Social Welfare Evaluation and Intergenerational Equity

This chapter presents a brief overview of the axiomatic analysis of social evaluation criteria for intra- and intergenerational utility distributions. Analyzing finite-horizon and infinite-horizon utility distributions instead of social alternatives is called the “welfarist approach,” which has a firm theoretical background in social choice theory. Our main concern in analyzing the evaluation criteria for infinite-horizon utility distributions will be the logical compatibility between the two basic axioms requiring the efficiency and impartiality of the evaluation: the strong Pareto principle and an anonymity axiom.

This chapter examines the axiomatic foundations of social welfare orderings and quasi-orderings for intragenerational utility distributions assuming that the population size is fixed and finite. Utilitarianism, the leximin and maximin principles, and their compromises formulated in the forms of lexicographic composition and convex combination are, respectively, axiomatized using several versions of equity axioms as well as Pareto and anonymity axioms. Diagrammatic proofs are given for some of the results. Important in its own right, this chapter is also intended to serve as preliminary to the analysis of intergenerational welfare evaluation in the subsequent chapters.

This chapter analyzes intergenerational social welfare evaluation for infinite utility streams. An infinite utility stream represents an intergenerational utility distribution where each component corresponds to the utility level of each generation. We will establish some general results that show how a social welfare evaluation applied to utilities of the finite number of generations can be extended to a finitely anonymous infinite-horizon social welfare evaluation. Using the general results and axiomatizations of a specific social welfare ordering or quasi-ordering, we will present axiomatic characterizations of specific forms of an infinite-horizon extension of a finite-horizon social welfare evaluation.

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.

This chapter presents an extended framework for social evaluation with variable population size. We establish the welfarism theorem in the extended framework. Then, using the welfarist framework, we will present and axiomatize infinite-horizon extensions of critical-level generalized utilitarianism. The population ethics property of infinite-horizon extensions of critical-level generalized utilitarianism will be discussed.

This chapter discusses further issues regarding intergenerational social welfare evaluation that are not covered in the previous chapters. First, we review the analysis of representable social welfare orderings and the possibility of strongly anonymous social welfare orderings. Second, we will discusses a choice-theoretic approach to intergenerational resource allocation problems with variable population size.