  Two of the main factors shaping an individual's opinion are social
coordination and personal preferences, or personal biases. To understand the
role of those and that of the topology of the network of interactions, we study
an extension of the voter model proposed by Masuda and Redner (2011), where the
agents are divided into two populations with opposite preferences. We consider
a modular graph with two communities that reflect the bias assignment, modeling
the phenomenon of epistemic bubbles. We analyze the models by approximate
analytical methods and by simulations. Depending on the network and the biases'
strengths, the system can either reach a consensus or a polarized state, in
which the two populations stabilize to different average opinions. The modular
structure has generally the effect of increasing both the degree of
polarization and its range in the space of parameters. When the difference in
the bias strengths between the populations is large, the success of the very
committed group in imposing its preferred opinion onto the other one depends
largely on the level of segregation of the latter population, while the
dependency on the topological structure of the former is negligible. We compare
the simple mean-field approach with the pair approximation and test the
goodness of the mean-field predictions on a real network.
