Ordering pairwise comparison structures

Following an introduction to the merits of pairwise comparison methods, we present various ordering algorithms for complete binary preferential structures. These procedures generalize the well-known numbering algorithm to the intransitive case. A new form of independence of irrelevant alternatives is presented. Moreover, various other criteria and characterizations for these algorithms are presented. Aside from solving ranking problems and making explicit value criteria and structures of human preference, our algorithms are applicable to subjects such as task-sequencing and artificial intelligence projects.