  In this paper, we discuss a voting model by considering three different kinds
of networks: a random graph, the Barab\'{a}si-Albert(BA) model, and a fitness
model. A voting model represents the way in which public perceptions are
conveyed to voters. Our voting model is constructed by using two types of
voters--herders and independents--and two candidates. Independents conduct
voting based on their fundamental values; on the other hand, herders base their
voting on the number of previous votes. Hence, herders vote for the majority
candidates and obtain information relating to previous votes from their
networks. We discuss the difference between the phases on which the networks
depend. Two kinds of phase transitions, an information cascade transition and a
super-normal transition, were identified. The first of these is a transition
between a state in which most voters make the correct choices and a state in
which most of them are wrong. The second is a transition of convergence speed.
The information cascade transition prevails when herder effects are stronger
than the super-normal transition. In the BA and fitness models, the critical
point of the information cascade transition is the same as that of the random
network model. However, the critical point of the super-normal transition
disappears when these two models are used. In conclusion, the influence of
networks is shown to only affect the convergence speed and not the information
cascade transition. We are therefore able to conclude that the influence of
hubs on voters' perceptions is limited.
