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 ≡ lim t→∞ 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 ∈ {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 ∈ {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.

We propose a method of detecting non-self-correcting information cascades in experiments in which subjects choose an option sequentially by observing the choices of previous subjects. The method uses the correlation function C(t) between the first and the t + 1-th subject's choices. C(t) measures the strength of the domino effect, and the limit value c ≡ limt→∞ C(t) determines whether the domino effect lasts forever (c > 0) or not (c = 0). The condition c > 0 is an adequate condition for a non-self-correcting system, and the probability that the majority's choice remains wrong in the limit t → ∞ is positive. We apply the method to data from two experiments in which T subjects answered two-choice questions: (i) general knowledge questions (Tavg = 60) and (ii) urn-choice questions (T = 63). We find c > 0 for difficult questions in (i) and all cases in (ii), and the systems are not self-correcting.