Information cascade on networks and phase transitions
Abstract
Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barab\'asi-Albert(BA) model, and lattice networks -- by using one parameter ω; ω=1,0, -1 respectively correspond to these networks. ω is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In ω -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\'olya 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 ω. At ω=1, in the BA model, this transition disappears. Both phase transitions disappear at ω=-1 in the lattice case. In conclusion, as the performance near the lattice case, ω-1 exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves.