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Maximal Social Welfare Relations on Infinite Populations Satisfying Permutation Invariance

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  • Jeremy Goodman
  • Harvey Lederman

Abstract

We study social welfare relations (SWRs) on infinite utility streams. Our main result is a new characterization of a utilitarian SWR on lotteries over welfare distributions for an infinite population. We characterize this SWR as the maximally complete SWR over lotteries on such distributions which satisfies Strong Pareto, Permutation Invariance (elsewhere called "Relative Anonymity" and "Isomorphism Invariance"), Dominance, Ex Ante Indifference, and an Additive Invariance axiom.

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  • Jeremy Goodman & Harvey Lederman, 2024. "Maximal Social Welfare Relations on Infinite Populations Satisfying Permutation Invariance," Papers 2408.05851, arXiv.org.
    • Handle: RePEc:arx:papers:2408.05851
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    1. Geir B. Asheim, 2010. "Intergenerational Equity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 197-222, September.
    2. Asheim, Geir B. & d'Aspremont, Claude & Banerjee, Kuntal, 2010. "Generalized time-invariant overtaking," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 519-533, July.
    3. 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.
    4. , R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    5. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75(5), pages 765-765.
    6. 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.
    7. 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.
    8. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    9. 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.
    10. Van Liedekerke, Luc & Lauwers, Luc, 1997. "Sacrificing the Patrol: Utilitarianism, Future Generations and Infinity," Economics and Philosophy, Cambridge University Press, vol. 13(2), pages 159-174, October.
    11. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    12. Lauwers, Luc, 1998. "Intertemporal objective functions: Strong pareto versus anonymity," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 37-55, January.
    13. Lauwers, Luc & Vallentyne, Peter, 2004. "Infinite Utilitarianism: More Is Always Better," Economics and Philosophy, Cambridge University Press, vol. 20(2), pages 307-330, October.
    14. Pivato, Marcus & Fleurbaey, Marc, 2024. "Intergenerational equity and infinite-population ethics: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).
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