Opinion formation in dynamic social networks

Opinion dynamics in a society of interacting agents may lead to consensus or to the coexistence of different opinions. The interplay between social network change and opinion formation is complex, because the agents, their social interactions and the changing social structure over time, are themselves complex. DeGroot proposed a prescriptive model for achieving consensus, where agents revise their opinions at each time step by taking a weighted average of the opinions of neighbours. This thesis contains three main contributions. First, we introduce a generalisation of the DeGroot model and examine the long-time behaviour of the model, with and without insistent agents. Second, we consider opinion formation on networks which are themselves dynamic, where the dynamics may be completely random or based on homophily and triadic closure. The weights that agents place on the opinions of neighbours are also dynamic, based on a rule where weights decrease with increased difference in opinions. Third, we examine the effect of a sudden, temporary or permanent shift in the opinions of some agents. Two dynamics are considered for the network change over time; random switching (RS) network dynamics, and homophily and triadic closure (HT) network dynamics. We prove that the RS network dynamics enhances consensus formation and network connectivity, compared to the HT network dynamics where we show by simulation that different opinions can persist. We investigate the in uence of the presence of a minority of insistent agents and prove that for a connected static network, insistent agents with the same opinion in uence the final opinions to converge to their own opinion, thus leading to consensus. In contrast, lack of consensus persists when insistent agents have different opinions. This conclusion also holds for the RS network dynamics model. However, for the HT network dynamics model, coexistence of different opinions can persist even when insistent agents have the same opinion. This finding regarding the HT dynamics is of particular interest as it relates to observations in the real-world. We also investigate the in uence of a sudden shift in the opinions of some agents on the outcome of final opinions. The case of either a temporary shift in opinions or a permanent shift in opinions is examined. Additionally, the in uence of the time of the introduction of a shift, the number and the network positions of initial recipients of the shift in opinions is investigated. The overall effect of an opinion shift is measured by its in uence on the stabilisation time of the final opinions.