Differently from the regular classification task, in ordinal classification there is an order in the classes. As a consequence not all classification errors matter the same: a predicted class close to the groundtruth one is better than predicting a farther away class. To account for this, most previous works employ loss functions based on the absolute difference between the predicted and groundtruth class {\em labels}. We argue that there are many cases in ordinal classification where label values are arbitrary (for instance 1\ldots $C$, being $C$ the number of classes) and thus such loss functions may not be the best choice. We instead propose a network architecture that produces not a single class prediction but an ordered vector, or ranking, of all the possible classes from most to less likely. This is tanks to a loss function that compares groundtruth and predicted rankings of these class labels, not the labels themselves. Another advantage of this new formulation is that we can enforce consistency in the predictions, namely, predicted rankings come from some unimodal vector of scores with mode at the groundtruth class. We compare with the state of the art ordinal classification methods, showing that ours attains equal or better performance, as measured by common ordinal classification metrics, on three benchmark datasets. Furthermore, it is also suitable for a new task on image aesthetics assessment, \textit{i.e.}, most voted score prediction. Finally, we also apply it to building damage assessment from satellite images, providing an analysis of its performance depending on the degree of imbalance of the dataset.