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 Barabási-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 Pólya 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.

37 pages 13 figures

References in corpus (14)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Herd behavior and aggregate fluctuations in financial markets
• A survey of random processes with reinforcement
• Universal scaling behavior of non-equilibrium phase transitions
• Transmission of Information and Herd Behavior: an Application to Financial Markets
• Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
• Tactical Voting in Plurality Elections
• Phase transition and information cascade in a voting model
• Digital herders and phase transition in a voting model
• Information cascade, Kirman's ant colony model, and kinetic Ising model
• Correlation function for generalized Pólya urns: Finite-size scaling analysis
• Information cascade on networks
• Quantum statistics and networks by asymmetric preferential attachment of nodes -- between bosons and fermions
• Universal function of the non-equilibrium phase transition of nonlinear Pólya urn