Classical retrieval and overlap measures satisfy the requirements for rankings based on a Lorenz curve

Classical information retrieval and overlap measures such as the Jaccard index, the Dice coefficient and Salton’s cosine measure can be characterized by Lorenz curves. This result demonstrates the existence of a formal link between information retrieval and the information sciences on the one hand, and concentration and diversity theory, as used, e.g., in social economics and ecology on the other.