  We investigate different opinion formation models on adaptive network
topologies. Depending on the dynamical process, rewiring can either (i) lead to
the elimination of interactions between agents in different states, and
accelerate the convergence to a consensus state or break the network in
non-interacting groups or (ii) counter-intuitively, favor the existence of
diverse interacting groups for exponentially long times. The mean-field
analysis allows to elucidate the mechanisms at play. Strikingly, allowing the
interacting agents to bear more than one opinion at the same time drastically
changes the model's behavior and leads to fast consensus.
