Multidimensional Opinion Dynamics with Confirmation Bias: A Multi-Layer Framework
This addresses the problem of understanding opinion formation in social networks for researchers in social science and network theory, but it is incremental as it extends existing models to multidimensional settings with confirmation bias.
The paper tackles the problem of modeling multidimensional opinion dynamics with confirmation bias in social networks, showing that under certain conditions the dynamics converge to a unique steady state independent of initial conditions, and for affine functions, the steady state can be computed via a finite search or closed form.
We study multidimensional opinion dynamics under confirmation bias in social networks. Each agent holds a vector of correlated opinions across multiple topic layers. Peer interaction is modeled through a static, informationally symmetric social channel, while external information enters through a dynamic, informationally asymmetric source channel. Source influence is described by nonnegative state-dependent functions of agent--source opinion mismatch, which captures confirmation bias without hard thresholds. For general Lipschitz source-influence functions, we give sufficient conditions under which the dynamics are contractive and converge to a unique steady state independent of the initial condition. For affine confirmation-bias functions, we show that the steady state can be computed through a finite sign-consistency search and identify a regime in which it admits a closed form. For broader classes of bounded nonlinear source-influence functions, we derive explicit lower and upper bounds on the fixed point. Numerical examples and a study on a real-world adolescent lifestyle network illustrate the role of multidimensional coupling and show that source-design conclusions can change qualitatively when confirmation bias is ignored.