The problem of ranking k ≥ 3 objects by pairwise comparisons is analyzed. A new criterion for optimal ranking in terms of the pairwise dominance probabilities is introduced, and its application based on corresponding estimated probabilities is discussed and demonstrated. Ranking by pairwise comparisons in situations where ordering according to values of a common performance measure is possible is also discussed with special reference to ordering portfolios. The new criterion calls for maximizing the probability of a full agreement between an ordering and all the induced pairwise comparisons (over all orderings). A specific example is used to demonstrate the new method in the context of portfolio analysis, to compare with the method of Owen and Rabinovitch, and to indicate the need for further research.
