The nearest adjoining order method for pairwise comparisons in the form of difference of ranks

The problem of ranking of elements from some finite set on the basis of nearest adjoining order (NAO) method for pairwise comparisons is investigated in this paper. It is assumed that in the set under consideration there exists a weak preference relation, which is to be identified (estimated) on the basis of pairwise comparisons in the form of difference of ranks. Moreover, the results of comparisons may be disturbed with random errors; the assumptions made about error distributions are not restrictive. The paper comprises: the problem formulation (definitions, assumptions, and optimisation problem, which provides the NAO solution) and the theoretical background – the form of distributions of random variables which make it possible to determine the properties of NAO solution, in particular, evaluation of the probability that the NAO solution is equivalent to the errorless one. The approach presented in the paper can be extended to the case of more than one comparison for each pair of elements, i.e., completely formalised multi-experts ranking procedure.