Symmetric Convex Mechanism of Opinion Formation Predicts Directions of Users’ Opinions Trajectories

The symmetric convex mechanism of opinion formation requires an individual's opinion at the next time moment to be an average of their current opinion and opinions of their acquaintances. In this paper, we evaluate to what extent this dependency can describe the real data. Combining machine learning and social network analysis approaches, we retrieve a time series of VKontakte users' opinions as well as information about the friendship network connecting them. Our main result is that if absolute values of users' opinion transformations are huge enough, then its directions can be predicted by the proposed mechanism with sufficiently high accuracy. Namely, we report that if magnitudes are greater than 0.3, then accuracy is over 0.7. In turn, for changes whose absolute values exceed 0.6, accuracy is near one. Moreover, the dependency itself is monotonically increasing.