On the Existence of Paretian Social Welfare Relations for Infinite Utility Streams with Extended Anonymity

Abstract

In this paper, we examine the restrictions that any concept of extended anonymity must satisfy in order to be compatible with the existence of a Paretian social welfare relation (SWR). We completely characterize the class of permissible permutations associated with any Paretian SWR; that is, those permutations with respect to which every utility stream is pronounced to be indifferent to the corresponding permuted utility stream, according to the Paretian SWR. Based on the characterization result, we propose a particular class of extensions of anonymity, which allows comparisons of utility streams that are related to each other by an infinite number of permutations of a specific type. The merits of this particular class of extensions are discussed.