ON THE CONSENSUS THRESHOLD FOR THE OPINION DYNAMICS OF KRAUSE–HEGSELMANN

Abstract

In the consensus model of Krause–Hegselmann, 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 ∊. A randomly chosen agent takes the average of the opinions of all neighboring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold ∊c of this model. We claim that ∊c can take only two possible values, depending on the behavior of the average degree d of the graph representing the social relationships, when the population N approaches infinity: if d diverges when N→∞, ∊c equals the consensus threshold ∊i~0.2 on the complete graph; if instead d stays finite when N→∞, ∊c =1/2 as for the model of Deffuant et al.