Consensus Group Decision Making Under Model Uncertainty with a View Towards Environmental Policy Making

In this paper we propose a consensus group decision making scheme under model uncertainty consisting of an iterative two-stage procedure based on the concept of Frechet barycenter. Each stage consists of two steps: the agents first update their position in the opinion metric space adopting 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 stage. In cases of large heterogeneous groups, the procedure can be complemented by an auxiliary initial homogenization stage, 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.