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How can extremism prevail ? A study based on the Relative agreement model

How can extremism prevail ? A study based on the Relative agreement model. G. Deffuant, G. Weisbuch, F. Amblard, T. Faure. Influence of extremists. The extremists win : Majority to one extreme (Germany in the thirties, islamic revolution…) Bipolarisation (affaire Dreyfus, religion wars…)

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How can extremism prevail ? A study based on the Relative agreement model

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

  2. 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. 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. With a uniform distribution of the opinions of width w • [w/2u]=1 [w/2u]=2 • nb attractors approximately the integer part of w/2u

  5. 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. Relative agreement j i xj xi hij hij-ui • Relative agreement :

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

  8. Variation of the relative agreement • (i influences j) ui< uj 1 ui> uj xi ui> 2uj xj- uj xj xj+ uj

  9. Same uncertainty for all agents (0.5)

  10. Same uncertainty for all agents

  11. Population with extremists u U : initial uncertainty of moderate agents ue : initial uncertainty of extremists pe : initial proportion of extemists d : bias between positive and negative extremists x +1 -1

  12. Central convergence (U=0.4, pe=0.2)

  13. Both extremes convergence(U=1.4, pe=0.2)

  14. Single extreme convergence (U=1.4, pe=0.05)

  15. 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. Exploration of the parameter space

  17. 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

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