Economics serving society

Anonymous social influence

Manuel Förster, Michel Grabisch, Agnieszka Rusinowska

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Let’s suppose a theoretical situation in which individuals have expressed a Yes or No opinion of a certain proposition. Following a possible influence among them, they might change their minds. A fundamental question arises: will the individuals in this group converge on a consensus or will their opinions end up polarised? To build their model, Manuel Förster, Michel Grabisch and Agnieszka Rusinowska assume an anonymous influence: each one knows of the choices of the others, but not the opinions of particular individuals. This allows the modelling of mass psychology or herding behaviour.
Several conclusions emerge. First, the aggregated opinions of individuals take the form of anonymous influence only when we use ordered weighted averages. Second, this model encompasses other existing theoretical methods, which give it its strength (models of classic majorities, fuzzy majorities (“most”, “at least some”, and the like).
But above all, the authors explain the necessary and sufficient conditions under which, using the anonymous influence hypothesis, individuals converge on a consensus opinion. These theoretical conditions give clarify a shared intuition: there will be convergence when there is a critical mass of individuals of the same opinion, resulting in the recruitment of new agents, and so on. Finally (and of particular interest to theoreticians), this model is generalisable via the combination of functions of aggregation and taking into account “important” (or what we might call “influential”) agents.
Original title of the article: Anonymous social influence
Published in : Games and Economic Behavior, Vol. 82 (2013), 621-635
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