Information Cascade and Bayes Formula

  • Masato Hisakado
  • Shintaro Mori
Part of the Agent-Based Social Systems book series (ABSS, volume 14)


We consider a voting experiment using two-choice questions. An urn X is chosen at random from two urns A or B, which contain red and blue balls in different configurations. Subjects sequentially guess whether X is A or B by 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 describe the sequential voting process by a stochastic differential equation. The model suggests the possibility of a phase transition when q changes. When there is not the phase transition, in the limit t →, we can choose the correct pod. When there is the phase transition, the votes sometimes converge to the wrong equilibrium. We consider the method to estimate the ratio of red and blue balls, q using the Bayes formula, and study whether we correct the wrong decisions even if there is the phase transition.


  1. Anderson LR, Holt CA (1997) Information cascades in the laboratory. Am Eco Rev 87(5):847–862Google Scholar
  2. Bikhchandani S, Hirshleifer D, Welch I (1992) A theory of fads, fashion, custom, and cultural change as information cascades. J Polit Econ 100:992–1026CrossRefGoogle Scholar
  3. Galam G (1990) Social paradoxes of majority rule voting and renormalization group. Stat Phys 61:943–951CrossRefGoogle Scholar
  4. Hino M, Irie Y, Hisakado M, Takahashi T, Mori S (2016) Detection of phase transition in generalized Póla urn in information cascade experiment. J Phys Soc Jpn 85(3):034002–034013CrossRefGoogle Scholar
  5. Hisakado M, Mori S (2010) Phase transition and information cascade in a voting model. J Phys A 43:315027CrossRefGoogle Scholar
  6. Hisakado M, Mori S (2011) Digital herders and phase transition in a voting model. J Phys A 22:275204CrossRefGoogle Scholar
  7. Hisakado M, Mori S (2016) Phase transition of Information cascade on network. Physica A 450:570–584CrossRefGoogle Scholar
  8. Hisakado M, Sano F, Mori S (2018) Pitman-Yor process and empirical study of choice behavior. J Phys Soc Jpn 87(2):024002–024019CrossRefGoogle Scholar
  9. Ito Y, Ogawa K, Sakakibara H (1974a) Stu Jour 11(3):70 (in Japaneese)Google Scholar
  10. Ito Y, Ogawa K, Sakakibara H (1974b) Stu Jour 11(4):100 (in Japaneese)Google Scholar
  11. Kanazawa K, Sueshige T, Takayasu H, Takayasu M (2018) Derivation of Boltzmann equation for financial Browinian motion: direct observation of the collective motion of high frequency traders. Phys Rev Lett 120:138301CrossRefGoogle Scholar
  12. Mori S, Hisakado M, Takahashi T (2012) Phase transition to two-peaks phase in an information cascade voting experiment. Phys Rev E 86:26109–026118CrossRefGoogle Scholar
  13. Watts DJ (2002) A simple model of global cascades on random networks. Proc Natl Acad Sci USA 99(9):5766–5771CrossRefGoogle Scholar
  14. Watts DJ, Dodds PS (2007) Influentials, networks, and public opinion formation. J Consum Res 34:441–458CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Masato Hisakado
    • 1
  • Shintaro Mori
    • 2
  1. 1.Nomura Holdings, Inc.Chiyoda-kuJapan
  2. 2.Faculty of Science and Technology, Department of Mathematics and PhysicsHirosaki UniversityHirosakiJapan

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