Eur. Phys. J. B 61, 371-376 (2008)
https://doi.org/10.1140/epjb/e2008-00082-4

Dynamics of opinion formation in hierarchical social networks: Network structure and initial bias

¹ Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
² School of Physics and Electronic Information, Wenzhou University, Wenzhou, 325027, P.R. China

Corresponding author: ^a pmhui@phy.cuhk.edu.hk

Received: 9 July 2007
Revised: 6 December 2007
Published online: 29 February 2008

Abstract

The dynamics of opinion formation based on a majority rule model is studied in a network with the social hierarchical structure as one of its limits. The exit probability is found to change sensitively with the number of nodes in the system, but not with the parameter of homophyly characterizing the network structure. The consensus time is found to be a result of non-trivial interplay between the network structure characterized by the parameter of homophyly and the initial bias in opinion. For unbiased initial opinion, a common consensus is easier to be reached in a random network than a highly structured hierarchical network and it follows the behavior of the length of shortest paths. For biased initial opinion, a common consensus is easier to be reached in a hierarchical network, as the local majority opinion of the groups may take on the biased opinions and hence be the same.