Perron vector ordering for a subclass of tournament matrices

Abstract

We consider the class of n × n tournament matrices having scor vector [1 1 2 3 … n − 4 n − 3 n − 2 n − 2] 1 . For each such matrix, we give formulas for the entries in its perron vector in terms of the corresponding perron value. This leads to a discussion of the ordering of the entries in the perron vector, and so yields some insight into the Kendall Wei method for ranking players in a round robin competition. Finally, we characterize all matrices from this class such that the ordering of the entries in the perron vector coincides with the ordering of the entries in the score vector.