Detection of Phase Transition in Generalized Pólya Urn in Information Cascade Experiment

Hino, Masafumi; Irie, Y; Hisakado, Masato; Takahashi, Takehiro; Mori, Shintaro

doi:10.7566/jpsj.85.034002

Cited by 10 publications

(6 citation statements)

References 30 publications

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“…Information cascade is the tendency to choose the majority choice even if one thinks the minority option is correct or optimal [17,18]. In laboratory experiments, at most 63 subjects answered two-choice questions one by one after observing the previous subjects' choices [19,20]. The sequential choice processes were described as non-linear Pólya urn process.…”

Section: Introductionmentioning

confidence: 99%

Phase transition of social learning collectives and the echo chamber

Mori

Nakayama

Hisakado³

2016

Phys. Rev. E

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We study a simple model for social learning agents in a restless multi-armed bandit. There are N agents, and the bandit has M good arms that change to bad with the probability q c /N . If the agents do not know a good arm, they look for it by a random search (with the success probability q I ) or copy the information of other agents' good arms (with the success probability q O ) with probabilities 1 − p or p, respectively. The distribution of the agents in M good arms obeys the Yule distribution with the power-law exponent 1 + γ in the limit N, M → ∞ and γ = 1 +The system shows a phase transition at p c = q I q I +qo . For p < p c (> p c ), the variance of N 1 per agent is finite (diverges as ∝ N 2−γ with N ). There is a threshold value N s for the system size that scales as ln N s ∝ 1/(γ − 1). The expected value of the number of the agents with a good arm N 1

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Section: Introductionmentioning

confidence: 99%

Phase transition of social learning collectives and the echo chamber

Mori

Nakayama

Hisakado³

2016

Phys. Rev. E

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“…In EXP-I, we studied these points and concluded that the system is self-correcting for z 0 (T ) = 70% ± 5% and 80% ± 5% [16]. Our experiment for EXP-II and its analysis are under way [17].…”

Section: Resultsmentioning

confidence: 83%

“…Our results, unlike those of previous experiments [6,7,8], show the summary statistics of the number of subjects who have chosen each urn. The length T and number of questions I are 63 and 200, respectively, for q ∈ {2/3, 5/9} [17].…”

Section: Domino Effect and Detection Of Non-self-correcting Naturementioning

confidence: 99%

Detection of Non-self-correcting Nature of Information Cascade

Mori

Hino

Hisakado³

et al. 2016

Proceedings of ECCS 2014

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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.

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“…An information cascade experiment provides a concrete setup for the physical realization of the formation of the final imbalance [9]. The change in the number of stable states can be observed by controlling the uncertainty of the subjects [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…Equation (A1a) immediately yields Eq. (11). We now define u ± k (t) = e −G ± (t) y ± k (t), k = 1, 2, where G ± (t) was defined in Eq.…”

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Universal function of the non-equilibrium phase transition of nonlinear Pólya urn

Nakayama,

Mori

2020

Preprint

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We study the phase transition and the critical properties of a nonlinear Pólya urn, which is a simple binary stochastic process X(t) ∈ {0, 1}, t = 1, • • • with a feedback mechanism. Let f be a continuous function from the unit interval to itself, and z(t) be the proportion of the first t variables X(1), • • • , X(t) that take the value 1. X(t + 1) takes the value 1 with probability f (z(t)).When the number of stable fixed points of f (z) changes, the system undergoes a non-equilibrium phase transition and the order parameter is the limit value of the autocorrelation function. When the system is Z 2 symmetric, that is, f (z) = 1 − f (1 − z), a continuous phase transition occurs, and the autocorrelation function behaves asymptotically as ln(t + 1) −1/2 g(ln(t + 1)/ξ), with a suitable definition of the correlation length ξ and the universal function g(x). We derive g(x) analytically using stochastic differential equations and the expansion about the strength of stochastic noise. g(x) determines the asymptotic behavior of the autocorrelation function near the critical point and the universality class of the phase transition.

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Detection of Phase Transition in Generalized Pólya Urn in Information Cascade Experiment

Cited by 10 publications

References 30 publications

Phase transition of social learning collectives and the echo chamber

Phase transition of social learning collectives and the echo chamber

Detection of Non-self-correcting Nature of Information Cascade

Universal function of the non-equilibrium phase transition of nonlinear Pólya urn

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