Ranking by Relational Power based on Digraphs

In this paper we examine the ranking for the case of many judges and manyobjects. We use a directed graph to determine the ranking of the objects. A measureis the function whose domain is the collection of all directed graphs and range is theset of real vectors of as many components as the number of nodes, and the componentsare called relational power. We proposed two measures and showed the validity of themeasures from two aspects: axiomatization and the Shapley value. We also showed thecharacter of measures by some numerical examples