Reputation in Majority Rule Model leading to democratic states

Abstract

We study the Majority Rule (MR) model, a sociophysics model developed to describe how a group of agents with initial different opinions can reach consensus. At each instant of time, a group is selected at random and discuss among each other. After the discussion, all members of this discussion group follow the majority opinion. The number of agents in the discussion group is not fixed and it is selected each instant of time from a Gaussian distribution. The system dynamics stops when only one opinion survive. In this work we introduced in the MR model a ‘reputation’ for each agent, a weight to be considered in the system dynamics. Our results show that the introduction of reputation leads the system to a steady state in which not every agent on the system have exactly the same status, but a majority of them sharing the same opinion. In addition, our model with the inclusion of reputation do not show the critical point usually observed. Instead we have obtained the critical point p_c = 1, in contrast with the standard Majority Rule model.