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Mean Field Studies of a Society of Interacting Agents

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 239)

Abstract

We model a society of agents that interact in pairs by exchanging for/against opinions about issues using an algorithm obtained with methods of Bayesian inference and maximum entropy. The agents gauge the incoming information with respect to the mistrust attributed to the other agents. There is no underlying lattice and all agents interact among themselves. The interaction pair can be described as a dynamics along the gradient of the logarithm of the evidence. By using a symmetric version of the two-body interactions we introduce a Hamiltonian for the whole society. Knowledge of the expected value of the Hamiltonian is relevant information for the state of the society. In the case of uniform mistrust, independent of the pair of agents, the phase diagram of the society in a mean field approximation shows a phase transition that separates an ordered phase where opinions are to a large extent shared by the agents and a disordered phase of dissension of opinions.

Keywords

Entropic dynamics Social systems Agent models Mean field 

Notes

Acknowledgements

LS has a FAPESP fellowship grant \(n^o 2016/15860\)-3 and thanks CNPq fellowship grant \(n^o 134812/2016\)-6. Work supported by CNAIPS, the Center for Natural and Artificial Information Processing Systems of the University of São Paulo.

References

  1. 1.
    Alves, F., Caticha, N.: Sympatric multiculturalism in opinion models. In: Giffin, A., Knuth, K.H. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering: 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, July 2015. AIP Conference Proceedings vol. 1757, p. 060005 (2016)Google Scholar
  2. 2.
    Alves, F., Caticha, N.: Entropic Dynamics of Distrust and Opinions of Interacting Agents (In preparation) (2018)Google Scholar
  3. 3.
    Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591–646 (2009)CrossRefGoogle Scholar
  4. 4.
    Caticha, N., Vicente, R.: Agent-based Social Psychology: From Neurocognitive processes to Social data. Adv. Complex Syst. 14(5), 711–731 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Caticha, N., Cesar, J., Vicente, R.: For whom will the Bayesian agents vote? Front. Phys. 3(25), 1–14 (2015)Google Scholar
  6. 6.
    Galam, S.: Sociophysics: A Physicist’s Modeling of Psycho-political Phenomena. Springer, New York (2012)CrossRefGoogle Scholar
  7. 7.
    Haidt, J.: The emotional dog and its rational tail: a social intuitionist approach to moral judgment. Psychol. Rev. 108(4), 814–834 (2001)CrossRefGoogle Scholar
  8. 8.
    Haidt, J.: The new synthesis in moral psychology. Science 316(5827), 998–1002 (2007)CrossRefGoogle Scholar
  9. 9.
    Haidt, J., Kesebir, S.: Morality. Handbook of Social Psychology, vol. 3:III:22, pp. 797–832 (2010)Google Scholar
  10. 10.
    Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620–630 (1957)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jaynes, E.T.: Information Theory and Statistical Mechanics. II. Phys. Rev. 108(2), 171–190 (1957)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kinouchi, O., Caticha, N.: Optimal generalization in perceptions. J. Phys. A 25(23), 6243–6250 (1992)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Opper, M., Winther, O.: A Bayesian approach to on-line learning. In: Saad, D. (ed.) On-Line Learning in Neural Networks, pp. 363–378. Publications of the Newton Institute. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  14. 14.
    Vicente, R., Susemihl, A., Jericó, J.P., Caticha, N.: Moral foundations in an interacting neural networks society: A statistical mechanics analysis. Physica A 400(c), 124–138 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

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