Complex Systems Dynamics Meeting
The University of Manchester
14th February 2011
Opinion Dynamics
Linked and Weighted Opinions: Extensions to the
Axelrod Model
Anthony Woolcock
Supervisors:
Dr Colm Connaughton – Mathematics Dept, Warwick University
Yasmin Merali – Warwick Business School
Motivation for Social Dynamics
G. le Bon. The Crowd: A Study of the Popular Mind. Dover Publications 2002
Model Types
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Voter model
Bounded confidence model
Axelrod model
Language dynamics
Crowd behaviour
Castellano, C. Santo, F. and Vittorio, L.. Statistical Physics of Social Dynamics. Reviews of Modern Physics, 81, 2009
Axelrod’s Model - Definition
State
Interaction
Simulation end state (frozen state)
Axelrod’s Model - Definitions
• Feature (opinion) … F
e.g. Political view
• Trait (choice for that opinion) … q
e.g. Labour or Tory
• Homophily
similar individuals are more likely to interact
• Social influence
interaction effect is to become more similar
• Homogeneity (consensus)
• Heterogeneity (fragmentation)
R. Axelrod. The dissemination of culture. Journal of Conflict Resolution, 41(2): 203-226, 1997
Axelrod’s Model - Results
• State of an individual
e.g. (1, 2, 1) and (2, 2, 2)
• Set of connections between individuals
regular lattice, nearest neighbour connections
Probability of interaction between two neighbouring individuals
e.g. Overlap is 33.3%
Outcome of the interactions - Axelrod
e.g. (1, 2, 2) and (2, 2, 2) or
(2, 2, 1) and (2, 2, 2)
Axelrod’s results: homophily and social
influence can result in heterogeneity
R. Axelrod. The dissemination of culture. Journal of Conflict Resolution, 41(2): 203-226, 1997
Our Model - motivation
Alpha Model
“I’m more likely to adopt your political view if
we share religious views already”
Beta Model
“We’re all more likely to focus more on one of
the opinions”
Our Model – definition – Alpha model
•
State of an individual
e.g. (1, 2, 1) and (2, 2, 2)
• Set of connections between individuals :
regular lattice, nearest neighbour connections
Probability of interaction between two neighbouring individuals
e.g. Overlap is 33.3%
Outcome of the interactions - Our Model
i.e. (2, 2, 1) and (2, 2, 2)
“I’m more likely to adopt your political view if we share religious
views already”
Our Model – definition – Beta model
• State of an individual
e.g. (1, 2, 1) and (2, 2, 2)
• Set of connections between individuals :
regular lattice, nearest neighbour connections
Probability of interaction between two neighbouring individuals
overlap calculated with each opinion weighted with decreasing
importance
“We’re all more likely to focus more on one of the opinions”
Outcome of the interactions – Axelrod
e.g. (1, 2, 2) and (2, 2, 2) or (2, 2, 1) and (2, 2, 2)
Our Model – simulations
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Matlab, C
900 agents, square periodic lattice
Number of regions/ number of zones
Size of largest regions
Bond types
Spatial correlations
Frozen state/ dynamics
Our model – results – Alpha model - dynamics
“I’m more likely to adopt your political view if we share religious views already”
• Blah blah
Our model – results – Alpha model - frozen
“I’m more likely to adopt your political view if we share religious views already”
Our model – results – Beta model - dynamics
“We’re all more likely to focus more on one of the opinions”
• Blah
Our model – results – Beta model - frozen
“We’re all more likely to focus more on one of the opinions”
• Blah
Our model - conclusions
• Dynamics – Changes in feature rates
• Frozen state – Resilient in terms of type
Further work and open ends
• Investigate dynamics
• Analytical approaches
• Programming suitability
• Texts related to analytical approach
• Colm Connaughton, Yasmin Merali
• All at Warwick Complexity
• EPSRC