Functional equations and population ethics
The authors offer characterizations of social orderings of different states of variable size. The orderings may depend on length of life and lifetime utility of individuals. Axioms such as Independence of the Utilities of the Dead, Pareto Conditions, Anonimity Conditions (independence under permutation of individuals and of lifetimes), Continuity, (Weak) Existence of Critical Levels (rules out degenerate cases), Lifetime Substitution (existence of trade-offs between length of life and lifetime utility) are stated and consequences explored. The functional equations applied are of \(f(x)+g(y) = h(x+y)\) (Pexider) and \(F[G(x,y),z]=H[x,K(y,z)]\) (generalized associativity) types. The main results are two inequalities as necessary and sufficient conditions for two systems of axioms to be satisfied.
generalized assocativity and bisymmetry equations
scientific article; zbMATH DE number 1383754