When considering the social valuation of a life-year, there is a conflict between two basic intuitions: on the one hand, the intuition of universality, according to which the value of an additional life-year should be universal, and, as such, should be invariant to the context considered; on the other hand, the intuition of complementarity, according to which the value of a life-year should depend on what this extra life-year allows for, and, hence, on the quality of that life-year, because the quantity of life and the quality of life are complement to each other. This paper proposes three distinct accounts of the intuition of universality, and shows that those accounts either conflict with a basic monotonicity property, or lead to indifference with respect to how life-years are distributed within the population. Those results support the abandon of the intuition of universality. But abandoning the intuition of universality does not prevent a social evaluator from giving priority, when allocating life-years, to individuals with the lowest quality of life.