Expected cost bounds for the selection and ordering procedures based on binary-type questions

The problems considered in this paper are similar to those studied by Arrow, Pesotchinsky and Sobel (1981). We search for the optimal methods of ordering of a sample or of identifying sample order statistics by asking binary type questions and employing the criterion which defines the cost of a question as the number of responses. The asymptotic results show that our procedures with simple algorithms are comparable (in terms of cost) with the best known methods for ordering by using pairwise comparisons.