Modelling Group Opinion Shift to Extreme : the Smooth Bounded Confidence   Model
  We consider the phenomenon of opinion shift to the extreme reported in the social psychology literature. We argue that a good candidate to model this phenomenon can be a new variant of the bounded confidence (BC) model, the smooth BC model which we propose in this paper. This model considers individuals with a continuous opinion and an uncertainty. Individuals interact by random pairs, and attract each other&#8217;s opinion proportionally to a Gaussian function of the distance between their opinions. We first show that this model presents a shift to the extreme when we introduce extremists (very convinced individuals with extreme opinions) in the population, even if there is the same number of extremists located at each extreme. This behaviour is similar to the one already identified with other versions of BC model. Then we propose a modification of the smooth BC model to account for the social psychology data and theories related to this phenomenon. The modification is based on the hypothesis of perspective taking (empathy) in the context of consensus seeking. 
Guillaume Deffuant (LISC), Frederic Amblard (LISC), Gerard Weisbuch   (LPS)