Filter bubble effect in the multistate voter model

Social media influence online activity by recommending to users content strongly correlated with what they have preferred in the past. In this way, they constrain users within filter bubbles strongly limiting their exposure to new or alternative content. We investigate this type of dynamics by considering a multistate voter model where, with a given probability lambda, a user interacts with "personalized information, " suggesting the opinion most frequently held in the past. By means of theoretical arguments and numerical simulations, we show the existence of a nontrivial transition between a region (for small lambda) where a consensus is reached and a region (above a threshold lambda c) where the system gets polarized and clusters of users with different opinions persist indefinitely. The threshold always vanishes for large system size N, showing that a consensus becomes impossible for a large number of users. This finding opens new questions about the side effects of the widespread use of personalized recommendation algorithms.& nbsp;& nbsp;Published under an exclusive license by AIP Publishing.