Journal of Economic Literature Classification Numbers: D60, D70, D90.

The paper examines the problem of aggregating infinite utility streams with a social welfare function which respects the Anonymity and Weak Pareto Axioms. It provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Anonymity and Weak Pareto Axioms exists on precisely those domains which do not contain any set of the order type of the set of positive and negative integers. The criterion is applied to decide on possibility and impossibility results for a variety of domains. It is also used to provide an alternative formulation of the characterization result in terms of the accumulation points of the domain