Consensus effects of social media synthetic influence groups on scale-free networks

Online platforms for social interactions are an essential part of modern society. With the advance of technology and the rise of algorithms and AI, content is now filtered systematically and facilitates the formation of filter bubbles. This work investigates the social consensus under limited visibility in a two-state majority-vote model on Barab\'asi-Albert scale-free networks. In the consensus evolution, each individual assimilates the opinion of the majority of their neighbors with probability $1-q$ and disagrees with chance $q$, known as the noise parameter. We define the visibility parameter $V$ as the probability of an individual considering the opinion of a neighbor at a given interaction. The parameter $V$ enables us to model the limited visibility phenomenon that produces synthetic neighborhoods in online interactions. We employ Monte Carlo simulations and finite-size scaling analysis to obtain the critical noise parameter as a function of the visibility $V$ and the growth parameter $z$. We find the critical exponents $\beta/\bar{\nu}$, $\gamma/\bar{\nu}$ and $1/\bar{\nu}$ of and validate their unitary relation for complex networks. Our analysis shows that installing and manipulating synthetic influence groups critically undermines consensus robustness.