Improved pairwise comparison transitivity using strategically selected reduced information

To judge the mutual relationship among elements, pairwise comparisons (PC) are widely used in decision modelling. PC is especially useful when the involved elements are intangible. Frequently, the number of elements to be compared may be very large. When dealing with n elements, the number of PCs is, under the reciprocity hypothesis, n(n − 1)/2. PCs are compiled in so-called pairwise comparison matrices (PCM). In the presence of missing entries due to uncertainty or lack of information, decision-making must be performed from the available incomplete information. Making all the comparisons in the complete case may be tedious, strenuous and time-consuming for the actors, may blur the body of judgment, and produce weak priorities and unreliable decisions, thus leading to wrong and harmful conclusions. We claim that a sample of PCs involving less than that number of comparisons may be suitable to develop sound decisions. As the problem has no general solution, we analyse and solve the case in which PCs focus on comparing the elements against only a reduced number of pivotal specific elements. This case include, among others, two practical cases: the actor is more familiar with those pivotal specific elements, and the Best-Worst method [1] has been used to identify the two extreme elements in the set. The approach, developed within the linearization theory [2], is supported with rigorous Mathematics, numerical tests and examples and may be implemented using straightforward and simple computational codes.