The Copeland ratio ranking method for abstract decision problems

This paper deals with the problem of ranking a finite number of alternatives on the basis of a dominance relation. We firstly investigate some disadvantages of the Copeland ranking method, of the degree ratio ranking method and of the modified degree ratio ranking method which were characterized by using clone properties and classical axiomatic properties. Then, we introduce some alternative axiomatic properties and propose a new ranking method which is defined by the Copeland ratio of alternatives (i.e., the Copeland score of an alternative divided by its total degree). We show that this proposed ranking method coincides with the Copeland ranking method, the degree ratio ranking method and the modified degree ratio ranking method for abstract decision problems with complete and asymmetric dominance relations. Subsequently, we prove that this new ranking method is able to overcome the mentioned disadvantages of these ranking methods. After that, we provide a characterization for the Copeland ratio ranking method using the introduced axiomatic properties.