A Theory of Diversity

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 uni‐dimensional 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.     

Preference for Flexibility in a Savage Framework

We study preferences over Savage acts that map states to opportunity sets and satisfy the Savage axioms. Preferences over opportunity sets may exhibit a preference for flexibility due to an implicit uncertainty about future preferences reflecting anticipated unforeseen contingencies. The main result of this paper characterizes maximization of the expected indirect utility in terms of an ‘Indirect Stochastic Dominance’ axiom that expresses a preference for ‘more opportunities in expectation.’ The key technical tool of the paper, a version of Möbius inversion, has been imported from the theory of nonadditive belief functions; it allows an alternative representation using Choquet integration, and yields a simple proof of Kreps' (1979) classic result.     

JOINT PRODUCT COST ALLOCATION IN THE CONTEXT OF COST-PLUS PRICING DETERMINATIONS WITH NON-UNIFORM MARKUPS

Companies that use cost-based pricing sometimes manufacture products that involve joint cost allocation. A problem with this is that, while product prices are a function of the full cost, joint cost allocation methods using net realizable values depend on the product prices. This paper demonstrates that when all costs and production quantities are known or can be budgeted, it is possible to simultaneously determine unique product prices (having non-uniform markup rates) and cost allocations using the net realizable value method.