In this paper, we study intertemporal social welfare evaluations when agents have heterogeneous preferences that are interpersonally noncomparable. We first show that even if all agents share the same preferences, there is a conflict between the axioms of Pareto principle, time consistency, and equity requiring society to reduce inequality regardless of the past. We argue that responsibility for past choices should be taken into account and, thus, the equity axiom is not compelling. Then we introduce another form of equity that takes the past into consideration and is compatible with time consistency. Using this form of equity and time consistency, we characterize maximin and leximin social welfare criteria that are history‐dependent.