  Online users tend to select claims that adhere to their system of beliefs and
to ignore dissenting information. Confirmation bias, indeed, plays a pivotal
role in viral phenomena. Furthermore, the wide availability of content on the
web fosters the aggregation of likeminded people where debates tend to enforce
group polarization. Such a configuration might alter the public debate and thus
the formation of the public opinion. In this paper we provide a mathematical
model to study online social debates and the related polarization dynamics. We
assume the basic updating rule of the Bounded Confidence Model (BCM) and we
develop two variations a) the Rewire with Bounded Confidence Model (RBCM), in
which discordant links are broken until convergence is reached; and b) the
Unbounded Confidence Model, under which the interaction among discordant pairs
of users is allowed even with a negative feedback, either with the rewiring
step (RUCM) or without it (UCM). From numerical simulations we find that the
new models (UCM and RUCM), unlike the BCM, are able to explain the coexistence
of two stable final opinions, often observed in reality. Lastly, we present a
mean field approximation of the newly introduced models.
