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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

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
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?
motivation
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.

what do we do
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.
evolution of mutually exclusive opinions
Evolution of mutually exclusive opinions

: =2:3

Time 0

: =3:4

Time 1

stable state

(no one in local

minority opinion)

Time 2

a opinion spread for initially
A. Opinion spread for initially

: =2:3

stable state : =1:4

b opinion spread for initially
B. Opinion spread for initially

: =1:1

stable state : =1:1

phase transition on square lattice
“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

2 classes of network differ in degree k distribution

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

phase transition for both classes of network
“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?

invasion percolation
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).

invasion percolation1
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).

clusters formed by minority opinion at f c
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.

summary
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”.