Amblard F. , Deffuant G., Weisbuch G. C emagref-LISC ENS-LPS

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. Modellers How to improve the model Experts 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 • …

6. Using/understanding of the final model • Using the model as a data transformation (inputs->model->outputs) 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…

7. Opinion dynamics model

8. 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)

9. 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

10. First model (BC) • Bounded Confidence Model • Agent-based model • Each agent: • Opinion o  [-1;1] (Initial Uniform Distribution) • Uncertainty u  + • Pair interaction between agents (a, a’) • If |o-o’|<u o=µ.(o-o’) • µ = speed of opinion change = ct • Same dynamics for o’ • No dynamics on uncertainty (at this stage)

11. Homogeneous population (u=ct) • u=1.00 u=0.5

12. A brief analytical result… • Number of clusters = [w/2u] • w is width of the initial distribution • u the uncertainty

13. Heterogeneous population (ulow,uhigh)

14. Introduction of uncertainty dynamics • With the same condition: • If |o-o’|<u o=µ.(o-o’) u=µ.(u-u’)

15. Uncertainty dynamics

16. Main problem with BC modelis the influence profile oi oi-ui oi oi+ui oj

17. 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

18. j i oj oi hij hij-ui Relative Agreement Model Relative agreement

19. Relative Agreement Model Modifications of the opinion and the uncertainty are proportional to the “relative agreement” hijis the overlap between the two segments if  Most certain agents are more influential

20. Continuous interaction functions o-u  o  o+u o-u  o  o+u o’-u’ o’ o’+u’ o’-u’ o’ o’+u’ h 1 -h h 1 -h

21. Continuous influence • No more sudden decrease in influence

22. Result with initial u=0.5 for all

23. Constant uncertainty in the population u=0.3(opinion segments)

24. u o +1 -1 Introduction of extremists • U : initial uncertainty of moderated agents • ue : initial uncertainty of extremists • pe : initial proportion of extremists • δ : balance between positive and negative extremists

25. Convergence cases

26. Central convergence (pe = 0.2, U = 0.4, µ = 0.5,  = 0, ue = 0.1, N = 200).

27. Central convergence(opinion segments)

28. Both extremes convergence ( pe = 0.25, U = 1.2, µ = 0.5,  = 0, ue = 0.1, N = 200)

29. Both extremes convergence(opinion segment)

30. Single extreme convergence(pe = 0.1, U = 1.4, µ = 0.5,  = 0, ue = 0.1, N = 200)

31. Single extreme convergence(opinion segment)

32. Unstable Attractors: for the same parameters than before, central convergence

33. 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 = p’+2+ p’-2

34. Synthesis of the different cases with y • Central convergence • y = p’+2+ p’-2 = 0² + 0² = 0 • Both extreme convergence • y = p’+2+ p’-2 = 0.5² + 0.5² = 0.5 • Single extreme convergence • y = p’+2+ p’-2 = 1² + 0² = 1 • Intermediary values for y = intermediary situations • Variations of y in function of U and pe

35. δ = 0, ue = 0.1, µ = 0.2, N=1000 (repl.=50) • white, light yellow => central convergence • orange => both extreme convergence • brown => single extreme

36. 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

37. pe = 0.125 δ = 0 (U > 1) => central conv. Or single extreme (0.5 < U < 1) => both extreme conv. (u < 0.5) => several convergences between central and both extreme conv.

38. Tuning the balance between the two extremesδ = 0.1, ue = 0.1, µ = 0.2

39. Influence of the balance(δ = 0;0.1;0.5)

40. Conclusion • For a low uncertainty of the moderate (U), the influence of the extremists is limited to the nearest => 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)

41. Modèle réalisé • Modèle stochastique • Trois types de liens : • Voisinage • Professionnels • Aléatoires • Attribut des liens : • Fréquence d’interactions • Paramètres du modèles : • densité et fréquence de chacun des types, • dl, •  relation d’équivalence pour les liens professionnels

42. First studies on network

43. Network topologies • At the beginning: • Grid (Von Neumann and De Moore neighbourhoods) => better visualisation • What is planned • Small World networks (especially β-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

44. Convergence casesCentral convergence

45. Both Extremes Convergence

46. Single Extreme Convergence

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

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

49. Nb of iteration to convergence

50. Nb of clusters (VN)