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Fleurbaey-Michel conjecture on equitable weak Paretian social welfare order. (English) Zbl 1236.91063
Summary: The paper examines the problem of explicit description of a social welfare order over infinite utility streams, which respects anonymity and weak Pareto axioms. It provides a complete characterization of the domains of one period utilities, for which it is possible to explicitly describe a weak Paretian social welfare order satisfying the anonymity axiom. For domains containing any set of order type similar to the set of positive and negative integers, every equitable social welfare order satisfying the weak Pareto axiom is non-constructive. The paper resolves a conjecture by M. Fleurbaey and P. Michel [J. Math. Econ. 39, No. 7, 777–802 (2003; Zbl 1046.91104)] that there exists no explicit (that is, avoiding the axiom of choice or similar contrivances) description of an ordering which satisfies weak Pareto and indifference to finite permutations. It also provides an interesting connection between the existence of social welfare function and the constructive nature of social welfare order by showing that the domain restrictions for the two are identical.

91B14 Social choice
91B15 Welfare economics
Full Text: DOI
[1] Basu, K.; Mitra, T., Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian, Econometrica, 71, 5, 1557-1563, (2003) · Zbl 1153.91648
[2] Crespo, J.A.; Núñez, C.; Rincón-Zapatero, J.P., On the impossibility of representing infinite utility streams, Economic theory, 40, 1, 47-56, (2009) · Zbl 1159.91010
[3] Diamond, P., The evaluation of infinite utility streams, Econometrica, 33, 1, 170-177, (1965) · Zbl 0127.36602
[4] Dubey, R.S., Mitra, T., 2011. On equitable social welfare functions satisfying the weak pareto axiom: a complete characterization. International Journal of Economic Theory, forthcoming (doi:10.1111/j.1742-7363.2011.00161.x).
[5] Fleurbaey, M.; Michel, P., Intertemporal equity and the extension of the Ramsey criterion, Journal of mathematical economics, 39, 7, 777-802, (2003) · Zbl 1046.91104
[6] Halpern, J., The independence of the axiom of choice from the Boolean prime ideal theorem, Fundamenta mathematicae, 55, 57-66, (1964) · Zbl 0151.01002
[7] Koopmans, T., Stationary ordinal utility and impatience, Econometrica, 28, 2, 287-309, (1960) · Zbl 0149.38401
[8] Koopmans, T.; Diamond, P.; Williamson, R., Stationary utility and time perspective, Econometrica, 32, 1, 82-100, (1964) · Zbl 0131.18603
[9] Lauwers, L., Ordering infinite utility streams comes at the cost of a non-Ramsey set, Journal of mathematical economics, 46, 1, 32-37, (2010) · Zbl 1197.91085
[10] Mathias, A., Happy families, Annals of mathematical logic, 12, 1, 59-111, (1977) · Zbl 0369.02041
[11] Ramsey, F.P., On a problem of formal logic, Proceedings of the London mathematical society, 2, 1, 264-286, (1928) · JFM 55.0032.04
[12] Sierpinski, W., Cardinal and ordinal numbers, (1965), PWN-Polish Scientific Publishers · Zbl 0131.24801
[13] Svensson, L., Equity among generations, Econometrica, 48, 5, 1251-1256, (1980) · Zbl 0436.90029
[14] Szpilrajn, E., Sur l’extension de l’ordre partiel, Fundamenta mathematicae, 16, 386-389, (1930) · JFM 56.0843.02
[15] Zame, W., Can utilitarianism be operationalized?, Theoretical economics, 2, 187-202, (2007)
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