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

2026-06-22

AI Summary

This study investigates the construction of social welfare orderings over infinite utility streams that satisfy consequentialist fairness axioms—specifically, strong equity, Hammond equity, or the Pigou–Dalton transfer principle. By employing lexicographic preference relations, the paper provides the first explicit construction of such social welfare orderings under well-ordered utility domains. Its central contribution lies in demonstrating that the existence of these orderings is equivalent to the existence of non-Ramsey sets, thereby revealing their inherently non-constructive nature. Furthermore, the work elucidates a deep logical connection between fairness criteria and the Axiom of Choice through tools from ordinal theory and set theory.

Abstract

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.

Problem

• social welfare orders
• consequentialist equity axioms
• Strong Equity
• Hammond Equity
• Pigou-Dalton transfer principle

Innovation

• constructive social welfare orders
• consequentialist equity axioms
• lexicographic preferences
• non-Ramsey sets
• infinite utility streams