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.

翻译：本文提出了一种在模型不确定性条件下的共识群体决策方案，该方案基于弗雷歇重心的概念，采用迭代两阶段流程。每个步骤包含两个阶段：首先，各主体通过局部重心（由主体间的直接互动定义）更新其在意见度量空间中的位置；随后，协调者根据全局重心提出提案，并在每个步骤中检验共识是否达成。针对大规模异质性群体，该流程可辅以初始同质性预处理步骤——基于意见空间中的聚类方法，生成适用于前述流程的大规模同质群体。通过环境经济学中的实例，本文对该方案进行了说明。