On the Representation and Construction of Equitable Social Welfare Orders

TL;DR

This paper investigates the representation of social welfare orders on infinite utility streams, proving that such orders cannot be explicitly represented with real values and are linked to non-constructive non-Ramsey sets.

Contribution

It establishes the non-existence of real-valued representations for certain social welfare orders satisfying specific axioms and connects their existence to non-constructive set theory.

Findings

No real-valued representation exists for the social welfare orders studied.

Existence of such orders implies the existence of a non-Ramsey set.

These orders cannot be explicitly described.

Abstract

This paper examines the representation and explicit description of social welfare orders on infinite utility streams. It is assumed that the social welfare orders under investigation satisfy upper asymptotic Pareto and anonymity axioms. We prove that there exists no real-valued representation of such social welfare orders. In addition, we establish that the existence of a social welfare order satisfying the anonymity and upper asymptotic Pareto axioms implies the existence of a non-Ramsey set, which is a non-constructive object. Thus, we conclude that the social welfare orders under study do not admit explicit description.