Additively-separable and rank-discounted variable-population social welfare functions: A characterization

Economic policy evaluations require social welfare functions for variable-size populations. Two important candidates are critical-level generalized utilitarianism (CLGU) and rank-discounted critical-level generalized utilitarianism, which was recently characterized by Asheim and Zuber (2014) (AZ). AZ introduce a novel axiom, existence of egalitarian equivalence (EEE). First, we show that, under some uncontroversial criteria for a plausible social welfare relation, EEE suffices to rule out the Repugnant Conclusion of population ethics (without AZ’s other novel axioms). Second, we provide a new characterization of CLGU: AZ’s set of axioms is equivalent to CLGU when EEE is replaced by the axiom same-number independence. •One candidate social welfare function is critical-level generalized utilitarianism (CLGU).•Another is rank-discounted generalized utilitarianism (RDGU).•Asheim & Zuber characterize RDGU with Existence of egalitarian equivalence (EEE) and others.•We prove: EEE (plus widely accepted axioms) is sufficient to avoid the repugnant conclusion.•We prove: replacing EEE with Same-number separability in A&Z’s characterization yields CLGU.