Pairwise Comparison and Ranking in Tournaments

Since, however, other ranking procedures have been proposed, e.g., by WeiKendall [3], the problem arises how to characterize the "goodness" of any such procedure. In this paper we give such a characterization in terms of the "underlying probability structure" and then exhibit a class of such structures for which the usual ranking procedure by scores si is optimal. In order to keep what follows as intuitive as possible we shall from now on use the terminology referring to chess tournaments, i.e., "player" for "item," "game" for "comparison" and "won," "lost" or "drawn" for the possible results of any comparison.