A branch and bound algorithm to construct a consensus ranking based on Kendall’s T

The aim of this paper is to present a branch and bound algorithm, which allows the construction of a consensus ranking out of a set of complete rankings over all alternatives. Each ranking of this set corresponds to the judgement of a decision maker with respect to the given list of alternatives. The method itself is based on the use of Kendall’s rankcorrelation coefficient so as to be able to compare the decision makers’ rankings, and to take the ordinal character of the rankings fully into account. Through the introduction of the concept of piecewise rankcorrelation coefficients, a recursion formula is derived, which enables one to obtain the necessary tool to setup the branch and bound algorithm.