Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi-criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi-criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one.