Reaching consensus in multiagent decision making

A group decision making procedure, when developed in a dynamic context, grows from both an evolving knowledge base and the changes in the positions of the components, or experts, of the group. Agreement and compromise go with and drive the steps of the procedure. Let us consider the case that a committee of experts is constituted to take decisions about a subject of social interest. Usually the job ends if a majority of the members of the committee have not too different opinions about the last state of the decision. We intend to clarify the meaning of the statement "have not too different opinions," to define a structure for the concept of consensus. We assume that an external chairman, with complete information about the state of all the components of group, urges or invites decision makers to reach a consensus. The judgements of the experts are represented, in this framework, by points in a metric space, and the consensus is obtained by a dynamical construction of a maximal winning coalition contained in a ball with a fixed and suitably small diameter. This also allows us to deal with the concept of consensus in terms of algorithm. © 2010 Wiley Periodicals, Inc.