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A model of anonymous influence with anti-conformist agents
Michel Grabisch  1, 2, *@  , Alexis Poindron * , Agnieszka Rusinowska  3, *@  
1 : Centre d'Economie de la Sorbonne
CNRS : UMR8174, Université Pierre et Marie Curie (UPMC) - Paris VI, Université Paris VII - Paris Diderot, École normale supérieure [ENS] - Paris
2 : Ecole d'Économie de Paris - Paris School of Economics  (EEP-PSE)  -  Website
Ecole d'Économie de Paris
48 boulevard Jourdan 75014 Paris -  France
3 : PSE - CNRS, University Paris 1, Centre d'Economie de La Sorbonne
Paris School of Economics - CNRS, Univ Paris 1, Centre d'Economie de la Sorbonne
* : Corresponding author

We study a stochastic model of anonymous inuence with conformist and anti-conformist individuals. Each agent with a 'yes' or 'no' initial opinion on a certain issue can change his opinion due to social inuence. We consider anonymous inuence which depends on the number of agents having a certain opinion, but not on their identity. An individual is conformist/anti-conformist if his probability of saying 'yes' increases/decreases with the number of `yes'- agents. In order to consider both conformists and anti-conformists in a society, we investigate a generalized aggregation mechanism. It uses the ordered weighted averages which are the only anonymous aggregation functions. Additionally, every agent has a coefficient of conformism wihch is a real number from -1 till , with the two extreme values corresponding to a pure anti-conformist and a pure conformist, respectively. We assume that both pure conformists and anti-conformists are present in a society, and we deliver a qualitative analysis of convergence in the model, i.e., find all terminal classes and conditions for their occurrence.


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