Optimal sequencing in incomplete pairwise comparisons for large-dimensional problems

In this paper we propose a flexible method for optimally choosing and sequencing in time a subset of pairwise comparisons between the alternatives in large-dimensional decision problems, where it is unfeasible to submit all the possible questions to the decision maker (DM). Two criteria are taken into account in defining the choice rule: the fair involvement of all the alternatives in the pairwise comparisons and the consistency of the elicited judgements. The combination of the two criteria guarantees the best reliability of the already collected information. The method indicates at each step the two alternatives to be compared next and stops the process on the basis of a rule that takes into account both the reliability of the already elicited judgements and the necessity of bounding the potentially large number of judgements to be submitted to the DM.