Consider a set of elements which we want to rate using information about their bilateral relationships. For instance sports teams and the outcomes of their games, journals and their mutual citations, web sites and their link structure, or social alternatives and the tournament derived from the voters' preferences. A wide variety of scoring methods have been proposed to deal with this problem. In this paper we axiomatically characterize two of these scoring methods, variants of which are used to rank web pages by their relevance to a query, and academic journals according to their impact. These methods are based on the Perron–Frobenius theorem for non-negative matrices.