Consensus, contagion and clustering in a space-time model of public opinion formation

We study a simple model of public opinion formation that posits that interaction between neighbouring agents leads to bandwagons in the dynamics of individual opinions, as well as in that of the aggregate process. We show that in different specifications of the model, there is a tendency for the process to show consensus on one of the two competing opinions. We show how a publicly available poll of current public opinion may lead to a form of contagion, by which public opinion tends to agree with the poll. We point out that, in the absence of a poll, the process displays the feature that, after long time spans, a sequence of states occur which, when viewed locally, remain almost stationary and are characterized by large clusters of individuals of the same opinion. The running metaphor we use is that of a model of pre-electoral public opinion formation, with two candidates running. We provide some heuristic considerations on the implication that these findings could have in terms of space-time allocation of fundings in an electoral campaign.