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Physical Mechanism Underlying Opinion Spreading

Physical Mechanism Underlying Opinion Spreading. Jia Shao Shlomo Havlin, H. Eugene Stanley. J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103 , 018701 (2009). Questions. How can we understand, and model the coexistence of two mutually exclusive opinions?

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Physical Mechanism Underlying Opinion Spreading

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  1. Physical Mechanism Underlying Opinion Spreading Jia Shao Shlomo Havlin, H. Eugene Stanley J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103, 018701 (2009).

  2. Questions • How can we understand, and model the coexistence of two mutually exclusive opinions? • Is there a simple physical mechanism underlying the spread of mutually exclusive opinions?

  3. Motivation • Coexistence of two (or more) mutual exclusive opinions are commonly seen social phenomena. Example: US presidential elections • Community support is essential for a small population to hold their belief. Example:the Amish people • Existing opinion models fail to demonstrate both.

  4. What do we do? • We propose a new opinion model based on local configuration of opinions (community support), which shows the coexistence of two opinions. • If we increase the concentration of minority opinion, people holding the minority opinion show a “phase transition” from small isolated clusters to large spanning clusters. • This phase transition can be mapped to a physical process of water spreading in the layer of oil.

  5. Evolution of mutually exclusive opinions : =2:3 Time 0 : =3:4 Time 1 stable state (no one in local minority opinion) Time 2

  6. A. Opinion spread for initially : =2:3 stable state : =1:4

  7. B. Opinion spread for initially : =1:1 stable state : =1:1

  8. “Phase Transition” on square lattice Phase 1 Phase 2 B largest size of the second largest cluster ×100 A critical initial fraction fc=0.5

  9. Edges connect randomly Preferential Attachment 2 classes of network: differ in degree k distribution Poisson distribution: Power-law distribution: (i) Erdős-Rényi (ii)scale-free µ µ Log P(k) µ Log k

  10. “Phase Transition” for both classes of network fc≈0.46 fc≈0.30 (b) scale-free (a) Erdős-Rényi µ Q1: At fc , what is the distribution of cluster size“s”? Q2: What is the average distance“r” between nodes belonging to the same cluster?

  11. Invasion Percolation Example: Inject water into layer containing oil • Invasion percolation describes the evolution of the front between two immiscible liquids in a random medium when one liquid is displaced by injection of the other. • Trapped region will not be invaded. A: Injection Point D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).

  12. Invasion Percolation Trapped Region of size s P(s) ~ s-1.89 S Fractal dimension: 1.84 s ~r1.84 S. Schwarzer et al., Phys. Rev. E. 59, 3262 (1999).

  13. Clusters formed by minority opinion at fc r Cumulative distribution function P(s’>s) ~ s-0.89 r/s(1/1.84) Const. s ~ r1.84 PDF P(s) ~ s-1.89 Conclusion: “Phase transition” of opinion model belongs to the same universality class of invasion percolation.

  14. Summary • Proposed an opinion model showing coexistence of two opinions. • The opinion model shows phase transition at fc. • Linked the opinion model with an oil-field-inspired physics problem, “invasion percolation”.

  15. Thank you!

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