Maximal sensitivity under Strong Anonymity

This paper re-examines the incompatibility of Strong Pareto, as an axiom of sensitivity, and Strong Anonymity, as an axiom of impartiality, when comparing well-being profiles with a countably infinite number of components. We ask how far the Paretian principle can be extended without contradicting Strong Anonymity. We show that Strong Anonymity combined with four auxiliary axioms has two consequences: (i) There is sensitivity for an increase in one well-being component if and only if a co-finite set of other well-being components are at least ɛ (>0) higher, and (ii) adding people to an infinite population cannot have positive social value.