The closed loop between opinion formation and personalised recommendations

In social media, recommender systems are responsible for directing the users to relevant content. In order to enhance the users' engagement, recommender systems adapt their output to the expected reactions of the users, which are in turn affected by the recommended contents. In this work, we model a single user that interacts with an online news aggregator, with the purpose of making explicit the feedback loop between the evolution of the user's opinion and the personalised recommendation of contents. We assume that the user has a scalar opinion on a certain issue: this opinion is influenced by all received news, which are characterized by a binary position on the issue at hand. The user has a confirmation bias, that is, a preference for news that confirm her current opinion. At the same time, we assume that the recommender has the goal of maximizing the number of user's clicks (as a measure of her engagement): in order to fulfil its goal, the recommender has to compromise between exploring the user's preferences and exploiting them. After defining suitable metrics for the effectiveness of the recommender systems and for its impact on the opinion, we perform both extensive numerical simulations and a mathematical analysis of the model. We find that personalised contents and confirmation bias do affect the evolution of opinions: the extent of these effects is inherently related to the effectiveness of the recommender. We also show that by tuning the amount of randomness in the recommendation algorithm, one can reduce the impact of the recommendation system on the opinions.