REPUTATION IN MAJORITY RULE MODEL LEADING TO DEMOCRATIC STATES

In this work we introduce a mechanism, Reputation, that limits the persuasion capacity of the agents in the Majority Rule model. It is realistic to believe that the individuals will change their opinions under the influence of highly respected persons. To include this characteristic, we introduce the Reputation, which is a score for each agent and it is compared with other agents before each opinion's flip. In traditional consensus models one can find, for an initial opinion greater than certain threshold, two absorbent states in the long run, all agents with opinions $+ 1$ or $-1$. This situation, with fixed points with all spins parallel, describe the opinion in a dictatorship, and do not represent a common situation in public debates and real opinion dynamics. In this work we select \textbf{g} agents as part of the discussion group and interact among each other to follow the most popular opinion in the group. The average Reputation of the majority opinion, $\langle r \rangle$ is calculated. However, only the agents with Reputations smaller than $\langle r \rangle$ will flip to follow the dominant opinion. We show that the inclusion of the Reputation change this behavior in Majority Rule models, reaching a consensus with a majority spins parallel (but not all agents on network), which corresponds to a democracy-like situation. We believe that the inclusion of agents? reputation makes the consensus models more realistic.