Perron vector ordering for a subclass of tournament matrices (Q1300853)

This paper gives formulas for the Perron vector of a tournament matrix having score vector \([1, 1, 2, 3,\dots, n-3,n-2, n-2]^t\). This offers some insight into the relation between the ranking of tournament results by the score vector, and the Kendall-Wei proposal of ranking by the size order of the Perron-vector entries [cf. \textit{M. G. Kendall}, Biometrics 11, 43-62 (1955) and \textit{T. H. Wei}, The algebraic foundations of ranking theory, Ph.D. Thesis, Cambridge Univ., Cambridge (1952)]. In particular, a characterization is offered of all matrices of this type for which the two rankings are equivalent.