Report
Detection of phase transition in generalized P\'olya urn in information cascade experiment
| العنوان: | Detection of phase transition in generalized P\'olya urn in information cascade experiment |
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| المؤلفون: | Hino, Masafumi, Irie, Yosuke, Hisakado, Masato, Takahashi, Taiki, Mori, Shintaro |
| المصدر: | J.Phys.Soc.Jpn. 85 (3), 034002-034013, 2016 |
| سنة النشر: | 2015 |
| المجموعة: | Condensed Matter Physics (Other) Statistics |
| مصطلحات موضوعية: | Physics - Data Analysis, Statistics and Probability, Condensed Matter - Statistical Mechanics, Statistics - Methodology |
| الوصف: | We propose a method of detecting a phase transition in a generalized P\'olya 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 P\'olya 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. Comment: 26 pages, 12 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.7566/JPSJ.85.034002 |
| URL الوصول: | http://arxiv.org/abs/1507.07269 |
| رقم الانضمام: | edsarx.1507.07269 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.7566/JPSJ.85.034002 |
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