If on a set of objects are given certain binary relations, that determine the advantages of one object over the other object, then their ordering is possible with a help of paired comparisons. The method of paired comparisons allows an estimation of such characteristics of objects, which are not measurable in the usual sense, that is with technical devices and tools. Practical applications of the method in ranking, prioritization and decision-making are unique in the sense that it allows utilization ofsubjective preferences of judges. Since the objects are compared in pairs, judges can concentrate their attention on only two objects at time. It is believed that such an approach avoids the effect of so-called sensory fatigue, when evaluating more thantwo objects at a time leads to confusion and lack of concentration. Moreover, observing just two objects permits better discrimination between very fine differences in the objects. This method represents a simpler but strong alternative to other rankingtechniques, which may require complex experiment planning procedures. Another distinctive advantage of our approach is that the method does not deny the existence of circular triads, and in some cases allows identification of such triads. We see the method of paired comparisons as by far more superior than other ranking techniques. In this paper it is considering the case when the elements of comparisons are random with partly unknown probabilities. To determine them, it is using the method of maximum authenticity and the method of minimizing the aggregate quadratic error. It is shown that the estimates of the maximum authenticity of the probabilities are determined by some equation, has a unique solution. For optimal averaged estimates are received an explicit formulas.
Якщо на множинi об"єктiв задаються певнi бiнарнi вiдношення, що визначають переваги одного об"єкта над iншим, то їх впорядкування можливе за допомогою попарних порiвнянь. В роботi розглядається випадок, коли елементи матрицi порiвнянь випадковi з частково невiдомими ймовiрностями. Для їх визначення застосовується метод максимальної вiрогiдностi та метод мiнiмiзацiї усередненої середньоквадратичної похибки. Показано, що оцiнки максимальної вiрогiдностi ймовiрностей визначаються iз деякого рiвняння, що має єдиний розв"язок. Для оптимальних усереднених оцiнок ймовiрностей одержанi явнi формули.
