1. 1 ICTP 27/05/02 How can extremism prevail ? A study based on the Relative agreement model G. Deffuant, G. Weisbuch, F. Amblard, T. Faure

2. ICTP 27/05/02 Influence of extremists The extremists win : –Majority to one extreme (Germany in the thirties, islamic revolution…) –Bipolarisation (affaire Dreyfus, religion wars…) The extremists remain marginal

3. ICTP 27/05/02 Bounded confidence An opinion x has an uncertainty u. First model : all agents have the same uncertainty if : then : No dynamics on the uncertainty

4. ICTP 27/05/02 [w/2u]=1[w/2u]=2 nb attractors approximately the integer part of w/2u With a uniform distribution of the opinions of width w

5. ICTP 27/05/02 New model with dynamics of uncertainties Give more influence to more confident agents Avoid the discontinuity of the influence when the difference of opinions grows Explore the influence of extremists

6. ICTP 27/05/02 Relative agreement j i h ij h ij -u i xjxj xixi Relative agreement :

7. ICTP 27/05/02 The modification of the opinion and the uncertainty are proportional to the relative agreement : if  More certain agents are more influential Relative agreement dynamics

8. ICTP 27/05/02 Variation of the relative agreement xjxj x j + u j x j - u j xixi u i < u j u i > u j 1 u i > 2u j (i influences j)

9. ICTP 27/05/02 Same uncertainty for all agents (0.5)

10. ICTP 27/05/02 Same uncertainty for all agents

11. ICTP 27/05/02 Population with extremists u x -1 +1+1 U : initial uncertainty of moderate agents ue : initial uncertainty of extremists pe : initial proportion of extemists  : bias between positive and negative extremists

12. ICTP 27/05/02 Central convergence (U=0.4, pe=0.2)

13. ICTP 27/05/02 Both extremes convergence (U=1.4, pe=0.2)

14. ICTP 27/05/02 Single extreme convergence (U=1.4, pe=0.05)

15. ICTP 27/05/02 Convergence indicator p’ + and p’ - are the proportion of initially moderate agents which were attracted to the extreme opinion regions y = p’ + 2 + p’ - 2 central convergence : y close to 0 both extreme convergence : y close to 0.5 single extreme convergence : y close to 1

16. ICTP 27/05/02 Exploration of the parameter space

17. ICTP 27/05/02

21. Conclusion In the model, the convergence to the extremes takes place : –when the initially moderate agents hare very uncertain –by the action of the medium opinion attracted by the extremes The convergence to a single extreme occurs when the uncertainty is even higher, and results of fluctuations of medium opinion agents