How can extremism prevail? An opinion dynamics model studied with heterogeneous agents and networks

1
How can extremism prevail? An opinion dynamics
model studied with heterogeneous agents and
networks

• Amblard F., Deffuant G., Weisbuch G.
• Cemagref-LISC
• ENS-LPS

2
Context

• European project FAIR-IMAGES
• Modelling the socio-cognitive processes of
  adoption of AEMs by farmers
• 3 countries (Italy, UK, France)
• Interdisciplinary project
• Economics
• Rural sociology
• Agronomy
• Physics
• Computer and Cognitive Sciences

3
Modelling Methodology
Implementation Theoretical study
Model proposal
Comparison with data expertise
4
Many steps and then many models

• Cellular automata
• Agent-based models
• Threshold models

5
Final (???) model

• Huge model integrating
• Multi-criteria decision (homo socio-economicus)
• Expert systems (economic evaluation)
• Opinion dynamics model
• Information diffusion
• Institutional action (scenarios)
• Social networks
• Generation of virtual populations

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Using/understanding of the final model

• Using the model as a data transformation
  (inputs-gtmodel-gtoutputs) we study correlations
  between inputs and outputs
• Model highly stochastic, then many replications
• To understand the correlations?
• We have to get back to basics
• Study each one of the component independently

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Opinion dynamics model
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Bibliography

• Opinion dynamics models
• Models of binary opinions and vote models
  (Stokman and Van Oosten, Latané and Nowak, Galam,
  Galam and Wonczak, Kacpersky and Holyst)
• Models with continuous opinions, negotiation
  framework, collective decision-making (Chatterjee
  and Seneta, Cohen et al., Friedkin and Johnsen)
• Threshold Models (BC) (Krause, Deffuant et al.,
  Dittmer, Hegselmann and Krause)

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Opinion dynamics model

• Basic features
• Agent-based simulation model
• Including uncertainty about current opinion
• Pair interactions
• The less uncertain, the more convincing
• Influence only if opinions are close enough
• When influence, opinions move towards each other

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First model (BC)

• Bounded Confidence Model
• Agent-based model
• Each agent
• Opinion o ? -11 (Initial Uniform Distribution)
• Uncertainty u ? ?
• Pair interaction between agents (a, a)
• If o-oltu
• ?oµ.(o-o)
• µ speed of opinion change ct
• Same dynamics for o
• No dynamics on uncertainty (at this stage)

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Homogeneous population (uct)
u1.00 u0.5
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A brief analytical result

• Number of clusters w/2u
• w is width of the initial distribution
• u the uncertainty

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Heterogeneous population (ulow ,uhigh)
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Introduction of uncertainty dynamics

• With the same condition
• If o-oltu
• ?oµ.(o-o)
• ?uµ.(u-u)

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Uncertainty dynamics
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Main problem with BC modelis the influence
profile
?oi
oi-ui
oi
oiui
oj
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Relative Agreement Model (RA)

• N agents i
• Opinion oi (init. uniform distrib. 1 1)
• Uncertainty ui (init. ct. for the population)
• Opinion segment oi - ui oi ui
• Pair interactions
• Influence depends on the overlap between opinion
  segments
• No influence if they are too far
• The more certain the more convincing
• Agents are influenced each other in opinion and
  uncertainty

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Relative Agreement Model

• Relative agreement

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Relative Agreement Model

• Modifications of the opinion and the uncertainty
  are proportional to the relative agreement
• hij is the overlap between the two segments
• if
• ? Most certain agents are more influential

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• Continuous interaction functions

o 
o-u 
ou
o 
o-u 
ou
ou
o
o-u
ou
o
o-u
h
1
-h
h
1
-h
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Continuous influence

• No more sudden decrease in influence

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Result with initial u0.5 for all
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Constant uncertainty in the population
u0.3(opinion segments)
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Introduction of extremists

• U initial uncertainty of moderated agents
• ue initial uncertainty of extremists
• pe initial proportion of extremists
• d balance between positive and negative
  extremists

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Convergence cases
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Central convergence (pe 0.2, U 0.4, µ 0.5,
? 0, ue 0.1, N 200).
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Central convergence(opinion segments)
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Both extremes convergence ( pe 0.25, U 1.2,
µ 0.5, ? 0, ue 0.1, N 200)
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Both extremes convergence(opinion segment)
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Single extreme convergence(pe 0.1, U 1.4, µ
0.5, ? 0, ue 0.1, N 200)
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Single extreme convergence(opinion segment)
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Unstable Attractors for the same parameters than
before, central convergence
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Systematic exploration

• Introduction of the indicator y
• p prop. of moderated agents that converge to
  positive extreme
• p- prop. Of moderated agents that converge to
  negative extreme
• y p2 p-2

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Synthesis of the different cases with y

• Central convergence
• y p2 p-2 0² 0² 0
• Both extreme convergence
• y p2 p-2 0.5² 0.5² 0.5
• Single extreme convergence
• y p2 p-2 1² 0² 1
• Intermediary values for y intermediary
  situations
• Variations of y in function of U and pe

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d 0, ue 0.1, µ 0.2, N1000 (repl.50)

• white, light yellow gt central convergence
• orange gt both extreme convergence
• brown gt single extreme

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What happens for intermediary zones?

• Hypotheses
• Bimodal distribution of pure attractors (the
  bimodality is due to initialisation and to random
  pairing)
• Unimodal distribution of more complex attractors
  with different number of agents in each cluster

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pe 0.125 d 0 (U gt 1) gt central conv. Or
single extreme (0.5 lt U lt 1) gt both extreme
conv. (u lt 0.5) gt several convergences between
central and both extreme conv.
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Tuning the balance between the two extremesd
0.1, ue 0.1, µ 0.2
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Influence of the balance(d 00.10.5)
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Conclusion

• For a low uncertainty of the moderate (U), the
  influence of the extremists is limited to the
  nearest gt central convergence
• For higher uncertainties in the population,
  extremists tend to win (bipolarisation or conv.
  To a single extreme)
• When extremists are numerous and equally
  distributed on the both sides, instability
  between central convergence and single extreme
  convergence (due to the position of the central
  group and to the decrease of the uncertainties)

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Modèle réalisé

• Modèle stochastique
• Trois types de liens
• Voisinage
• Professionnels
• Aléatoires
• Attribut des liens
• Fréquence dinteractions
• Paramètres du modèles
• densité et fréquence de chacun des types,
• dl,
• ? relation déquivalence pour les liens
  professionnels

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First studies on network
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Network topologies

• At the beginning
• Grid (Von Neumann and De Moore neighbourhoods) gt
  better visualisation
• What is planned
• Small World networks (especially ß-model enabling
  to go from regular networks to totally random
  ones)
• Scale-free networks
• Why focus on abstract networks?
• Searching for typical behaviours of the model
• No data available

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Convergence casesCentral convergence
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Both Extremes Convergence
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Single Extreme Convergence
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Schematic behaviours

• Convergence of the majority towards the centre
• Isolation of the extremists (if totally isolated
  gt central convergence)
• If extremists are not totally isolated
• If balance between non-isolated extremists of
  both side gt double extr. conv.
• Else gt single extr. conv.

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Problems

• Criterions taken for the totally connected case
  does not enable to discriminate
• With networks gt more noisy situation to analyse
• Totally connected case gt only pe, delta and U
  really matters
• Network case
• Population size
• Ue matters (high Ue valorise central conv.)

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Nb of iteration to convergence
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Nb of clusters (VN)
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Nb clusters (dM)
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Network efficience
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Conclusion

• Many simulations to do
• Currently running on a cluster of computers
• Submitted to the first ESSA Conference
• 18-22 September
• Gröningen