In this paper, we try to propose a toy model, which follows the majority rule with the Fermi function, to uncover the role of the heterogeneous interaction between individuals in opinion formation. In order to do this, we define the impact factor IFi, says individual i, as the exponential function of its connectivity k(i) with the tunable parameter beta.beta also shows the public information that can be collected by individuals in the system. We realize our model in scale-free networks with mean connectivity < k >. We find that much more public information (beta > beta(2)) and less public information (beta < beta(1)) cannot let either of the two opinions be the majority during the opinion formation. Furthermore, beta(1) is a constant and equal to -0.76(+/- 0.04), and beta(2) decreases as a power-law function of the mean connectivity < k > of the network. Our work can provide some perspectives and tools to understand the diversity of opinion in social networks. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.
