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Cet article propose d'adapter un modèle simple de propagation de maladie à la persuasion politique. Plus précisément, nous étudions comment une politique présentée par un leader se diffuse dans un comité divisé en deux groupes : les adhérents et les opposants. A chaque date, les agents des deux groupes se rencontrent et s'influencent mutuellement en fonction de la force de persuasion du leader. Si la force de persuasion du leader domine (est dominée), alors certains opposants (adhérents) deviennent des adhérents (opposants). De plus, les agents peuvent également changer d'opinion simplement en raison de la force d'attraction symbolique de chaque groupe ou du leader. A long terme, il apparaît qu'une force d'attraction élevée puisse compenser une force de persuasion faible pour s'assurer que plus de la moitié des membres souscrivent à la politique présentée par le leader. Une telle situation est stable. Inversement, une force de persuasion élevée, lorsque la force d'attraction du groupe du leader est relativement faible, peut générer l'apparition d'un cycle de deux périodes, via l'occurrence d'une bifurcation flip, telle que le leader perd la majorité d'une période à l'autre. JEL. C61, D72

We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and non-Bayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. non-Bayesian), the sources of information (e.g., observation vs. communication), and the structure of social networks in which individuals are situated on three key questions: (1) whether social learning will lead to consensus, i.e., to agreement among individuals starting with diff erent views; (2) whether social learning will effectively aggregate dispersed information and thus weed out incorrect beliefs; (3) whether media sources, prominent agents, politicians and the state will be able to manipulate beliefs and spread misinformation in a society.

Mathematical models describing relationships in a group of individuals are known for a long time. The basic idea underlying these models can be described as follows. There are affective (emotionally colored) not necessarily symmetrical relationships between any two members of the group. In general, these relationships vary over time and can be described by numerical functions of time. The value of the corresponding function is positive if the first individual has a positive attitude toward the second one and negative if the attitude is negative. While interacting, two individuals share their views on other members of the group. It affects the dynamics of group relationships. At the same time, the model uses principles such as "if the person whom I dislike says something unpleasant about a third person then I improve my opinion of this third person." This paper also deals with the modeling of group interactions, with the difference that the considered interactions have features of mass (not paired) communications, i.e., the opinion of each individual is equally available to all the others (at the same time, affective relations are paired). This situation occurs, for example, in communities of users of internet forums and blogging platforms. Another important difference is due to the fact that individuals do not discuss other members of the group, but discuss various issues on the topic (e.g., political) of interest to all members of the group. The results of numerical experiments for the system are presented and a number of substantial conclusions are formulated. DOI:10.5901/mjss.2013.v4n10p380

John Stuart Mill advocated for increased interactions between individuals of dissenting opinions for the reason that it would improve society. Whether Mill and similar arguments that advocate for opinion diversity are valid depends on background assumptions about the psychology and sociality of individuals. The field of opinion dynamics is a burgeoning testing ground for how different combinations of sociological and psychological facts contribute to phenomena that affect opinion diversity, such as polarization. This paper applies some recent results from the opinion dynamics literature to assess the impacts of the Millian suggestion. The goal is to understand how the scope of the validity of Mill-style arguments depends on plausible assumptions that can be formalized using agent-based models, a common modeling approach in opinion dynamics. The most salient insight is that homophily (increased interactions between like-minded individuals) does not sufficiently explain decreased opinion diversity. Hence, decreasing homophily by increasing interactions between individuals of dissenting opinions is not the simple solution that a Millian-style argument may advocate.

A universal formula is shown to predict the dynamics of public opinion including eventual sudden and unexpected outbreaks of minority opinions within a generic parameter space of five dimensions. The formula is obtained combining and extending several components of Galam model of opinion dynamics, otherwise treated separately, into one single update equation, which then deploys in a social space of five dimensions. Four dimensions account for a rich diversity of individual traits within a heterogeneous population, including differentiated stubbornness, contrarianism, and embedded prejudices. The fifth dimension is the size for the discussing update groups. Having one single formula allows exploring the complete geometry of the underlying landscape of opinion dynamics. Attractors and tipping points, which shape the topology of the different possible dynamics flows, are unveiled. Driven by repeated discussions among small groups of people during a social or political public campaign, the phenomenon of minority spreading and parallel majority collapse are thus revealed ahead of their occurrence. Accordingly, within the opinion landscape, unexpected and sudden events like Brexit and Trump victories become visible within a forecast time horizon making them predictable. Despite the accidental nature of the landscape, evaluating the parameter values for a specific case allows to single out which basin of attraction is going to drive the associate dynamics and thus a prediction of the outcome becomes feasible. The model may apply to a large spectrum of social situations including voting outcomes, market shares and societal trends, allowing to envision novel winning strategies in competing environments.