion forces all their neighbors to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here, the opinion s is a real number between 0 and 1, and a parameter ∊ is introduced such that two agents are compatible if their opinions differ from each other by less than ∊. If two neighboring agents are compatible, they take the mean sm of their opinions and try to impose this value to their neighbors. We find that if all neighbors take the average opinion sm, the system reaches complete consensus for any value of the confidence bound ∊. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.