Template-Type:ReDIF-Paper 1.0
Title: A Theory of Diversity
Author-Name: Nehring,K. und C.Puppe
Author-Postal: Prof.Dr.Clemens Puppe
	Universitaet Bonn
	Wirtschaftstheorie III
	Adenauerallee 24-42
	D-53113 Bonn
Author-Phone: 0228 735747
Author-Homepage: 
Classification-JEL: D 11
Keywords: Diveristy, endangered species, similarity, set function, conjugate Moebius inversion
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.
Length:   pages
Creation-Date: 1999-09
Revision-Date: 
Handle: RePEc:bon:bonsfa:605