Infinite-horizon social evaluation with variable population size

Abstract

We present an infinite-horizon extension of the framework of variable-population social choice. Our first main result is the welfarism theorem using the axiom of intratemporal anonymity. By this theorem, the ranking of social alternatives is determined by an intratemporally anonymous and finitely complete quasi-ordering [which we call social welfare relation (SWR)] defined on the set of all streams of utility vectors of generations. We introduce three SWRs: the critical-level generalized utilitarian (CLGU) SWR, the critical-level generalized overtaking (CLGO) SWR, and the critical-level generalized catching-up (CLGC) SWR. They are infinite-horizon extensions of the critical-level generalized utilitarianism. We characterize (in terms of subrelation) the CLGU SWR with five axioms: Strong Pareto, Finite Anonymity, Weak Existence of Critical Levels, Restricted Continuity, and Existence Independence. Further, the CLGO and the CLGC SWRs are characterized by adding consistency axioms. We also present infinite-horizon reformulations of some population ethics axioms. In particular, we characterize the CLGO and the CLGC SWRs associated with a positive critical level by using the axiom of avoidance of the repugnant conclusion.