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This paper deals with group decision making and, in particular, with rank aggregation, which is the problem of aggregating individual preferences (rankings) in order to obtain a consensus ranking. Although this consensus ranking is usually a permutation of all the ranked items, in this paper we tackle the situation in which some items can be tied, that is, the consensus shows that there is no preference among them. This problem has arisen recently and is known as the Optimal Bucket Order Problem (OBOP).

In this paper we propose two improvements to the standard greedy algorithm usually considered to approach the bucket order problem: the Bucket Pivot Algorithm (BPA). The first improvement is based on the introduction of the Utopian Matrix, a matrix associated to a pair order matrix that represents the precedences in a collection of rankings. This idealization constitutes a superoptimal solution to the OBOP …