Efficient sampling of pairwise comparisons in decision-making

Performing pairwise comparisons (PCs) that reflect preferences between pairs of decision-making elements is an approach widely used in decision modelling. For complex problems, the number of elements to be pairwise compared may be very large, something that may lead to a final calculation of not well-supported priorities and, as a consequence, to the drawing of wrong practical conclusions. Decision-making must usually be performed from the available incomplete body of information, and this article explores the possibility of producing reliable results by using just a sample of comparisons. We analyse and solve two specific cases of considerable interest: the sample consists of: (i) a balanced and unbiased set of PCs; and (ii) the PCs obtained by comparing all the elements against a reduced number of pivotal elements. This latter sample includes two practical cases: one in which the eliciting actor is more familiar with the pivotal specific elements; and another in which the Best-Worst method has been previously used to identify the two extreme elements under comparison. The approach employed, developed within linearisation theory, is supported with suitable proofs and examples.