Detection of phase transition in generalized Pólya urn in information cascade experiment

Abstract

We propose a method of detecting a phase transition in a generalized Pólya urn in an information cascade experiment. The method is based on the asymptotic behavior of the correlation $C(t)$ between the first subject's choice and the $t+1$-th subject's choice, the limit value of which, $c\equiv {\lim }_{t\to \infty }C(t)$, is the order parameter of the phase transition. To verify the method, we perform a voting experiment using two-choice questions. An urn X is chosen at random from two urns A and B, which contain red and blue balls in different configurations. Subjects sequentially guess whether X is A or B using information about the prior subjects' choices and the color of a ball randomly drawn from X. The color tells the subject which is X with probability $q$. We set $q\in \{5/9,6/9,7/9,8/9\}$ by controlling the configurations of red and blue balls in A and B. The (average) lengths of the sequence of the subjects are 63, 63, 54.0, and 60.5 for $q\in \{5/9,6/9,7/9,8/9\}$, respectively. We describe the sequential voting process by a nonlinear Pólya urn model. The model suggests the possibility of a phase transition when $q$ changes. We show that $c>0(=0)$ for $q=5/9,6/9(7/9,8/9)$ and detect the phase transition using the proposed method.

26 pages, 12 figures

References in corpus (9)

• Statistical physics of social dynamics
• A survey of random processes with reinforcement
• Sociophysics: A review of Galam models
• Is the Voter Model a model for voters?
• Correlated Binomial Models and Correlation Structures
• Information cascade, Kirman's ant colony model, and kinetic Ising model
• Correlation function for generalized Pólya urns: Finite-size scaling analysis
• Bayesian decision making in human collectives with binary choices
• Finite-size scaling analysis of binary stochastic processes and universality classes of information cascade phase transition

Cited by in corpus (3)

• Phase transition of social learning collectives and "Echo chamber"
• Universal function of the non-equilibrium phase transition of nonlinear Pólya urn
• Detection of non-self-correcting nature of information cascade