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Satisfaction in societies with opinion leaders and mediators: properties and an axiomatization

In this paper we propose the opinion leader-follower through mediators systems (OLFM systems) a multiple-action collective choice model for societies. In those societies three kind of actors are considered: opinion leaders that can exert certain influence over the decision of other actors, followers that can be convinced to modify their original decisions, and independent actors that neither are influenced nor can influence; mediators are actors that both are influenced and influence other actors. This is a generalization of the opinion leader-follower systems (OLF systems) proposed by van den Brink R, et al. (2011). The satisfaction score is defined on the set of actors. For each actor it measures the number of society initial decisions in which the final collective decision coincides with the one that the actor initially selected. We generalize in OLFM systems some properties that the satisfaction score meets for OLF systems. By using these properties, we provide an axiomatization of the satisfaction score for the case in which followers maintain their own initial decisions unless all their opinion leaders share an opposite inclination. This new axiomatization generalizes the one given by van den Brink R, et al. (2012) for OLF systems under the same restrictions.