Deffuant model with general opinion distributions: First impression and critical confidence bound

Authors

  • Yilun Shang

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    1. SUTD-MIT International Design Center, Singapore University of Technology and Design, Singapore
    • Correspondence to: Yilun Shang; SUTD-MIT International Design Center, Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682. E-mail: shylmath@hotmail.com

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Abstract

In the Deffuant model for social influence, pairs of adjacent agents interact at a constant rate and mix up their opinions (represented by continuous variables) only if the distance between opinions is short according to a threshold. We derive a critical threshold for the Deffuant model on math formula, above which the opinions converge toward the average value of the initial opinion distribution with probability one, provided the initial distribution has a finite second order moment. We demonstrate our theoretical results by performing extensive numerical simulations on some continuous probability distributions including uniform, Beta, power-law and normal distributions. Noticed is a clear differentiation of convergence rate that unimodal opinions (regardless of being biased or not) achieve consensus much faster than even or polarized opinions. Hereby, the emergence of a single mainstream view is a prominent feature giving rise to fast consensus in public opinion formation and social contagious behavior. Finally, we discuss the Deffuant model on an infinite Cayley tree, through which general network architectures might be factored in. © 2013 Wiley Periodicals, Inc. Complexity 19: 38–49, 2013

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