A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances.

Preference rankings usually depend on the characteristics of both the individuals judging a set of objects and the objects being judged. This topic has been handled in the literature with log-linear representations of the generalized Bradley-Terry model and, recently, with distance-based tree models for rankings. A limitation of these approaches is that they only work with full rankings or with a pre-specified pattern governing the presence of ties, and/or they are based on quite strict distributional assumptions. To overcome these limitations, we propose a new prediction tree method for ranking data that is totally distribution-free. It combines Kemeny's axiomatic approach to define a unique distance between rankings with the CART approach to find a stable prediction tree. Furthermore, our method is not limited by any particular design of the pattern of ties. The method is evaluated in an extensive full-factorial Monte Carlo study with a new simulation design.