Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 How can extremism prevail? An opinion dynamics model studied with heterogeneous agents and networks Amblard F., Deffuant G., Weisbuch G. C emagref-LISC ENS-LPS

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Modelling Methodology Modellers Experts Model proposal How to improve the model Implementation Theoretical study Comparison with data expertise

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Many steps and then many models… Cellular automata Agent-based models Threshold models …

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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 –…

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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…

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Opinion dynamics model

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Homogeneous population (u=ct) u=1.00u=0.5

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 A brief analytical result… Number of clusters = [w/2u] –w is width of the initial distribution –u the uncertainty

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Heterogeneous population (u low,u high )

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Introduction of uncertainty dynamics With the same condition: If |o-o’|<u  o=µ.(o-o’)  u=µ.(u-u’)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Uncertainty dynamics

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Main problem with BC model is the influence profile oioi ojoj oioi o i +u i o i -u i

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Relative Agreement Model (RA) N agents i –Opinion o i (init. uniform distrib. [–1 ; +1]) –Uncertainty u i (init. ct. for the population) –Opinion segment [o i - u i ; o i + u i ] 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Relative Agreement Model Relative agreement j i h ij h ij -u i ojoj oioi

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Relative Agreement Model Modifications of the opinion and the uncertainty are proportional to the “relative agreement” h ij is the overlap between the two segments if  Most certain agents are more influential

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 –Continuous interaction functions o o-u o+u o’+u’o’o’-u’ h1-h o o-u o+u o’+u’o’o’-u’ h1-h

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Continuous influence No more sudden decrease in influence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Result with initial u=0.5 for all

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Constant uncertainty in the population u=0.3 (opinion segments)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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 u o

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Convergence cases

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Central convergence (p e = 0.2, U = 0.4, µ = 0.5,  = 0, u e = 0.1, N = 200).

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Central convergence (opinion segments)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Both extremes convergence ( p e = 0.25, U = 1.2, µ = 0.5,  = 0, u e = 0.1, N = 200)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Both extremes convergence (opinion segment)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Single extreme convergence (p e = 0.1, U = 1.4, µ = 0.5,  = 0, u e = 0.1, N = 200)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Single extreme convergence (opinion segment)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Unstable Attractors: for the same parameters than before, central convergence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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’ p’ - 2

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Synthesis of the different cases with y Central convergence –y = p’ p’ - 2 = 0² + 0² = 0 Both extreme convergence –y = p’ p’ - 2 = 0.5² + 0.5² = 0.5 Single extreme convergence –y = p’ p’ - 2 = 1² + 0² = 1 Intermediary values for y = intermediary situations Variations of y in function of U and p e

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 δ = 0, u e = 0.1, µ = 0.2, N=1000 (repl.=50) white, light yellow => central convergence orange => both extreme convergence brown => single extreme

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 p e = δ = 0 (U > 1) => central conv. Or single extreme (0.5 both extreme conv. (u several convergences between central and both extreme conv.

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Tuning the balance between the two extremes δ = 0.1, u e = 0.1, µ = 0.2

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Influence of the balance (δ = 0;0.1;0.5)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 First studies on network

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Convergence cases Central convergence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Both Extremes Convergence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Single Extreme Convergence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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.

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 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.)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Nb of iteration to convergence

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Nb of clusters (VN)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Nb clusters (dM)

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Network efficience

Frédéric Amblard - RUG-ICS Meeting - June 12, 2003 Conclusion Many simulations to do… Currently running on a cluster of computers Submitted to the first ESSA Conference September Gröningen