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Dynamics of Extremism Convergence: Relative Agreement Study

Explore how extremism prevails through the Relative Agreement model, analyzing influences, uncertainties, and convergence patterns in agent opinions. Discover insights on extremism dynamics and the role of uncertainties in opinion formation.

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Dynamics of Extremism Convergence: Relative Agreement Study

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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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