Dominance relations and ranking when quantity and quality both matter: Applications to US universities and econ. departments worldwide

In this article, we propose to extend the concept of stochastic dominance, extensively used in decision theory and social choice, to the comparison of composite outcomes, both the quality and quantity of which do matter. Unanimity of judgment among new classes of functions is also studied. We introduce and characterize axiomatically a new index, called Importance, which allows us to rank institutions on clear grounds using the information contained in any set of available unanimous bilateral comparisons (an incomplete tournament). This theory is applied to the ranking of U.S. research universities taking into account both the volume of publications and their impact. We also compare and rank academic departments in economics taking both the size of the department and the prestige of its members into account.