Classification of rankings within a Kemeny distance framework

Typically, ranking data consist of a set of individuals, or judges, who have ordered a set of items—or objects—according to their overall preference or some pre-specified criterion. When each judge has expressed his or her preferences according to his own best judgment, such data are characterized by systematic individual differences. In the literature, several approaches have been proposed to decompose heterogeneous populations of judges into a defined number of homogeneous groups. Often, these approaches work by assuming that the ranking process is governed by some distance-based probability models. We use the flexible class of methods proposed by Ben-Israel and Iyigun, which consists in a probabilistic distance clustering approach, and define the disparity between a ranking and the center of a cluster as the Kemeny distance. This class of methods allows for probabilistic allocation of cases to classes, thus being a form of soft or fuzzy, clustering. The allocation probability is unequivocally related to the chosen distance measure.