Comparing distance to consensus of collective relations using OWA operators

Abstract

Consensus is understood as a unanimous agreement by all experts in a group. The goal of consensus is not the selection of several options but to develop one decision that suits the interests of the entire group under consideration. In this paper, it is assumed that collective preferences are developed with the help of commonly used ordered weighted averaging operators but resultant relations do not exhibit any property of a consensus type. That is, consensus is not reached at the first attempt of ranking alternatives. Under such circumstances, the measure of distance to consensus can be successfully used to determine how far a group collectively is from consensus. The aim of this paper is to compare, where possible, the distance to consensus of collective relations compiled with the help of most commonly used ordered weighted averaging operators. The innovative part is that this measure helps in defining an upper and lower bound of distance to consensus of the resultant collective relations. With such an analysis at hand, experts can choose a suitable ordered weighting averaging operator to formulate a collective relation that exhibits a lower distance to consensus.