Heterogeneous believes, segregation and extremism in the making of   public opinions
  The connection between contradictory public opinions, heterogeneous believes and the emergence of democratic or dictatorial extremism is studied extending our former two state dynamic opinion model. Agents are attached to a social-cultural class. At each step they are distributed randomly in different groups within their respective class to evolve locally by majority rule. In case of a tie the group adopts either one opinion with respective probabilities k and (1-k). The value of k accounts for the average of individual biases driven by the existence of heterogeneous believes within the corresponding class. It may vary from class to class. The process leads to extremism with a full polarization of each class along either one opinions. For homogeneous classes the extremism can be along the initial minority making it dictatorial. At contrast heterogeneous classes exhibit a more balanced dynamics which results in a democratic extremism. Segregation among subclasses may produce a coexistence of opinions at the class level thus averting global extremism. The existence of contradictory public opinions in similar social-cultural neighborhoods is given a new light. 
Serge Galam