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Fleurbaey–Michel conjecture on equitable weak Paretian social welfare order

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  • Dubey, Ram Sewak
Abstract
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 Fleurbaey and Michel (2003) 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.

Suggested Citation

  • Dubey, Ram Sewak, 2011. "Fleurbaey–Michel conjecture on equitable weak Paretian social welfare order," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 434-439.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:434-439
    DOI: 10.1016/j.jmateco.2011.05.003
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    References listed on IDEAS

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    1. Fleurbaey, Marc & Michel, Philippe, 2003. "Intertemporal equity and the extension of the Ramsey criterion," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 777-802, September.
    2. Ram Sewak Dubey & Tapan Mitra, 2011. "On equitable social welfare functions satisfying the Weak Pareto Axiom: A complete characterization," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 231-250, September.
    3. Juan Crespo & Carmelo Nuñez & Juan Rincón-Zapatero, 2009. "On the impossibility of representing infinite utility streams," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 47-56, July.
    4. Kaushik Basu & Tapan Mitra, 2003. "Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian," Econometrica, Econometric Society, vol. 71(5), pages 1557-1563, September.
    5. Lauwers, Luc, 2010. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 32-37, January.
    6. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
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    Citations

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    Cited by:

    1. José Carlos R. Alcantud, 2013. "The impossibility of social evaluations of infinite streams with strict inequality aversion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 123-130, November.
    2. Dubey, Ram Sewak & Laguzzi, Giorgio & Ruscitti, Francesco, 2021. "On social welfare orders satisfying anonymity and asymptotic density-one Pareto," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 26-33.
    3. José Carlos R. Alcantud & María D. García-Sanz, 2013. "Evaluations of Infinite Utility Streams: Pareto Efficient and Egalitarian Axiomatics," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 432-447, July.
    4. Dubey, Ram Sewak, 2016. "A Note On Social Welfare Orders Satisfying Pigou-Dalton Transfer Principle," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(2), pages 243-262, December.
    5. Ram Dubey & Tapan Mitra, 2014. "Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 591-602, October.
    6. Adachi, Tsuyoshi & Cato, Susumu & Kamaga, Kohei, 2014. "Extended anonymity and Paretian relations on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 24-32.
    7. Dubey, Ram Sewak, 2016. "On construction of social welfare orders satisfying Hammond equity and Weak Pareto axioms," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 119-124.
    8. Pivato, Marcus, 2022. "A characterization of Cesàro average utility," Journal of Economic Theory, Elsevier, vol. 201(C).
    9. Dubey, Ram Sewak & Mitra, Tapan, 2014. "On construction of equitable social welfare orders on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 53-60.
    10. Jeremy Goodman & Harvey Lederman, 2024. "Maximal Social Welfare Relations on Infinite Populations Satisfying Permutation Invariance," Papers 2408.05851, arXiv.org, revised Nov 2024.
    11. Kohei Kamaga, 2016. "Infinite-horizon social evaluation with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 207-232, June.

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