IDEAS home Printed from https://ideas.repec.org/p/ecl/corcae/05-06.html
   My bibliography  Save this paper

On the Existence of Paretian Social Welfare Relations for Infinite Utility Streams with Extended Anonymity

Author

Listed:
  • Basu, Kaushik

    (Cornell U)

  • Mitra, Tapan

    (Cornell U)

Abstract

In this paper, we examine the restrictions that any concept of extended anonymity must satisfy in order to be compatible with the existence of a Paretian social welfare relation (SWR). We completely characterize the class of permissible permutations associated with any Paretian SWR; that is, those permutations with respect to which every utility stream is pronounced to be indifferent to the corresponding permuted utility stream, according to the Paretian SWR. Based on the characterization result, we propose a particular class of extensions of anonymity, which allows comparisons of utility streams that are related to each other by an infinite number of permutations of a specific type. The merits of this particular class of extensions are discussed.

Suggested Citation

  • Basu, Kaushik & Mitra, Tapan, 2005. "On the Existence of Paretian Social Welfare Relations for Infinite Utility Streams with Extended Anonymity," Working Papers 05-06, Cornell University, Center for Analytic Economics.
    • Handle: RePEc:ecl:corcae:05-06
    as

    Download full text from publisher

    File URL: https://cae.economics.cornell.edu/05-06.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lauwers, Luc, 1995. "Time-neutrality and linearity," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 347-351.
    2. 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.
    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. Asheim, Geir B. & Buchholz, Wolfgang & Tungodden, Bertil, 2001. "Justifying Sustainability," Journal of Environmental Economics and Management, Elsevier, vol. 41(3), pages 252-268, May.
    5. Luc Lauwers, 1996. "Rawlsian equity and generalised utilitarianism with an infinite population (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 143-150.
    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. 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.
    8. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    9. Lauwers, Luc, 1998. "Intertemporal objective functions: Strong pareto versus anonymity," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 37-55, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    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. 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.
    5. Mohamed Ben Ridha Mabrouk, 2011. "Translation invariance when utility streams are infinite and unbounded," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(4), pages 317-329, December.
    6. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations," GE, Growth, Math methods 0511007, University Library of Munich, Germany.
    7. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality," GE, Growth, Math methods 0510013, University Library of Munich, Germany.
    8. Geir B. Asheim & Kuntal Banerjee, 2010. "Fixed‐step anonymous overtaking and catching‐up," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 149-165, March.
    9. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 393-414, September.
    10. Mabrouk, Mohamed, 2009. "On the extension of a preorder under translation invariance," MPRA Paper 15407, University Library of Munich, Germany.
    11. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    12. Kohei Kamaga & Takashi Kojima, 2010. "On the leximin and utilitarian overtaking criteria with extended anonymity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 377-392, September.
    13. Mabrouk, Mohamed, 2006. "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality," MPRA Paper 10512, University Library of Munich, Germany.
    14. Kohei Kamaga & Takashi Kojima, 2009. "$${\mathcal{Q}}$$ -anonymous social welfare relations on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 405-413, September.
    15. Susumu Cato, 2009. "Characterizing the Nash social welfare relation for infinite utility streams: a note," Economics Bulletin, AccessEcon, vol. 29(3), pages 2372-2379.
    16. Kuntal Banerjee, 2006. "On the Extension of the Utilitarian and Suppes–Sen Social Welfare Relations to Infinite Utility Streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 327-339, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Asheim, Geir B. & Kamaga, Kohei & Zuber, Stéphane, 2022. "Maximal sensitivity under Strong Anonymity," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. Geir B. Asheim & Tapan Mitra & Bertil Tungodden, 2016. "Sustainable Recursive Social Welfare Functions," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 165-190, Springer.
    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. 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.
    5. Jonsson, Adam & Voorneveld, Mark, 2018. "The limit of discounted utilitarianism," Theoretical Economics, Econometric Society, vol. 13(1), January.
    6. 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.
    7. 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.
    8. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2009. "A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 154-168, September.
    9. Geir B. Asheim & Kuntal Banerjee, 2010. "Fixed‐step anonymous overtaking and catching‐up," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 149-165, March.
    10. Basu, Kaushik & Mitra, Tapan, 2007. "Utilitarianism for infinite utility streams: A new welfare criterion and its axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 350-373, March.
    11. 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.
    12. Claude, d’ASPREMONT, 2005. "Formal welfarism and intergenerational equity," Discussion Papers (ECON - Département des Sciences Economiques) 2005051, Université catholique de Louvain, Département des Sciences Economiques.
    13. Alcantud, José Carlos R. & Dubey, Ram Sewak, 2014. "Ordering infinite utility streams: Efficiency, continuity, and no impatience," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 33-40.
    14. Kohei Kamaga & Takashi Kojima, 2010. "On the leximin and utilitarian overtaking criteria with extended anonymity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 377-392, September.
    15. Sakamoto, Norihito & 坂本, 徳仁, 2011. "Impossibilities of Paretian Social Welfare Functions for Infinite Utility Streams with Distributive Equity," Discussion Papers 2011-09, Graduate School of Economics, Hitotsubashi University.
    16. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
    17. Michele Lombardi & Kaname Miyagishima & Roberto Veneziani, 2016. "Liberal Egalitarianism and the Harm Principle," Economic Journal, Royal Economic Society, vol. 126(597), pages 2173-2196, November.
    18. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    19. Kohei Kamaga & Takashi Kojima, 2009. "$${\mathcal{Q}}$$ -anonymous social welfare relations on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 405-413, September.
    20. Christopher Chambers, 2009. "Intergenerational equity: sup, inf, lim sup, and lim inf," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 243-252, February.

    More about this item

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecl:corcae:05-06. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/cacorus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.