# Determining influential models

Working paper

Issue number:

2016.38

Series:

Documents de travail du Centre d'Economie de la Sorbonne

Publisher:

Centre d'Economie de la Sorbonne

Year:

2016

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.