Incomplete pairwise comparison matrices based on graphs with average degree approximately 3

Abstract A crucial, both from theoretical and practical points of view, problem in preference modelling is the number questions to ask decision maker. We focus on incomplete pairwise comparison matrices based graphs whose average degree approximately 3 (or a bit more), i.e., each item compared three others average. In range matrix sizes we considered, $$n=5,6,7,8,9,10$$ n = 5 , 6 7 8 9 10 , this requires 1.4 n 1.8 edges, resulting completion ratios between 33% ( $$n=10$$ ) 80% $$n=5$$ ). analyze several types union two spanning trees (three them building additional ordinal information ranking), 2-edge-connected random 3-(quasi-)regular with minimal diameter (the length maximal shortest path any vertices). The weight vectors are calculated natural extensions, case, most popular weighting methods, eigenvector method logarithmic least squares. These ones complete matrix, their distances (Euclidean, Chebyshev Manhattan), rank correlations (Kendall Spearman) similarity (Garuti, cosine dice indices) computed order have cardinal, proximity views during comparisons. Surprisingly enough, only star centered at best second items perform well among using ranking. edge-disjoint almost always analyzed graphs.