Heterogeneity and subjectivity in binary-state opinion formation systems

In society, there is heterogeneous interaction and randomness in human decision making. In order to unfold the roles and the competition of the two factors mentioned above in opinion formation, we propose a toy model, which follows a majority rule with a Fermi function, on scale-free networks with degree exponent gamma. The heterogeneous interaction is related to the connectivity of a person with the interactive parameter beta, and the randomness of human decision making is quantified by the interaction noise T. We find that a system with heterogeneity of network topology and interaction shows robustness perturbed by the interaction noise T according to the theoretical analysis and numerical simulation. Then, when T -> 0, the homogeneous interaction (beta similar or equal to 0) has a powerful implication for the emergence of a consensus state. Furthermore, the emergence of the two extreme values shows the competition of the heterogeneity of interaction and the subjectivity of human decision making in opinion formation. Our present work provides some perspective on and tools for understanding the diversity of opinion in our society.