Global consensus making on multiplex scale-free networks

Most individuals, if not all, are active in various social networks. Opinion formation is an outcome of social interactions and information propagation occurring in such social systems. In this paper, we study on opinion formation on multiplex networks composed of two layers, each of which is a scale-free network, with a special focus on global consensus making in such networks. We impose a new rule of pair-wise interactions under inter-layer interplay termed as compromise following which two interacting nodes have a tendency to make a fair compromise in both senses of inter-and intra-layer interplay. It is found that in a duplex network composed of two identical layers, an increase in tolerance range in a layer declines the opinion diversity on the other layer and the two critical confidence bounds for achieving global consensus in both layers follow a one-sum rule; that is, each of the layers reaches a global consensus if the sum of two critical bounds on the two layers is approximately equal to 1, a double of critical bound on a single-layer network. However, in duplex networks of two non-identical layers with layer-layer coupling quantified by a link overlap parameter, the rule does not hold any longer. In this case, due to the larger portion of low-degree nodes in typical scale-free networks, a layer only can reach a complete consensus if its associated tolerance range is as large as nearly 0.5 even when the tolerance range on the other layer is utmost.