Making Decisions in Multi Partitioning

Starting from individual judgments given as categories (i.e., a profile of partitions on an X item set), we attempt to establish a collective partitioning of the items. For that task, we compare two combinatorial approaches. The first one allows to calculate a consensus partition, namely the median partition of the profile, which is the partition of X whose sum of distances to the individual partitions is minimum. Then, the collective classes are the classes of this partition. The second one consists in first calculating a distance D on X based on the profile and then in building an X-tree associated to D. The collective classes are then some of its subtrees. We compare these two approaches and more specifically study in what extent they produce the same decision as a set of collective classes.