Introducing heterogeneity and the cost of opinion change on bounded confidence opinion models

Laura Hernandez, Hendrik Schawe


The diffusion of opinions in a society is usually studied by the means of models based on agents that interact among them through dynamical rules that define the evolution of the opinion of each agent. The global outcome of such dynamics is taken as the opinion that the society holds on a particular subject. In most studies the dynamics is governed by interactions that model well-known social facts like homophily and social influence, which have both a tendency to homogenize the opinions in the society. However, it has been shown that according to the chosen parameters, the result may be either consensus (almost all the agents carry the same opinion) or the coexistence of groups holding different opinions. Among the continuous opinion models, the Hagselmann-Krause model proposes a dynamics based on bounded confidence, meaning that the opinion of each active agent may be influenced only by those agents whose opinions are already near to his. The homogeneous case has been thoroughly investigated and the critical confidence value for the transition between full consensus and fragmentation has been obtained. In this work we investigate the heterogeneous version of this model, where the confidence is an idiosyncratic property of the agent. Until now this case has been considered by mixing two populations of close and open minded agents. Instead, we draw the confidences for each agent from parametrized uniform distributions between a lower bound \epsilon_l and an upper bound \epsilon_u. By a systematic study of the whole parameter space (\epsilon_l,\epsilon_u) we show a non-monotonous behavior of the steady state of the dynamics: e.g., increasing the confidence of the most open minded agents (i.e., increasing \epsilon_u) may lead to a loss of consensus. A finite size analysis and careful study of the dynamics allows us to identify the mechanism behind this surprising behavior. We also consider the situation when the change of opinion involves a cost for the agent that counterbalances the homophily term. This is the case when the opinion change calls for a drastic behavioral change. Climate change or public health issues are typical examples of subjects where the growth of public attention requires an important change in the agents’ behavior. We observe that the introduction of cost leads to fragmented opinions in heterogeneous societies, but has only very little influence on homogeneous societies.

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