Opinion formation in a locally interacting community with recommender.

We present a user of model interaction based on the physics of kinetic exchange, and extend it to individuals placed in a grid with local interaction. We show with numerical analysis and partial analytical results that the critical symmetry breaking transitions and percolation effects typical of the full interaction model do not take place if the range of interaction is limited, allowing for the co-existence of majorty and minority opinions in the same community. We then introduce a peer recommender system in the model, showing that, even with very local iteraction and a small probability of appeal to the recommender, its presence is sufficient to make both symmetry breaking and percolation reappear. This seems to indicate that one effect of a recommendation system is to uniform the opinions of a community, reducing minority opinions or making them disappear. Although the recommender system does uniform the community opinion, it doesn't constrain it, in the sense that all opinions have the same probability of becoming the dominating one. We do a partial study, however, that suggests that a "mischievous" recommender might be able to bias a community so that one opinion will emerge over the opposite with overwhelming probability.