Ranking institutions within a discipline : the steep mountain of academic excellence

We present a novel algorithm to rank smaller academic entities such as university departments or research groups within a research discipline. The Weighted Top Candidate (WTC) algorithm is a generalisation of an expert identification method. The axiomatic characterisation of WTC shows why it is especially suitable for scientometric purposes. The key axiom is stability - the selected institutions support each other's membership. The WTC algorithm, upon receiving an institution citation matrix, produces a list of institutions that can be deemed experts of the field. With a parameter we can adjust how exclusive our list should be. By completely relaxing the parameter, we obtain the largest stable set - academic entities that can qualify as experts under the mildest conditions. With a strict setup, we obtain a short list of the absolute elite. We demonstrate the algorithm on a citation database compiled from game theoretic literature published between 2008-2017. By plotting the size of the stable sets with respect to exclusiveness, we can obtain an overview of the competitiveness of the field. The diagram hints at how difficult it is for an institution to improve its position.