The Sznajd model with limited persuasion: competition between high-reputation and hesitant agents

In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion may convince its neighbors with probability p, which induces an increase of the group's reputation. On the other hand, there is always a probability q = 1 - p of the neighbors keeping their opinions, which induces a decrease of the group's reputation. These rules describe a competition between groups with high-reputation and hesitant agents, which makes the full-consensus states (with all spins pointing in one direction) more difficult to reach. As consequences, the usual phase transition does not occur for p < p(c) similar to 0.69 and the system presents realistic democracy-like situations, where the majority of spins are aligned in a certain direction, for a wide range of parameters.