Ordinal measurement, preference aggregation and interlaboratory comparisons

Abstract

The classical problem of a single consensus ranking determination for m rankings of n alternatives has a potential of wide applications in information technologies, and particularly in measurement and instrumentation. The Kemeny rule is one of deeply justified ways to solve the problem allowing to find such a linear order (Kemeny ranking) of alternatives that a distance (defined in terms of a number of pair-wise disagreements between rankings) from it to the initial rankings is minimal. But the approach can result in considerably more than one optimal solutions what can reduce its applicability. By computational experiments outcomes, the paper demonstrates that a set of Kemeny rankings cardinality can be extremely large in small size cases (m=4,n=15…20) and, consequently, special efforts to build an appropriate convoluting solution are needed. Application of the model to one of practical metrological problems, such as interlaboratory comparisons, is proposed and examined.