On Representation and Construction of Equitable Social Welfare Orders on Infinite Utility Streams

Abstract

This paper studies the nature of social welfare orders on infinite utility streams, satisfying the consequentialist equity principles known as Hammond Equity and Pigou-Dalton transfer principle. The first result shows that every social welfare order satisfying Hammond Equity and the Strong Pareto axioms is non-constructive in nature for all non-trivial domains, Y. It also constitutes another instance of the correspondence principle. The second result of this paper shows that the existence of a social welfare order satisfying Pigou-Dalton transfer principle necessarily entails the existence of a non-Ramsey set, a non-constructive object. The second result is also an example of a representable social welfare order which cannot be constructed.