Optimization method of selecting the resulting ranking of objects presented inrank scale of measurement

At present, there is no optimal method for constructing the resulting ranking, known as the Kemeny-Snell median, according to the matrix criterion between orderings of objects by experts, represented by matrices of binary relations on a set of pairs of objects. However, the task of constructing the resulting ranking according to the matrix criterion between orderings of objects by experts represented by matrices of binary relations on a set of pairs of objects can be reduced to an equivalent optimization problem if the ranking of objects is presented in a ranking scale of measurements. In this case, the distance between the object rankings presented in the form of vector rank ratings, including taking into account the ratings of objects with related ranks, acts as an optimality criterion. The article shows that the introduced distances between the ranking of objects in the rank scale satisfy the traditional axioms of metric space. The validity of the transition from the statement of the problem of constructing the Kemeny-Snell median by the matrix criterion to the statement of the problem by the criterion of proximity between rankings in the rank scale is related to the fact that between the rankings represented by the binary relations matrices on the set of pairs of objects and the rankings in the rank scale, As shown in this article, there is a one-to-one correspondence.