Про медіану кемені - снелла та коефіцієнта узгодженності думок експертів

Abstract

Розглядається проблема визначення строгого результуючого ранжування альтернатив на основi ранжувань альтернатив, якi задали експерти. Дослiджено зв'язок мiж медiаною Кеменi- Снелла та коефiцiєнтом узгодженостi думок експертiв.

The problem of determination of strict resulting ranking of alternatives based on the rankings of alternatives which were given by experts is considered. Important here is how consistent the opinions of experts are. The ranking of experts are given in the form of ranking matrixes or directly in the form of rank alternatives. We investigate the validity of the geometric approach to the resulting collective opinion depending on the consistency of the experts' opinions. Consistency of rankings of all members of the expert committee or their parts is estimated by coe cient of concordance. Kemeny-Snell median is considered as the resulting strict ranking of alternatives. The relationship between strict Kemeny-Snell median and consistency coe cient of expert opinion is investigated. Thus the problem of Kemeny-Snell median determining is considered in the equivalent formulation of alternatives linear ordering. The result obtained is inequality, which sets limits of the possible values for the median distance depending on the consistency of experts' opinions. This inequality depends on the largest and the smallest number of the experts who prefer one alternative over another.