Consensus in preference-approvals: A weighted distance approach

Abstract

Measuring consensus level for a set of preferences requires a proper distance defined on the considered domain. We focus on preference-approvals which are extensions of ordinal preferences by the approval information. For any given set of alternatives, a preference-approval is defined by a weak ordering of the alternative set, subsets of approved and disapproved alternatives and a consistency condition. We propose a method of using weighted distances for ordering and approval components. A consensus measure based on this distance is provided which is sensitive to the position of the disagreements on ordering and approval.