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

TL;DR

This paper introduces a modified two-dimensional Sznajd model incorporating agent reputation, revealing how reputation dynamics influence consensus formation and lead to realistic democracy-like states without a traditional phase transition.

Contribution

It proposes a novel reputation-based persuasion mechanism in the Sznajd model, showing how it affects consensus and phase transition behavior.

Findings

No phase transition for p < 0.69

Reputation dynamics create democracy-like states

Consensus is harder to achieve with reputation competition

Abstract

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 their 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 to keep 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 be reached. As consequences, the usual phase transition does not occur for $p<p_{c} \sim 0.69$ 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.