Further results on the consensus problem

In this paper, we develop additional results on the problem of reaching a consensus of opinion between two decisionmakers provided with different information. Specifically, we study the problem where the two decisionmakers may have different underlying probability models. We develop results characterizing the likelihood of an agreement being reached eventually in terms of the nature of the inter-decisionmaker communications. We also study the problem when the decisionmakers are aware of the possibility that they may have different models. In this case, the decisionmakers can reach a deadlock state where neither decisionmaker can learn additional information from the consensus process, and they cannot reach a consensus decision. This surprising result indicates that incorporating human uncertainty in probability assessment into the asymptotic agreement problem can lead to outcomes not anticipated in the general theory previously developed.