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 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.
