UNDERSTANDING COMPLEX SYSTEMS Symposium May 1921, 2003 Department of Physics University of Illinois

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UNDERSTANDING COMPLEX SYSTEMSSymposium May
19-21, 2003Department of PhysicsUniversity of
Illinois at Urbana-Champaign

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• Simulating Opinion Propagation
• in different Social Environments
• By
• Ioannis Tziligakis, Physics,UIUC

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System Definition (RIC MODEL)

• Society Nested list of agents
• Agent List with 4 elements
• Opinion State Integer 0 or 1
• Conversion Probability N(µ,s)
• Personality Type
• Rebel Disagrees with everyone
• Independent Opinion not affected
• Conformist Tends to agree
• Social Status Real in (0,1)
• Higher value ? Higher Status

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Parameters

• N of agents
• R of Rebels
• I of Independents
• C N - I R of Conformists
• p probability of an agent being in
• opinion state 1
• (µR,sR), (µI,sI), (µC,sC) parameters
• of probability of conversion for each
• personality type
• Pinc percentage increase in conversion
  probability
• Strange Status range

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Initial Society Example

• 1,0.1543,0,0.3873,0,0.0992,1,0.8759,
  1,0.5662,2,0.6441,
• 1st. Element ? opinion
• 2nd. Element ? conversion probability
• 3rd. Element ? personality type
• 0 ? Independent
• 1 ? Rebel
• 2 ? Conformist
• 4th. Element ? social status.

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Random Pairings

• Interactions between agents are dyadic.
• Interaction means we apply some conversion
  rules
• Create a list of (n/2) pairings

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Conversion Rules

• Each personality type has its own conversion
  rules
• Change of opinion occurs according to a
  Metropolis type updating
• If U0,1 lt Conv. Prob. ? Change
• A rebel if he disagrees with you he wont
  change. If he agrees he might change according to
  the metropolis step
• ? (6 rules) (0,0)2 , (1,1)2, (0,1), (1,0)
• An independent he will change according to the
  metropolis step
• ? 4 rules (1,x)2, (0,x)2

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Conversion Rules Continued

• Conformist Agent 1,0.4373,2,0.3712 paired with
  an agent in a different opinion
  0,0.7836,2,0.9764.
• Agent will change opinion based on his/her
  conversion probability AND the social status
  (e.g. the agent will change the opinion only if
  the other agent has a social status within a
  certain range).
• If it fails to change opinion, the conversion
  probability will be increased, making it more
  likely that he will convert at the next encounter
  with an agent having that different opinion
  (Bandwagon Effect).
• (6 rules (0,1)2 , (1,0)2, (0,0), (1,1))

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Results

• In all case studies described in this section,
  the following same parameters were used to
  create the society of agents.
• - n total number of agents 100.
• - p probability of an agent being in opinion
  state 1 0.7.
• - rmu mu value (mean), according to a normal
  distribution, for the probability of a rebel
  changing his/her opinion state 0.1.
• - rsi sigma value (std. deviation), according
  to a normal distribution, for the probability of
  a rebel changing his/her opinion state 0.09.
• - imu mu value (mean), according to a normal
  distribution, for the probability of an
  independent changing his/her opinion state 0.1.
• - isi sigma value (std. deviation), according
  to a normal distribution, for the probability of
  an independent changing his/her opinion state
  0.09.
• - cmu mu value (mean), according to a normal
  distribution, for the probability of a conformist
  changing his/her opinion state 0.6.
• - csi sigma value (std. deviation), according
  to a normal distribution, for the probability of
  a conformist changing his/her opinion state
  0.1.
• The values of Pinc and Strange were modified
  according to the case being simulated.

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Case 1Bandwagon effect in a society of
conformists , not considering the social status
(pinc 0.005)
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Case 2Bandwagon effect in a society of
conformists , not considering the social status
(pinc 0.01)
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Case 3Bandwagon effect in a society of
conformists , with social status (pinc 0.01,
Strange0.1 )
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Case 4Bandwagon effect in a society of
conformists , with social status (pinc 0.01,
Strange0.3 )
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Case 5Bandwagon effect in a society of 99
conformists and 1 independent , considering the
social status (pinc 0.01 strange 0.3)
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Case 6Bandwagon effect in a society of 99
conformists and 1 independent , without social
status (pinc 0.01 )
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Case 8Bandwagon effect in a society of 99
conformists and 1 Rebel , without social status
(pinc 0.01)
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Case 7Bandwagon effect in a society of 99
conformists and 1 Rebel , considering the social
status (pinc 0.01 strange 0.3)
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Conclusions

• To summarize, we observe that the interplay
  between social status and the bandwagon effect
  has the following characteristics
• 1) If the society is solely comprised by
  conformists, and their social status is not
  considered, then the bandwagon effect tends to
  impose the rule of the majority faster. Indeed,
  initially prevailing opinion dominates over the
  other at about 200 time steps ( cases 1 and 2 ).
• 2) The introduction of social status results in
  limiting the range of interactions between the
  different agents, slowing down the process of
  reaching the one prevailing opinion equilibrium
  state ( cases 3 and 4 ).
• 3) In a case when we introduced rebels or
  independents, with small conversion
  probabilities, if the society is not stratified
  (social status is not considered), then the
  convergence to an equilibrium state is broken and
  there is no prevailing opinion ( cases 6 and 8 ).
• 4) If the range of interactions is reduced by
  introducing social status, than the action of
  rebels and independents is limited. Although
  equilibrium is not reached, the system spends
  more time preferring, by majority, one opinion
  versus the other. ( cases 5 and 7 ).