A simple model for the diffusion of ideas

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A simple model for the diffusion of ideas

• Luis Da Costa
• LIVIA, University of Quebec
• CSSS 2005

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General idea

• To study how the micro-relations between
  individuals shape (and build from scratch) a
   society 

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Modeling some success

• One way to attack the problem
• Model the social network as a graph
• Apply graph theory to it
• Work with hypothesis
• Then derive certain properties about it

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But  the most anthropological aspects of these
models have not been well understood 

• For example,
• What are the social and cultural forces behind
  the aggregation of individuals?
• Is the low-level aware of the high-level? (is our
  aggregation preferential, depending on what we
  want to achieve, as a society?)
• How does the spread of ideas shape these
  communities?

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What do we want to study?

• What are the dynamics of the creation/elimination
  of ideas?
• What are the dynamics of the acceptance of an
  idea in a society?
• Are these dynamics (in)dependent of the
  underlying topologies (patterns)?

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MODEL

• Network of individuals, each one implementing a
  local exchange of ideas with his  friends 

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MODEL exchange (I)
(i25,i57,i813,i1100,i1111)
(i15,i103,i333,i813,i1100)
c2
c3
(i15,i57,i813,i1111,i1112)
c1
c4
(i15,i17,i33,i103,i333)
((i1,w1),(i2,w2),(i3,w3),(i4,w4),(i5,w5))
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MODEL exchange (II)
((i15,c1),(i17,c1),(i33,c1),(i103,c1),(i333,c1))
((i15,c2),(i103,c2),(i333,c2),(I813,c2),(I1100,c2)
)
My friends opinions
((i25,c3),(i57,c3),(i813,c3),(i1100,c3),(i1111,c3)
)
((i15,c4),(i57,c4),(i813,c4),(i1111,c4),(i1112,c4)
)
((i15,c1 c2 c4),(i17,c1), (i25,c3),(i33,c1)
,(i57,c3 c4),(i103,c1 c2),
(i333,c1 c2 ), (i813,c2 c3
c4) , (i1100,c2 c3) , (i1111,c2 c3),
(i1102,c2 c3))
i15,c1 c2 c4 is accepted by A
by comparing it with a random belief in
A. -gt if we choose (i1,w1), i15 is accepted
with probability
((i1,w1),(i2,w2),(i3,w3),(i4,w4),(i5,w5))
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MODEL the world

• Netlogo

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MODEL attachment

• Random, Less-popular , Most-popular
• Init neighborhood defines friendship

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MODEL experiments (I)

• Netlogo Without movement

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MODEL experiments (II)

• Friendship decay exponential decay
• Half decay distance dx

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MODEL experiments (II)

• Netlogo with movement

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CONCLUSIONS,COMMENTS, etc

• Model simple enough to be analyzed
  mathematically lets do it!
• There is quite a few parameters to adjust/play
  with population, decay of friendship, where to
  look There is a need of a structured tool
• Percolation model?

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A simple model for the diffusion of ideas

• Luis Da Costa
• LIVIA, University of Quebec
• CSSS 2005