On personal recommendations in social networks

Abstract

Social networks in which algorithms actively influence humans through personal recommendations are ubiquitous. While opinion dynamics is an established tool to analyze these systems, existing models typically do not capture how individual agents process personal recommendations. In this work, we introduce a model for personal recommendations that is analytically tractable and consistent with the confirmation bias phenomenon from behavioral psychology. We describe how individuals process recommendations based on prior beliefs and a sensitivity parameter using a Gaussian influence function. Using this model, we analyze the effect of different recommendation policies. For broadcast policies, where recommendations are homogeneous across the agents, a bifurcation analysis shows that the system exhibits bistability, which may result in unintended consequences. For personally targeted policies, we first derive optimal personal recommendations and then extend to robust convergence when the agents' sensitivity to personal recommendations is uncertain. The collective behavior of the proposed model and the derived policies are illustrated and evaluated through numerical simulations.