Opinion Formation Models in Static and Dynamic Social Networks

We study models of opinion formation on static as well as dynamic networks where interaction among individuals is governed by widely accepted social theories. In particular, three models of competing opinions based on distinct interaction mechanisms are studied. A common feature in all of these models is the existence of a tipping point in terms of a model parameter beyond which a rapid consensus is reached. In the first model that we study on a static network, a node adopts a particular state (opinion) if a threshold fraction of its neighbors are already in that state. We introduce a few initiator nodes which are in state ‘1’ in a population where every node is in state ‘0’. Thus, opinion ‘1’ spreads through the population until no further influence is possible. Size of the spread is greatly affected by how these initiator nodes are selected. We find that there exists a critical fraction of initiators pc that is needed to trigger global cascades for a given threshold φ. We also study heuristic strategies for selecting a set of initiator nodes in order to maximize the cascade size. The structural properties of networks also play an important role in the spreading process. We study how the dynamics is affected by changing the clustering in a network. It turns out that local clustering is helpful in spreading. Next, we studied a model where the network is dynamic and interactions are homophilic. We find that homophily-driven rewiring impedes the reaching of consensus and in the absence of committed nodes (nodes that are not influenceable on their opinion), consensus time Tc diverges exponentially with network size N . As we introduce a fraction of committed nodes, beyond a critical value, the scaling of Tc becomes logarithmic in N . We also find that slight change in the interaction rule can produce strikingly different scaling behaviors of Tc. However, introducing committed agents in the system drastically improves the scaling of the consensus time regardless of the interaction rules considered. Finally, a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field is studied. The mean-field