Gaëtan Fournier : gaetan.fournier[at]univ-amu.fr
Evgeny Tsodikovich : evgeny.tsodikovich[at]univ-amu.fr
Are all people equal on social media or do popular voices dominate the conversation? This paper widens the scope of analysis of opinion dynamic models by introducing a novel heuristic: individuals express their opinion or hide it, as a function of their popularity. Intuitively, individuals who hide their opinion could be interpreted as individuals who have a low popularity such that even if they speak-up (or tweet) they will not be heard. Popular individuals express their opinion and can interact with like-minded or ideologically-opposed peers, namely expression entails debates and discussions. In the presence of hidden opinions, I show that the interactions between popular individuals and the magnitude of their influence explains whether consensus or polarization prevails. The primary mechanism at play is that the influence structure allows for consensus of opinion locally but communication between ideologically opposed expressers lead to global disagreement. The main contribution of this paper is to provide a unifying theoretical framework to assess different long-run opinion patterns with a focus on the topology of the network. I provide a measure of polarization and I run simulations to show the extent to which the topology of the network affects long-run opinion patterns.