A Multidimensional Opinion Evolution Model with Confirmation Bias

In this paper, we present a novel opinion dynamics model in vector spaces. We define individuals and information sources, where individuals’ opinions evolve over time and are represented by vectors. The information sources are characterized by constant opinion vectors, while confirmation bias is explicitly incorporated into the model to account for individuals’ selective information acquisition from information sources that align with their existing opinions. Drawing inspiration from the Friedkin-Johnsen model, this mechanism combines an individual’s innate opinion, the opinions of their social network neighbors, and the influence of information sources. The social network operates on trust and remains static, while the information sources introduce dynamics through weighted norms based on the distance between an individual’s and the information source’s opinion vector. We characterize the convergence conditions for the proposed dynamics and present approximation and exact computation methods for steady-state values under both affine and non-linear state-dependent confirmation bias weight functions.