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Information Cascade, Kirman’s Ant Colony Model, and Kinetic Ising Model

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

Abstract

We discuss a voting model in which voters can obtain information from a finite number of previous voters. It is the equilibrium process. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) \(\tanh \)-type herders. In the case (i), we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of r select the correct (wrong) candidate. We show that there is no phase transition when r is finite. If the annealing schedule is adequately slow from finite r to infinite r, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman’s ant colony model, and it follows beta-binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model. As case (i) is the limit of case (iii) when \(\tanh \) function becomes a step function, the phase transition can be observed in infinite-size limit. We can confirm that there is no phase transition when the reference number r is finite. This chapter is based on Hisakado and Mori (Physica A 417:63–75, 2015).

References

  1. Alfarano S, Lux T, Wagner F (2005) Estimation of agent-based models: the case of asymmetric herding model. Comput Econ 26(1):19–49CrossRefGoogle Scholar
  2. Anderson LR, Holt CA (1997) Information cascdes in the laboratory. Am Econ Rev 87(5):847–862Google Scholar
  3. Bekers R, Deneubourg JL, Gross S (1992) Modulation of trial laying in the ant Lasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source. J Insect Behav 6:751–759CrossRefGoogle Scholar
  4. Bikhchandani S, Hirshleifer D, Welch I (1992) A theory of Ffads, fashion, custom, and cultural changes as information cascades. J Polit Econ 100:992–1026CrossRefGoogle Scholar
  5. Böhm W (2000) The correlated random walk with boundaries: a combinatorial solution. J Appl Prob 37:470–479CrossRefGoogle Scholar
  6. Camazine S, Sbeyd J (1991) A model of collective nectar source selection by honey bees: Self-organization through simple rules. J Theor Biol 149:547–471CrossRefGoogle Scholar
  7. Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Rev Mod Phys 81:591CrossRefGoogle Scholar
  8. Cont R, Bouchaud J (2000) Herd behavior and aggregate fluctuations in financial markets. Macroecon Dyn 4:170–196CrossRefGoogle Scholar
  9. Couzin ID, Krause J, James R, Ruxton GR, Franks NR (2002) Collective memory and spatial sorting in animal groups. J Theor Biol 218:1–11CrossRefGoogle Scholar
  10. Curty P, Marsili M (2006) Phase coexistence in a forecasting game. JSTAT P03013Google Scholar
  11. Eguíluz V, Zimmermann M (2000) Transmission of information and herd behavior: an application to financial markets. Phys Rev Lett 85:5659–5662CrossRefGoogle Scholar
  12. Galam S (2008) A review of Galam models. Int J Mod Phys C 19:409–440CrossRefGoogle Scholar
  13. Geman S, Geman D (1984) Stochastic relaxation, Gibbs, distribution, and the Bayesian restoration of images. IEEE Trans PAMI 6:721–741CrossRefGoogle Scholar
  14. Hisakado M, Mori S (2010) Phase transition and information cascade in a voting model. J Phys A 43:315207CrossRefGoogle Scholar
  15. Hisakado M, Mori S (2011) Digital herders and phase transition in a voting model. J Phys A 44:275204CrossRefGoogle Scholar
  16. Hisakado M, Mori S (2012) Two kinds of phase transitions in a voting model. J Phys A 45:345002–345016CrossRefGoogle Scholar
  17. Hisakado M, Mori S (2015) Information cascade, Kirman’s ant colony model and Ising model. Physica A 417:63–75CrossRefGoogle Scholar
  18. Hisakado M, Kitsukawa K, Mori S (2006) Correlated binomial models and correlation structures. J Phys A 39:1 5365–15378Google Scholar
  19. Kadanoff L (1966) Scling laws for Ising model near T c. Physics 2:263CrossRefGoogle Scholar
  20. Kirman A (1993) Ants, rationality, and recruitment. Q J Econ 108:137–156CrossRefGoogle Scholar
  21. Konno N (2002) Limit theorems and absorption problems for quantum random walks in one dimension. Quantum Inf Comput 2:578–595Google Scholar
  22. Meunier H, Leca JB, Deneubourg JL, Petit O (2007) Group movement decisions in capuchin monkeys: the utility of an experimental study and a mathematical model to explore the relationship between individual and collective behaviours. Behavior 143:1511CrossRefGoogle Scholar
  23. Milgram S, Bickman L, Berkowitz L (1969) Note on the drawing power of clowds of different size. J Pers Soc Psychol 13:79–82CrossRefGoogle Scholar
  24. Mori S, Hisakado M, Takahashi T (2012) Phase transition to two-peaks phase in an information cascade experiment. Phys Rev E 86:26109CrossRefGoogle Scholar
  25. Partridge BL (1982) The structure and function of fish schools. Sci Am 245:90–99Google Scholar
  26. Pratt SC, Mallon E, Sumpter DJL, Franks RN (2002) Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis. Behav Ecol Sociobiol 52:117–127CrossRefGoogle Scholar
  27. Stauffer D (2002) Sociophysics: the Sznajd model and its applications. Comput Phys Commun 146(1):93–98CrossRefGoogle Scholar
  28. Tarde G (1890) Les lois de l’imitation. Felix Alcan. ParisGoogle Scholar
  29. Ward AJ, Sumpter DJ, Cauzin ID, Hart PJ, Krause J (2008) Quorum decision-making facilitates information transfer in fish shoals. Proc Natl Acad Sci 205(19):6948–6953CrossRefGoogle Scholar
  30. Watts DJ, Dodds PS (2007) Influentials, networks, and public opinion formation. J Consum Res 34:441–458CrossRefGoogle Scholar
  31. Young (2011) The dynamics of social innovation. Proc Natl Acad Sci 108(4):21285–21291CrossRefGoogle 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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