Consensus, Negotiation and Mediation

Abstract

Carl Wagner and I articulated a mathematical model of aggregating vectors to reach consensus which has been the subject of subsequent controversy in the literature.

We formulated a model of convergence toward consensus applied to an allocation matrix of vectors. In our collaboration, we laid great emphasis on the merits of assigning weights and weighted averaging that converged toward the consensual allocation. In this paper, I will consider the application of the model to negotiation. I investigate the rationality of blocking convergence toward consensus, most decisively, by assigning a weight of zero to all other members of the group. The basic rationale for blocking convergence in this way is to prevent one from being co-opted in the process of negotiation. Nevertheless, blocking convergence results in the decomposition of society and failure to base policy on consensus. To prevent such decomposition, I consider adopting a mediator who is a default referee in the aggregation process. The default referee connects the group by receiving a standard positive weight from all involved and giving positive weight to all others to yield convergence and consensus. The assignments of the default referee to others may be egalitarian or differential and yet equality effective in producing convergence.