Abstract
This paper develops a discrete-time, non-linear, and time-variant model of opinion formation in a social network with global interactions to investigate the relationship between the final consensus belief and the set of agents’ initial opinions. The model uses a novel and considerably intuitive updating rule, according to which the weight placed by an agent on another one’s opinion in each period decreases continuously with the distance between their beliefs in the previous period. In this context, the first part of our analysis proves that agents’ beliefs converge and reach a consensus over time (under a fairly general set of conditions). For the two-agent case, it is then shown that the consensus belief is the simple arithmetic mean of the initial opinions. When there are three agents in the network, the combined use of computational and analytical methods reveals a relatively more complex polynomial relationship between long-run and initial beliefs. In particular, our results for the three-agent case imply that the deviation of the limiting belief from the corresponding average of the initial beliefs can be expressed as a third degree polynomial function incorporating the pairwise differences of agents’ starting beliefs.
Highlights
The structure of social networks has a central role in the process of opinion formation and information transmission among interacting agents
The analysis remains within the general context of bounded rationality but extends the previous modeling approaches by introducing an intuitive updating rule which assumes that the weight placed by an agent on another one’s opinion in each period continuously decreases with the distance between their beliefs in the previous period
We first study the fundamental questions of convergence and consensus and we investigate the relationship between the society’s consensus belief and the set of agents’ initial opinions
Summary
The structure of social networks has a central role in the process of opinion formation and information transmission among interacting agents (nodes). The relationship between the limiting consensus belief and the initial opinion vector can be rather complex (depending on the specific form of the updating rule) and remains an open question for research.
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