In this paper we propose a consensus group decision making scheme under model uncertainty consisting of an iterative two-stage procedure and based on the concept of Fréchet barycenter. Each step consists of two stages: the agents first update their position in the opinion metric space by a local barycenter characterized by the agents' immediate interactions and then a moderator makes a proposal in terms of a global barycenter, checking for consensus at each step. In cases of large heterogeneous ...