Extended Anonymity and Intergenerational Social Welfare Evaluation

Abstract

This chapter examines an extended anonymity axiom that is compatible with a strongly Paretian relation for infinite utility streams. It is well-known that the cyclicity of a permutation and the group structure of a set of permutations are both necessary and sufficient for the resulting anonymity axiom to be compatible with a Paretian social welfare quasi-ordering. The set of fixed-step permutations is an example of a group of cyclic permutations. Using the same analytical framework as that used in the previous chapter, we first examine an algebraic structure of a set of permutations that can be used to define a Pareto-compatible anonymity axiom. Then, using anonymity axioms defined by a group of cyclic permutations or the set of fixed-step permutations, we will consider general forms of a social welfare quasi-ordering that satisfy the extended anonymity axioms. Our main results are general characterizations of those general social welfare quasi-orderings. Using the general results, we will present axiomatizations of specific social welfare quasi-orderings that are associated with a sequence of specific finite-horizon social welfare orderings or quasi-orderings.KeywordsExtended anonymityFixed-step anonymityUtilitarianismLeximinGeneralized Pareto axiom