The Axelrod model has been exhaustively implemented to study a great variety of prob- lems: the nonequilibrium phase transition between monocultural and multicultural states [10], the cultural drift driven by noise [11, 12], nominal and metric features [13, 14], propa- ganda [15], time evolution dynamics [16], the resistance of a society to the spread of foreign cultural traits [17], finite size effects [18], the impact of the evolution of the network structure with cultural interaction [19], and mobility of social agents [20], among others. The dynamical influence on the society is described in the original Axelrod model using a dyad interaction which, at each time step, only comprises the source and the target of influence in a particular interaction. As discussed by A. Flache and M. W. Macy in Ref. [21], the influence a person feels from the society is a social phenomenon that cannot be reduced to the interactions within a dyad given by source-target couple of persons because the social pressure on the target to adopt an opinion is proportional to the number of people that the target perceives are supporting this opinion. On the contrary, the Axelrod model assumes that influence is interpersonal (dyadic). We are then in front of a two completely different assumption with respect to the way people interact in society: In Ref. [21] the authors explained that the central implications of Axelrod’s model profoundly change if the dyadic interaction is changed to social influence . The authors have shown that the combination of social influence with homophily (the principle that “likes attract”) solves two important problems which contradict the empirical pattern: On the other hand, one of the extensions of the Axelrod model that have been done consists of the study of Mass Media effects over the society [22–25]. Surprisingly, the Mass 1. dyadic interaction where it is supposed that two people in a relationship interact in isolation from others and 2. social influence which is multilateral and involves all network neighbors simultaneously. 1. the original Axelrod model predicts cultural diversity in very small societies, but mono- culture in larger ones [30] and 2. when cultural perturbation is present, diversity is obtained only in a very narrow window of noise level and this window decreases with increasing population size [10, 11]. 3