Weighted and unweighted distances based decision tree for ranking data

Abstract

Preference data represent a particular type of ranking data (widely used in sports, web search, social sciences), 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. The traditional metrics between rankings don’t take into account the importance of swapping elements similar among them (element weights) or elements belonging to the top (or to the bottom) of an ordering (position weights). By means of simulations, using weighted distances to build decision trees, we will compute the impact of different weighting structures both on splitting and on consensus ranking. The distances that will be used satisfy Kemenys axioms and, accordingly, a modified version of the rank correlation coefficient τx, proposed by Edmond and Mason, will be proposed and used for assessing the trees’ goodness.