On the construction and representation of social welfare orders satisfying consequentialist equity axioms

In this paper we examine the constructive nature of social welfare orders on infinite utility streams $X=Y^{\mathbb{N}}$ satisfying Strong Equity, Hammond Equity, or the Pigou–Dalton transfer principle. The constructive social welfare orders are described using lexicographic preference relations. Social welfare orders satisfying Strong Equity, Hammond Equity, or the Pigou–Dalton transfer principle admit explicit descriptions when $Y(<)$ is well-ordered. We describe restrictions on the domain $Y$ under which the existence of social welfare orders satisfying the aforementioned equity axioms entails the existence of a non-Ramsey collection. For this, we rely on the existence of a non-Ramsey collection, which is treated here as a nonconstructive object.