The original top scoring pair (TSP) classifier was proposed by Geman et al. (2004) for binary classification of diseases based on genetic profiles. We show the consistency of two versions of the TSP classifier and their two cross-validated counterparts relative to two different risks: the classical misclassification risk and an asymmetric version of this risk which gives more weight to the rarer class. A numerical study illustrates our results and sheds further light on the different TSP classification procedures.