The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis

• Published in: European journal of operational research Vol. 257; no. 1; pp. 197 - 208
• Main Authors: Lundy, Michele, Siraj, Sajid, Greco, Salvatore
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.02.2017; Elsevier Sequoia S.A
• Subjects: Comparative analysis; Decision analysis; Graph theory; Hierarchies; Mathematical programming; Multiple criteria analysis; Pairwise comparisons; Preferences; Spanning trees; Studies; Graph theory; Pairwise comparisons; Decision analysis; Spanning trees; Multiple criteria analysis
• DOI: 10.1016/j.ejor.2016.07.042
• ISSN: 0377-2217

•We introduce the geometric mean operator within the “spanning tree” prioritization approach.•We compare the preference vectors calculated from the “spanning tree” and row geometric mean prioritization methods.•We prove the equivalence of these preference vectors.•We establish the importance of this finding and provide guidelines for future work. Pairwise comparison is a widely used approach to elicit comparative judgements from a decision maker (DM), and there are a number of methods that can be used to then subsequently derive a consistent preference vector from the DM’s judgements. While the most widely used method is the eigenvector method, the row geometric mean approach has gained popularity due to its mathematical properties and its ease of implementation. In this paper, we discuss a spanning tree method and prove the mathematical equivalence of its preference vector to that of the row geometric mean approach. This is an important finding due to the fact that it identifies an approach for generating a preference vector which has the mathematical properties of the row geometric mean preference vector, and yet, in its entirety, the spanning tree method has more to offer than the row geometric mean method, in that, it is inherently applicable to incomplete sets of pairwise comparison judgements, and also facilitates the use of statistical and visual techniques to gain insights into inconsistency in the DM’s judgements.