The Robust Consensus of a Noisy Deffuant-Weisbuch Model

Jiangbo Zhang and Yiyi Zhao

Mathematical Problems in Engineering, 2018, vol. 2018, 1-10

Abstract:

We construct a new opinion formation of the Deffuant-Weisbuch model with the interference of the outer noise, where there are finite agents and the evolution is discrete-time. The opinion interaction occurs by one randomly chosen pair at each time step. The difference to the original Deffuant-Weisbuch model is that communications of any selected pairs will be affected by noises. The aim of this paper is to study the robust consensus of this noisy Deffuant-Weisbuch model. We first define the noise strength as the maximum noise absolute value. We will then show that when the noise strength is less than a certain threshold, this noisy model will achieve robust consensus when is sufficiently large; next we prove that the noisy model achieves robust consensus with a positive probability; finally, we demonstrate these results and provide numerical relations among the noise strength and some model parameters.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1065451

DOI: 10.1155/2018/1065451

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