Diversity and dissimilarity in lines and hierarchies

Within the multi-attribute framework of Nehring and Puppe [Econometrica, 70 (2002) 1155], hierarchies and lines represent the simplest and most fundamental models of diversity. In both cases, the diversity of any set can be recursively determined from the pairwise dissimilarities between its elements. The present paper characterizes the restrictions on the dissimilarity metric entailed by the two models. In the hierarchical case, this generalizes a classical result on the representation of ultrametric distance functions.  2003 Elsevier Science B.V. All rights reserved.