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Since there exist several completion methods to estimate the missing entriesof pairwise comparison matrices, practitioners face a difficult task inchoosing the best technique. Our paper contributes to this issue: we consider aspecial set of incomplete pairwise comparison matrices that can be representedby a weakly connected directed acyclic graph, and study whether the derivedweights are consistent with the partial order implied by the underlying graph.According to previous results from the literature, two popular procedures, theincomplete eigenvector and the incomplete logarithmic least squares methodsfail to satisfy the required property. Here, the recently introducedlexicographically optimal completion combined with any of these weightingmethods is shown to avoid ordinal violation in the above setting. Our findingprovides a powerful argument for using the lexicographically optimal completionto determine the missing elements in an incomplete pairwise comparison matrix.

How to choose a completion method for pairwise comparison matrices with missing entries: An axiomatic result