  We investigate a majority-vote model on two-layer multiplex networks with
community structure. In our majority-vote model, the edges on each layer encode
one type of social relationship and an individual changes their opinion based
on the majority opinions of their neighbors in each layer. To capture the fact
that different relationships often have different levels of importance, we
introduce a layer-preference parameter, which determines the probability of a
node to adopt an opinion when the node's neighborhoods on the two layers have
different majority opinions. We construct our networks so that each node is a
member of one community on each layer, and we consider situations in which
nodes tend to have more connections with nodes from the same community than
with nodes from different communities. We study the influence of the
layer-preference parameter, the intralayer communities, and interlayer
membership correlation on the steady-state behavior of our model using both
direct numerical simulations and a mean-field approximation. We find three
different types of steady-state behavior: a fully-mixed state, consensus
states, and polarized states. We demonstrate that a stronger interlayer
community correlation makes polarized steady states reachable for wider ranges
of the other model parameters. We also show that different values of the
layer-preference parameter result in qualitatively different phase diagrams for
the mean opinions at steady states.
