  We propose a general concealed voter model (GCVM), in which individuals
interact in two layers and can exchange their opinions in the internal layer.
This interaction is not allowed in a concealed voter model (CVM). By exchanging
opinions in the internal layer we mean that individuals share their real or
internal opinions with their close friends. The process of opinion formation in
GCVM is presented in the paper. We make the series of numerical simulations of
GCVM with different network structures (both external and internal) and get
some counterintuitive conclusions. For instance, we find out that sometimes
with a relatively simple network structure of an external layer the consensus
within the individuals' opinions cannot be reached, and if individuals in the
network are not good at expressing their opinions publicly (in an external
layer), exchanging opinions with their close friends (in an internal layer) is
almost useless.
