On Reaching a Consensus Using Degroot's Iterative Pooling

Abstract

We consider a group of k experts each having a subjective probability distribution for a parameter $\theta$. If the members of the group are allowed to know the others' opinions and they appreciate the others' skills, it is likely that each expert will modify his distribution to account for this new information. This process can be continued indefinitely leading to an iterative pooling process. The main issue is whether the experts'distributions will converge towards a common limit or consensus. Several authors have considered this iterative process when the experts' distributions at a given stage are linear opinion pools of the distributions at the previous stage. In this paper we extend the model for the specific case where the experts use logarithmic opinion pools and, more broadly, for pools in a wide class that generalizes both the linear and the logarithmic pools. It is shown that the consensus properties in the logarithmic pool case are essentially the same as in the linear pool case, and that this fact uniquely characterizes both pools in the wide class mentioned above.