MULTIPLE SOLUTIONS OF AN EXACT ALGORITHM FOR DETERMINATION OF ALL KEMENY RANKINGS: PRELIMINARY EXPERIMENTAL RESULTS

摘要

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 give considerably more than one optimal solutions what can reduce its applicability. On computational experiments outcomes, the paper demonstrates that a set of Kemeny rankings cardinality can be extremely large even in small size cases (m = 4, n = 15...20) and, consequently, special efforts to build an appropriate convoluting solution are needed.