A Theory of Diversity

K. und C.Puppe Nehring
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K. und C.Puppe Nehring: Postal: Prof.Dr.Clemens Puppe Universitaet Bonn Wirtschaftstheorie III Adenauerallee 24-42 D-53113 Bonn

Discussion Paper Serie A from University of Bonn, Germany

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 following Weitzman (1992,1998), 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 highly flexible yet tractable manner. Conjugate Moebius inversion serves as the unifying mathematical tool. A basic starting point is to think of the diversity of a set as an aggregate of the dissimilarities between its elements. This intuition is made formally precise, and the exact conditions of itsapplicability are characterized: the family of relevant attributes must satisfy a condition of acyclicity. The two most important attribute structures satisfying acyclicity, taxonomic hierarchies and lines representing uni-dimensional qualities, are studied in depth, and the entailed restrictions on the dissimilarity metric are characterized. In multi-dimensional settings, pairwise dissimilarity information among elements is typically insufficient to determine the diversity of their set. Using a parametrization of the hypercube as the simplest high-dimensional model, we discuss the new issues and phenomena that arise. Even simple instances of Noah's choice problem become combinatorially complex, and the quantitative behaviour of diversity differs fundamentally.

Keywords: Diveristy; endangered species; similarity; set function; conjugate Moebius inversion (search for similar items in EconPapers)
JEL-codes: D (search for similar items in EconPapers)
Date: Written 1999-09

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