Equity between overlapping generations

This note is a demonstration that, in the presence of overlapping generations and under standard conditions for a social welfare ordering (Pareto optimality, transitivity, independence), the only ordering consistent with utilitarianism for all people currently alive at any given point in time is one based on weighting all people equally, regardless of their date of birth. In particular, this implies that, under reasonable conditions, the appropriate choice for the pure rate of social time preference is equal to zero.