This paper examines in detail an alternative ranking problem for search engines, movie recommendation, and other similar ranking systems motivated by the requirement to not just accurately predict pairwise ordering but also preserve the magnitude of the preferences or the difference between ratings. We describe and analyze several cost functions for this learning problem and give stability bounds for their generalization error, extending previously known stability results to non-bipartite ranking and magnitude of preference- preserving algorithms. We present algorithms optimizing these cost functions, and, in one instance, detail both a batch and an on-line version. For this algorithm, we also show how the leave-one-out error can be computed and approximated efficiently, which can be used to determine the optimal values of the trade-off parameter in the cost function. We report the results of experiments comparing these algorithms on several datasets and contrast them with those obtained using an AUC-maximization algorithm. We also compare training times and performance results for the on-line and batch versions, demonstrating that our on-line algorithm scales to relatively large datasets with no significant loss in accuracy.