Position Weighted Decision Trees for Ranking Data

Abstract

Preference data represent a particular type of ranking data where a group of people gives their preferences over a set of alternatives. Within this framework, distance-based decision trees represent a non-parametric tool for identifying the profiles of subjects giving a similar ranking. This paper aims at detecting, in the framework of (complete and incomplete) ranking data, the impact of the differently structured weighted distances for building decision trees. By means of simulations, we will compute the impact of higher/lower homogeneity in groups and different weighting structures both on splitting and on consensus ranking. The distances that will be used satisfy Kemeny’s axioms and, accordingly, a modified version of the rank correlation coefficient τx , proposed by Emond and Mason, will be proposed and used for rank aggregation and class label in the tree leaves.