Translation invariance when utility streams are infinite and unbounded

The translation‐invariance axiom consists in asserting the invariance of the ranking of two utility streams if one applies the same translation to both. This axiom is significant in the characterization of utilitarian criteria in finite dimension. This characterization is achieved thanks to the weak weighted utilitarianism theorem. The objective here is to extend this theorem to a space of infinite and unbounded utility streams. In the context of intergenerational choice, a consequence of the suggested generalization is that every maximal point with respect to a Paretian utilitarian order granting comparable considerations to the present and the future, is also a maximal point with respect to some future‐oriented criterion.