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In preference modelling, it is essential to determine the number of questionsand their arrangements to ask from the decision maker. We focus on incompletepairwise comparison matrices. First, optimal incomplete filling in patterns areidentified, resulting in weight vectors being closest (on average) to that ofthe complete case. These results are obtained by extensive numericalsimulations with large sample sizes. Optimal filling in sequences, formed byoptimal or near optimal filling patterns, are found in the GRAPH ofrepresenting graphs. The star graph is revealed to be optimal among spanningtrees, while the optimal graphs are always close to bipartite ones. Regulargraphs appear to also correspond to optimal cases, furthermore regularity holdsall optimal graphs, as the degrees of different vertices are always as close toeach other as possible. The practical relevance of the results includes thecases when the decision maker can abandon the problem at any period of theprocess, e.g., in online questionnaires. However, the found patterns arepotentially applicable in a wide range of models of preference and informationtheory.

Optimal sequences for pairwise comparisons: the graph of graphs approach