On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams

There exists a utilitarian tradition la Sidgwick of treating equal generations equally in the form of anonymity. Diamond showed that no social evaluation ordering over infinite utility streams satisfying the Pareto principle, Sidgwick's equity principle, and the axiom of continuity exists. We introduce two versions of egalitarianism in the spirit of the Pigou-Dalton transfer principle and the Lorenz domination principle, and examine their compatibility with the weak Pareto principle in the presence of a semi-continuity axiom. The social evaluation relation is not assumed to be either complete or transitive, yet Diamond's impossibility strenuously resurfaces.