cultural and multicultural (or global, polarized), respectively. A first order phase transition is obtained for F > 2 between the monocultural to a multicultural state for increasing value of the initial diversity q [9]. The Axelrod model has shown how diversity with local convergence can be obtained. Nevertheless, as mentioned before, there are two results of the model which contradict empirical patterns: (1) the Axelrod model predicts cultural diversity in very small societies, but monoculture in larger ones 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]. This has been justified as a consequence of the dyadic interaction considered between the agents of the society [21]. Following the proposition made by A. Flache et al in Ref. [21] we have developed a new interaction procedure in the Axelrod model to study the effects of the social influence between agents. Our approach is similar, but not exactly equal, to that proposed in Ref. [21]. In our case, at a given time t an agent i is randomly chosen for possible influence. Around any agent, we consider a neighborhood defined by a parameter p , which controls how many agents can be visited (in unitary steps) in each direction starting from that agent until the perimeter of the neighborhood is reached. One unit-step allows to move only in north-south or east-west direction. When p =1 the neighborhood obtained is therefore the well-known von Newmann neighborhood N 1 , which only includes the four closer neighbors of an agent ( N 1 = { j 1 , j 2 , j 3 , j 4 } ). In our case, p can take higher values to define bigger neighborhoods. In general, for a given value of p it is obtained N$_{p}$ = { j 1 , ..., j$_{α}$ } where α = α ( p ) = 2 p ( p + 1). This give four neighbors ( α = 4) for one step neighborhood ( p = 1), twelve neighbors ( α = 12) for two step neighborhood ( p = 2) and so forth. The social influence is defined as follows: when an agent i is selected for possible influence, all of its neighbors (according to the value of p ) are included in the set of influence I$_{i}$ with probability p$_{ij}$ α = O$_{ij}$ α /F , where O$_{ij}$ α is the cultural overlap between agent i and j$_{α}$ . The set I$_{i}$ obtained by this procedure becomes a set of traits’ influence over agent i ’s traits. In our model we have decided to include also agent i into the set I$_{i}$ with probability p$_{ii}$ = 1. III. THE MODEL FOR SELF-INCLUDED SOCIAL INFLUENCE WITH MASS MEDIA. 5