On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann
arXiv:cond-mat/0408648 · doi:10.1142/S0129183105007078
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 ε. A randomly chosen agent takes the average of the opinions of all neighbouring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold ε_c of this model. We claim that ε_c can take only two possible values, depending on the behaviour of the average degree d of the graph representing the social relationships, when the population N goes to infinity: if d diverges when N goes to infinity, ε_c equals the consensus threshold ε_i ~ 0.2 on the complete graph; if instead d stays finite when N goes to infinity, ε_c=1/2 as for the model of Deffuant et al.
arXiv comment15 pages, 7 figures, to appear in International Journal of Modern Physics C 16, issue 2 (2005)
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- The bridges to consensus: Network effects in a bounded confidence opinion dynamics model
- Order preservation in a generalized version of Krause's opinion dynamics model
- Dynamical phase transitions in Hegselmann-Krause model of opinion dynamics and consensus
- Noise Leads to Quasi-Consensus of Hegselmann-Krause Opinion Dynamics
- The Hegselmann-Krause dynamics for continuous agents and a regular opinion function do not always lead to consensus
- Further results on consensus formation in the Deffuant model
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