  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 Fr\'echet 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 groups the procedure can be complemented
by an auxiliary initial homogenization step, consisting of a clustering
procedure in opinion space, leading to large homogeneous groups for which the
aforementioned procedure will be applied.
  The scheme is illustrated in examples motivated from environmental economics.
