Collective Dynamics of Interacting Agents when Driven by PAM

The paper treats opinion dynamics under bounded confidence when agents employ, beside an arithmetic mean, means like a geometric mean, a power mean or a random mean in aggregating opinions. The different kinds of collective dynamics resulting for these means are studied and compared by simulations. Particular attention is given to the random mean which is a new concept introduced in this paper. All those concrete means are just particular cases of a PAM, that is a partial abstract mean, which also is a new concept. Such a PAM is investigated also analytically and it is shown in particular, that the collective dynamics for a PAM always stabilizes in a fragmented pattern of opinions.