Ordering infinite utility streams comes at the cost of a non-Ramsey set

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 nonconstructive 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 (1980) and of Bossert, Sprumont, and Suzumura (2006) do require the axiom of choice.