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A model of influence based on aggregation functions

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Abstract

The paper concerns a dynamic model of influence in which agents have to make a yes-no decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a Markov chain. In the paper, we investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents, possibly including himself. We provide a general analysis of convergence in the aggregation model and give more practical conditions based on influential players. We show that the process of influence converges always to one of the two consensus states, and there may exist other terminal classes, which are either cyclic or union of Boolean lattices. We give sufficient conditions for avoiding these additional terminal classes, based on properties of the graph of influence and influential players. We also introduce the notion of influential coalition and show that it can fully describe terminal classes. Some important families of aggregation functions are discussed.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2011/11058.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 11058.

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Length: 29 pages
Date of creation: Oct 2011
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Handle: RePEc:mse:cesdoc:11058

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Keywords: Influence; aggregation function; convergence; terminal class; infuential coalition; social network.;

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References

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Cited by:
  1. Manuel Förster & Michel Grabisch & Agnieszka Rusinowsk, 2013. "Anonymous Social Influence," Working Papers 2013.51, Fondazione Eni Enrico Mattei.

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