The Sznajd Consensus Model with Continuous Opinions

TL;DR

This paper extends the Sznajd consensus model to continuous opinions using a bounded confidence approach, demonstrating that the system reaches complete consensus under certain averaging dynamics.

Contribution

It introduces a continuous opinion version of the Sznajd model based on bounded confidence, analyzing consensus formation with different averaging rules.

Findings

System reaches complete consensus for any confidence bound when neighbors adopt the average opinion.

Weaker averaging rules also lead to consensus, depending on the dynamics.

The model bridges discrete and continuous opinion consensus models.

Abstract

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours 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 \epsilon is introduced such that two agents are compatible if their opinions differ from each other by less than \epsilon. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound \epsilon. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.