  A new model for the dynamics of opinion formation is proposed and analysed at
the mean-field level. It can be regarded as a generalization of the noisy voter
model in which agents update their binary states by copying others and by an
intrinsic mechanism affected by the degree of polarization in the system. It
also takes into account whether the agents enhance or reduce their intrinsic
mechanism upon increasing polarization. Four phases or shapes of the
steady-state probability of a fraction of agents in a given state are found
(unimodal, bimodal, W and M). In the unimodal (resp. bimodal) phase, the
copying (resp. intrinsic) mechanism is globally dominant, while in the W (resp.
M) phase the copying (resp. intrinsic) mechanism is the relevant one close to
the consensus states while it reduces its influence as approaching coexistence.
In the thermodynamic limit, the bimodal and W phases disappear, while the
unimodal and M phases prevail. The theoretical results, obtained analytically
from the master equation, and the numerical simulations are in good agreement.
