Information Cascade and Networks

In this chapter, we discuss a voting model on networks: random graph and Barabási-Albert(BA) model. It represents how voters are given the public perceptions. A voting model is constructed by two types of voters – herders and independents – and two candidates. The voting of independents is based on their fundamental values; on the other hand, the voting of herders is based on the number of previous votes. The herders vote for the majority candidates. The information of previous votes are obtained by networks. We discussed the difference of phases which depend on geometry. We can identify two kinds of phase transitions. One is an information cascade transition which is similar to a phase transition seen in Ising model. The other is the super-normal transition. It is the transition of convergence speed. In BA model, the critical point of information cascade transition is the same as the model in the random network model. On the other hand, the critical point of the super-normal transition disappears. In conclusion, the influence of networks can be seen in the convergence speed only and cannot be seen in the information cascade transition. In this mean, we can conclude that the influence of hubs is limited. This chapter is based on the conclusion of Hisakado and Mori (Physica A 450:570–584, 2016).