Pareto Principle and Intergenerational Equity : Immedi - ate

In an important contribution to the problem of aggregating infinite utility streams, Svensson (1980) shows the existence of a social welfare relation—a reflexive, transitive and complete binary relation over all possible infinite utility streams—that accommodates the axioms of Pareto and intergenerational equity. This possibility result is in sharp contrast with the seminal contribution by Diamond (1965) in the same context of aggregating infinite utility streams, who established the non-existence of a social welfare function—a function which aggregates an infinite utility stream into a real number—that satisfies the axioms of Pareto, intergenerational equity and continuity (in the sup metric). The axiom of continuity in Diamond’s result is shown to be redundant by Basu and Mitra (2003) recently: they show that, in aggregating infinite utility streams, there exists no social welfare function satisfying the axioms of Pareto and intergenerational equity. The possibility result by Svensson suggests the compatibility of the Pareto principle and intergenerational equity for a social welfare relation, while the impossibility results by Diamond, and Basu and Mitra suggest that the compatibility of the Pareto principle and intergenerational equity breaks down when a social welfare relation is replaced by a social welfare function. Though the possibility of accommodating both the Pareto principle and intergenerational equity for a social welfare relation in aggregating infinite utility streams can be obtained, it is not clear what structure such a social welfare relation may have and to what extent the possibility may be obtained. This is because, in proving his possibility result, Svensson uses a non-constructive method by making use of Szpilrajn’s lemma on extending a reflexive and transitive binary relation to a reflexive, transitive and complete binary relation. The purpose of this paper is therefore two-fold. First, we examine the scope of obtaining the possibility result for a social welfare relation to be