Reaching a Consensus in Predictive Loops

Predictions in digital platforms must adapt over time as individuals update their beliefs through social interactions. At the same time, changing predictions alter the content people are exposed to and, consequently, the very beliefs they aim to forecast. This recursive coupling between predictions and outcomes complicates the analysis of the long-term societal impact of predictive systems. In this work, we propose a minimal model combining opinion dynamics with concepts from performative prediction to highlight the qualitative implications of predictive loops on equilibrium outcomes in social networks. We assume a platform's predictions influence each individual's opinion, which then evolve through peer interactions and form the training data for future platform model updates. In this model, we show how standard predictive objectives can drive networks toward consensus even under conditions where classical opinion-dynamics models lead to disagreement. This emerges because predictive systems dynamically adapt to changing opinions, and learning objectives create spillover effects among individuals beyond the topology of the network. We complement our non-parametric theory with simulations of popular parametric learners on real social network data. Together, our results illustrate performativity as an important, yet so far neglected, qualifying factor in social networks.