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Multi-group binary choice with social interaction and a random communication structure—A random graph approach

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  • Löwe, Matthias
  • Schubert, Kristina
  • Vermet, Franck

Abstract

We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to differ from the interaction strength between the two groups. Given that the resulting graph is sufficiently dense we show that, with probability 1, the average decision in each of the two groups is the same as in the fully connected model. In particular, we show that there is a phase transition: If the interaction among a group and between the groups is strong enough the average decision per group will either be positive or negative and the decision of the two groups will be correlated. We also compute the free energy per particle in our model.

Suggested Citation

  • Löwe, Matthias & Schubert, Kristina & Vermet, Franck, 2020. "Multi-group binary choice with social interaction and a random communication structure—A random graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303678
    DOI: 10.1016/j.physa.2020.124735
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    References listed on IDEAS

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    Cited by:

    1. Michael Fleermann & Werner Kirsch & Gabor Toth, 2022. "Local Central Limit Theorem for Multi-group Curie–Weiss Models," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2009-2019, September.
    2. Tinggui Chen & Yulong Wang & Jianjun Yang & Guodong Cong, 2021. "Modeling Multidimensional Public Opinion Polarization Process under the Context of Derived Topics," IJERPH, MDPI, vol. 18(2), pages 1-34, January.
    3. Emily Tanimura, 2021. "Statistical discrimination without knowing statistics: blame social interactions?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03096126, HAL.

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