Directed propaganda in the majority-rule model

TL;DR

This paper investigates how directed propaganda influences opinion dynamics in the majority-rule model, revealing phase transitions and conditions for consensus, polarization, and the effects of external media influence on social opinion formation.

Contribution

It introduces a model incorporating directed propaganda into the majority-rule framework and analyzes the resulting phase transitions and opinion states.

Findings

Consensus occurs only without propaganda or when media favors one opinion.

Small propaganda influence leads to majority opinion dominance.

Strong propaganda influence causes opinion polarization and prevents consensus.

Abstract

Advertisement and propaganda have changed continuously in the past decades, mainly due to the people's interactions at online platforms and social networks, and operate nowadays reaching a highly specific online audience instead targeting the masses. The impacts of this new media effect, oriented directly for a specific audience, is investigated on this study, in which we focus on the opinion evolution of agents in the majority-rule model, considering the presence of directed propaganda. We introduce $p$ as the probability of a "positive" external propaganda and $q$ as the probability to the agents follow the external propaganda. Our results show that the usual majority-rule model stationary state is reached, with a full consensus, only for two cases, namely when the external propaganda is absent or when the media favors only one of the two opinions. However, even for a small influence of external propaganda, the final state is reached with a majority opinion dominating the population. For the case in which the propaganda influence is strong enough among the agents, we show that the consensus can not be reached at all, and we observe the polarization of opinions. In addition, we show through analytical and numerical results that the system undergoes an order-disorder phase transition that occurs at $q_c = 1/3$ for the case $p = 0.5$.