Abstract
The existence of a Paretian and finitely anonymous ordering in the set of infinite utility streams implies the existence of a non-Ramsey set (a non-constructive object whose existence requires The Axiom of Choice). Therefore, each Paretian and finitely anonymous quasi-ordering either is incomplete or does not have an explicit description. Hence, the possibility results of Svensson [Svensson, L.G., 1980. Equity among generations. Econometrica 48, 1251–1256] and of Bossert et al. [Bossert, W., Sprumont, Y., Suzumura, K., 2007. Ordering infinite utility streams. Journal of Economic Theory 135 (1), 579–589] do require The Axiom of Choice.
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