A Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot's Method

Abstract

Abstract DeGroot (1974) proposed a model in which a group of k individuals might reach a consensus on a common subjective probability distribution for an unknown parameter. This paper presents a necessary and sufficient condition under which a consensus will be reached by using DeGroot's method. This work corrects an incorrect statement in the original paper about the conditions needed for a consensus to be reached. The condition for a consensus to be reached is straightforward to check and yields the value of the consensus, if one is reached.