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Voter model on a directed network: Role of bidirectional opinion exchanges
The voter model with the node update rule is numerically investigated on a
directed network. We start from a directed hierarchical tree, and split and
rewire each incoming arc at the probability . In order to discriminate the
better and worse opinions, we break the symmetry () by
giving a little more preference to the opinion . It is found that
as becomes larger, introducing more complicated pattern of information flow
channels, and as the network size becomes larger, the system eventually
evolves to the state in which more voters agree on the better opinion, even
though the voter at the top of the hierarchy keeps the worse opinion. We also
find that the pure hierarchical tree makes opinion agreement very fast, while
the final absorbing state can easily be influenced by voters at the higher
ranks. On the other hand, although the ordering occurs much slower, the
existence of complicated pattern of bidirectional information flow allows the
system to agree on the better opinion.Comment: 5 pages, 3 figures, Phys. Rev. E (in press
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