  We investigate opinion dynamics and information spreading on networks under
the influence of content filtering technologies. The filtering mechanism,
present in many online social platforms, reduces individuals' exposure to
disagreeing opinions, producing algorithmic bias. We derive evolution equations
for global opinion variables in the presence of algorithmic bias, network
community structure, noise (independent behavior of individuals), and pairwise
or group interactions. We consider the case where the social platform shows a
predilection for one opinion over its opposite, unbalancing the dynamics in
favor of that opinion. We show that if the imbalance is strong enough, it may
determine the final global opinion and the dynamical behavior of the
population. We find a complex phase diagram including phases of coexistence,
consensus, and polarization of opinions as possible final states of the model,
with phase transitions of different order between them. The fixed point
structure of the equations determines the dynamics to a large extent. We focus
on the time needed for convergence and conclude that this quantity varies
within a wide range, showing occasionally signatures of critical slowing down
and meta-stability.
