  Herein, we consider a voting model for information cascades on several types
of networks -- a random graph, the Barab\'{a}si-Albert(BA) model, and lattice
networks -- by using one parameter $\omega$; $\omega=1,0, -1$ respectively
correspond to these networks. $\omega$ is related to the size of hubs. We
discuss the differences between the phases in which the networks depend. In
$\omega\ne -1$, without, the following two types of phase transitions can be
observed: information cascade transition and super-normal transition. The first
is the transition between a state where most voters make correct choices and a
state where most of them are wrong. This is an absorption transition that
belongs to the non-equilibrium transition. In the symmetric case, the phase
transition is continuous and the universality class is the same as nonlinear
P\'{o}lya model. In contrast, in the asymmetric case, there is a discontinuous
phase transition, where the gap depends on the network. The super-normal
transition is the transition of the convergence speed, and the critical point
of the convergence speed transition depends on $\omega$. At $\omega=1$, in the
BA model, this transition disappears. Both phase transitions disappear at
$\omega=-1$ in the lattice case. In conclusion, as the performance near the
lattice case, $\omega\sim-1$ exhibits the best performance of the voting in all
networks. As the hub size decreases, the performance improves.
