Universality of the Threshold for Complete Consensus for the Opinion Dynamics of Deffuant et al

TL;DR

This paper provides numerical evidence that in Deffuant et al.'s opinion dynamics model, the critical confidence bound for complete consensus is universally 1/2, regardless of social network structure.

Contribution

The study demonstrates that the threshold for total consensus in the Deffuant model is universally 1/2, independent of social topology, supported by strong numerical evidence.

Findings

Threshold for consensus is 1/2 across topologies

Consensus occurs when confidence bound exceeds 1/2

Universal threshold independent of social network structure

Abstract

In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly chosen pair of compatible agents get closer to each other. We provide strong numerical evidence that the threshold value of \epsilon above which all agents share the same opinion in the final configuration is 1/2, independently of the underlying social topology.