Determining the total order of sets from a ranking of elements
Given a ranking of the elements of a set and given a disjoint partition of the same set, the ranking does not generally imply a total order of the partition. In this paper we introduce the Kendall-tau partition ranking, a linear order of the subsets of the partition which follows from the given ranking. We prove that the Kendall-tau partition ranking is robust in the sense that it remains the same when removing subsets of the partition. Several results concerning the adequacy of the ranking for ordering the partition are given. Finally, an application with data in the Programme for International Student Assessment (PISA) is presented: countries are ordered from the ranking of its schools.
Palabras clave / Keywords: linear ordering problem rank aggregation problem Kendall-tau distance
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