We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: One is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms.
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