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Determining influential models

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Working paper
Michel Grabisch, Agnieszka Rusinowska
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Documents de travail du Centre d'Economie de la Sorbonne
Centre d'Economie de la Sorbonne
We consider a model of opinion formation based on aggregation functions. Each player modifies his opinion by arbitrarily aggregating the current opinion of all players. A player is influential for another player if the opinion of the first one matters for the latter. A generalization of influential player to a coalition whose opinion matters for a player is called influential coalition. In- fluential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and the convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. the standard opinion formation framework driven by the Markov chain theory. For the qualitative analysis of convergence, knowing the aggregation functions of the players is not required, but one only needs to know the influential coalitions for every player. We propose simple algorithms that permit to fully determine the influential coalitions. We distinguish three cases: the symmetric decomposable model, the anonymous model, and the general model.
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