ABSTRACT
In spite of its elegance, there is a real drawback to using paired comparisons: The number of pairs grows as the square of the number of elements. Ten elements means 45 comparisons, usually a manageable number, but 30 elements means 435 pairs and 100 means 4,950. Thus, there is considerable motivation for trying to reduce the number of comparisons while still retaining as much of the elegance of the pairwise dominance process as possible. Also, in many situations one may wish to employ the dominance concepts to yield an overall order in situations where, for circumstantial reasons, not all pairwise dominance relations are observed, resulting in incomplete dominance matrices. In this chapter we describe methods for arriving at orders from incomplete data, including expanding the methods beyond direct pair comparisons.
