An Agreement Index with Respect to a Consensus Preorder

In this paper, we propose an index to measure the agreement level of an individual preorder with respect to a collective preorder (or reference preorder). The originality of the proposed index consists in the two following facts: (i) it quantifies the agreement level between two preorders which are not necessarily complete (i.e. they may include the incomparability relation), a preference system rarely tackled in the literature and (ii) it takes into account the positions of the alternatives in the individual preorder. The proposed index is then used to compute, within the framework of a consensus preorder research, the agreement level of all group’s members with respect to a collective preorder.