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Maximal sensitivity under Strong Anonymity

Author

Listed:
  • Geir Asheim

    (UiO - University of Oslo)

  • Kohei Kamaga

    (Sophia University [Tokyo])

  • Stéphane Zuber

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper re-examines the incompatibility of Strong Pareto, as an axiom of sensitivity, and Strong Anonymity, as an axiom of impartiality, when comparing well-being profiles with a countably infinite number of components. We ask how far the Paretian principle can be extended without contradicting Strong Anonymity. We show that Strong Anonymity combined with four auxiliary axioms has two consequences: (i) There is sensitivity for an increase in one well-being component if and only if a co-finite set of other well-being components are at least ɛ (>0) higher, and (ii) adding people to an infinite population cannot have positive social value.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Geir Asheim & Kohei Kamaga & Stéphane Zuber, 2022. "Maximal sensitivity under Strong Anonymity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03856615, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03856615
    DOI: 10.1016/j.jmateco.2022.102768
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03856615
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    References listed on IDEAS

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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. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587, October.
    3. 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.
    4. Geir Asheim & Stéphane Zuber, 2013. "A complete and strongly anonymous leximin relation on infinite streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 819-834, October.
    5. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1995. "Intertemporal Population Ethics: Critical-Level Utilitarian Principles," Econometrica, Econometric Society, vol. 63(6), pages 1303-1320, November.
    6. Lauwers, Luc, 1998. "Intertemporal objective functions: Strong pareto versus anonymity," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 37-55, January.
    7. Geir B. Asheim & Kohei Kamaga & Stéphane Zuber, 2022. "Evaluating Climate Policies by the Pareto Principle: Efficiency When Future Identities Are Unobservable," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03760333, HAL.
    8. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
    9. 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.
    10. Feng, Tangren & Ke, Shaowei & McMillan, Andrew, 2022. "Utilitarianism and social discounting with countably many generations," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    11. Tapan Mitra & Kaushik Basu, 2007. "On the Existence of Paretian Social Welfare Quasi-Orderings for Infinite Utility Streams with Extended Anonymity," International Economic Association Series, in: John Roemer & Kotaro Suzumura (ed.), Intergenerational Equity and Sustainability, chapter 6, pages 85-99, Palgrave Macmillan.
    12. Hamkins, Joel David & Montero, Barbara, 2000. "Utilitarianism in Infinite Worlds," Utilitas, Cambridge University Press, vol. 12(1), pages 91-96, March.
    13. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    14. 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.
    15. Geir B. Asheim & Kohei Kamaga & Stéphane Zuber, 2022. "Infinite Population Utilitarian Criteria," CESifo Working Paper Series 9576, CESifo.
    16. Luc Lauwers, 2016. "Intergenerational Equity, Efficiency, and Constructibility," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 191-206, Springer.
    17. Blackorby, Charles & Donaldson, David, 1984. "Social criteria for evaluating population change," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 13-33, November.
    18. Sakai, Toyotaka, 2010. "A characterization and an impossibility of finite length anonymity for infinite generations," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 877-883, September.
    19. 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.
    20. Geir Asheim & Bertil Tungodden, 2004. "Resolving distributional conflicts between generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 221-230, July.
    21. Deschamps, Robert & Gevers, Louis, 1978. "Leximin and utilitarian rules: A joint characterization," Journal of Economic Theory, Elsevier, vol. 17(2), pages 143-163, April.
    22. 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.
    23. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
    24. Toyotaka Sakai, 2016. "Limit representations of intergenerational equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 481-500, August.
    25. 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.
    26. , R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    27. Luc Lauwers, 1997. "Continuity and equity with infinite horizons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 345-356.
    28. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
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