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- Title
A THEORY OF DIVERSITY.
- Authors
Nehring, Klaus; Puppe, Clements
- Abstract
How can diversity be measured? What does it mean to value biodiversity? Can we assist Noah in constructing his preferences? To address these questions, we propose a multi- attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set. We develop the basic intuitions and requirements for a theory of diversity and show that the multi-attribute approach satisfies them in a flexible yet tractable manner. A natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements. The multi-attribute framework allows one to make this program formally precise. It is shown that the program can be realized if and only if the family of relevant attributes is well-ordered ("acyclic"). Moreover, there is a unique functional form aggregating dissimilarity into diversity, the length of a minimum spanning tree. Examples are taxonomic hierarchies and lines representing unidimensional qualities. In multi-dimensional settings, pairwise dissimilarity information among elements is insufficient to determine their diversity. By consequence, the qualitative and quantitative behavior of diversity differs fundamentally.
- Subjects
BIODIVERSITY; ENDANGERED species; THEORY; TECHNICAL specifications; FAMILIES; ORDER
- Publication
Econometrica, 2002, Vol 70, Issue 3, p1155
- ISSN
0012-9682
- Publication type
Article
- DOI
10.1111/1468-0262.00321