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

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.

Aggregating Infinite Utility Streams with Inter-generational Equity: The Impossibility of Being Paretian

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, inter-generational equity and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in frameworks allowing for more general domains of utilities than those used in the existing literature.

Possibility Theorems for Aggregating Infinite Utility Streams Equitably

The standard route for aggregating infinite utility streams using a real-valued representation runs into well-known difficulties as soon as we insist on the axiom of inter-generational equity. The aim of this paper is to explore what is feasible without abandoning this axiom. The paper focusses its attention on the Pareto axiom and domain restrictions. It turns out that once we weaken these requirements, realvalued aggregation becomes possible in a variety of ways (though, of course, impossibility results lurk everywhere). By establishing a series of results, this paper tries to chalk out the frontier between what is possible and what is not.