  In preference modelling, it is essential to determine the number of questions
and their arrangements to ask from the decision maker. We focus on incomplete
pairwise comparison matrices. First, optimal incomplete filling in patterns are
identified, resulting in weight vectors being closest (on average) to that of
the complete case. These results are obtained by extensive numerical
simulations with large sample sizes. Optimal filling in sequences, formed by
optimal or near optimal filling patterns, are found in the GRAPH of
representing graphs. The star graph is revealed to be optimal among spanning
trees, while the optimal graphs are always close to bipartite ones. Regular
graphs appear to also correspond to optimal cases, furthermore regularity holds
all optimal graphs, as the degrees of different vertices are always as close to
each other as possible. The practical relevance of the results includes the
cases when the decision maker can abandon the problem at any period of the
process, e.g., in online questionnaires. However, the found patterns are
potentially applicable in a wide range of models of preference and information
theory.
