Multi-dimensional Ranking via Majorization

University ranking are ubiquitous as there are dozens of them. University ranking are not only used as tools in academia and funding agencies, but they are popular reading in newspapers and magazines as well. Also in academics is of major importance for decision-making. University ranking have been heavily criticized for a number of reasons, including that they are based on arbitrary choices about the key indicators, their special weights and so on. For these reasons, we argue that there is no meaning in ranking universities in an absolute ordered manner; instead universities should be ranked in "sets of equivalence". To this end, we introduce the mathematical concept of majorization and perform experiments on a dataset extracted from NTU Ranking. This approach is applicable to other entities, such as authors or other higher order multi-dimensional entities.