Group Reasoning in Social Environments

While modelling group decision making scenarios, the existence of a central authority is often assumed which is in charge of amalgamating the preferences of a given set of agents with the aim of computing a socially desirable out- come, for instance, maximizing the utilitarian or the egalitarian social welfare. Departing from this classical perspective and inspired by the growing body of literature on opinion formation and diffusion, a setting for group decision making is studied where agents are selfishly interested and where each of them can adopt her own decision without a central coordination, hence possibly disagreeing with the decision taken by some of the other agents. In particular, it is assumed that agents belong to a social environment and that their preferences on the available alternatives can be influenced by the number of “neighbors” agreeing/disagreeing with them. The setting is formalized and studied by modelling agents’ reasoning capabilities in terms of weighted propositional logics and by focusing on Nash-stable solutions as the prototypical solution concept. A thoroughly computational complexity analysis is conducted, too: A number of intractability results are pointed out, and qualitative restrictions on the underlying environments are introduced based on which a precise picture of the tractability frontier is depicted.