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Ordering infinite utility streams comes at the cost of a non-Ramsey set. (English) Zbl 1197.91085
Summary: 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 L.-G. Svensson [Econometrica 48, 1251–1256 (1980; Zbl 0436.90029)] and of W. Bossert, Y. Sprumont and K. Suzumura [J. Econ. Theory 135, No. 1, 579–589 (2007; Zbl 1186.91086)] do require the Axiom of Choice.

MSC:
91B14 Social choice
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