  We address the issue of the reducibility of the dynamics on a multilayer
network to an equivalent process on an aggregated single-layer network. As a
typical example of models for opinion formation in social networks, we
implement the voter model on a two-layer multiplex network, and we study its
dynamics as a function of two control parameters, namely the fraction of edges
simultaneously existing in both layers of the network (edge overlap), and the
fraction of nodes participating in both layers (interlayer connectivity or
degree of multiplexity). We compute the asymptotic value of the number of
active links (interface density) in the thermodynamic limit, and the time to
reach an absorbing state for finite systems, and we compare the numerical
results with the analytical predictions on equivalent single-layer networks
obtained through various possible aggregation procedures. We find a large
region of parameters where the interface density of large multiplexes gives
systematic deviations from that of the aggregates. We show that neither of the
standard aggregation procedures is able to capture the highly nonlinear
increase in the lifetime of a finite size multiplex at small interlayer
connectivity. These results indicate that multiplexity should be appropriately
taken into account when studying voter model dynamics, and that, in general,
single-layer approximations might be not accurate enough to properly understand
processes occurring on multiplex networks, since they might flatten out
relevant dynamical details.
