Opinion dynamics and consensus formation in a Deffuant model with extremists and moderates.

Among the different disciplines in the social, behavioral and economic sciences, a fundamental class of problems is related to the prediction of the final state of the presence of individual opinions in a large population. The main aspects investigated in the opinion dynamics are related to the possibility of reaching an agreement and the time needed. In general a consensus model allows to understand if a set of interacting agents can reach a consensus when choosing among several options: political vote, opinions, cultural features are well-known examples of them. Opinion dynamics models then can be seen as a sub-set of consensus models, when the options to choose from are opinions and the possible social consensus to be reached is the opinion agreement. Moreover, in large populations it is intuitive to find moderates, whose opinion is not at the extremes of the political opinion spectrum. Due to the wide range of their empirical presence, the study of their influence in the opinion dynamics processes is very important to enhance the comprehension of the political opinions evolution in large populations. The Deffuant model is aimed at studying consensus formation assuming that the opinion distribution of a population evolves via a sequence of random pairwise encounters. In this work we strive to extend the classical Deffuant model with the presence of moderates in addition to the extremists, so as to study the emergence of consensus with different initial configurations of opinions and parameters. Therefore, we assess the role and the importance of the moderates for the appearance of consensus in the opinion dynamics processes within in large populations. We show that the population behavior is affected by the presence of a critical number of moderates, in specific configurations of the model parameters: when this threshold is reached the opinions in the population progressively converge