On Social Welfare Functions on Infinite Utility Streams Satisfying Hammond Equity and Weak Pareto Axioms : A Complete Characterization

This paper examines the problem of aggregating infinite utility streams with a social welfare function that respects the Hammond Equity and Weak Pareto Axioms. The paper provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Hammond Equity and Weak Pareto Axioms exists on precisely those domains which are well-ordered sets in which the elements of the set are ordered according to the decreasing magnitude of the numbers belonging to the set. We show through examples how this characterization can be applied to obtain a number of results in the literature, as well as some new ones