Dealing with chaotic results of Kemeny ranking determination

Multidimensional ordinal measurement in a form of problem of a single consensus ranking determination for m rankings of n alternatives is considered in the paper. 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 computational experiments outcomes show that the approach can give considerably more than one optimal solutions what argues instability of the measurement procedure. Hence, special efforts to avoid this phenomenon are needed.