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A Two-Functional-Network Framework of Opinion Dynamics

A common trait involving the opinion dynamics in social networks is an anchor on interacting network to characterize the opinion formation process among participating social actors, such as information flow, cooperative and antagonistic influence, etc. Nevertheless, interacting networks are generally public for social groups, as well as other individuals who may be interested in. This blocks a more precise interpretation of the opinion formation process since social actors always have complex feeling, motivation and behavior, even beliefs that are personally private. In this paper, we formulate a general configuration on describing how individual's opinion evolves in a distinct fashion. It consists of two functional networks: interacting network and appraisal network. Interacting network inherits the operational properties as DeGroot iterative opinion pooling scheme while appraisal network, forming a belief system, quantifies certain cognitive orientation to interested individuals' beliefs, over which the adhered attitudes may have the potential to be antagonistic. We explicitly show that cooperative appraisal network always leads to consensus in opinions. Antagonistic appraisal network, however, causes opinion cluster. It is verified that antagonistic appraisal network affords to guarantee consensus by imposing some extra restrictions. They hence bridge a gap between the consensus and the clusters in opinion dynamics. We further attain a gauge on the appraisal network by means of the random convex optimization approach. Moreover, we extend our results to the case of mutually interdependent issues.