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Rankings as ordinal scale measurement results

Muravyov S. V.

Metrology and Measurement Systems

2007

Vol. 14, nr 1

9-23

Rankings (or preference relations, or weak orders) are sometimes considered to be non-empirical, non-objective, low-informative and, in principle, are not worthy to be titled measurements. A purpose of the paper is to demonstrate that the measurement result on the ordinal scale should be an entire (consensus) ranking of n objects ranked by m properties (or experts, or voters) in order of preference and the ranking is one of points of the weak orders space. The consensus relation that would give an integrative characterization of the initial rankings is one of strict (linear) order relations, which, in some sense, is nearest to every of the initial rankings. A recursive branch and bound measurement procedure for finding the consensus relation is described. An approach to consensus relation uncertainty assessment is discussed.