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A Complete and Strongly Anonymous Leximin Relation on Infinite Streams

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  • Geir B. Asheim
  • Stéphane Zuber

Abstract

Various extensions of the leximin order to the infinite dimensional setting have been suggested. They relax completeness and strong anonymity. Instead, by removing sensitivity to generations at infinite rank this paper defines a complete and strongly anonymous leximin relation on infinite streams. The order is axiomatized, and it is shown to be the limit of extended rank-discounted utilitarianism for any utility function, as the discount factor approaches zero.

Suggested Citation

  • Geir B. Asheim & Stéphane Zuber, 2011. "A Complete and Strongly Anonymous Leximin Relation on Infinite Streams," CESifo Working Paper Series 3578, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_3578
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    References listed on IDEAS

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    1. Brander, James A & Taylor, M Scott, 1998. "The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use," American Economic Review, American Economic Association, vol. 88(1), pages 119-138, March.
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    3. 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.
    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. 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.
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    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. 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.
    9. Kamaga, Kohei & Kojima, Takashi, 2008. "Q-anonymous social welfare relations on infinite utility streams," PIE/CIS Discussion Paper 391, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
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    13. Zame, William R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    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.
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    16. 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.
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    Citations

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    Cited by:

    1. José Alcantud, 2013. "Liberal approaches to ranking infinite utility streams: when can we avoid interference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 381-396, July.
    2. Michele Lombardi & Roberto Veneziani, 2009. "Liberal Egalitarianism and the Harm Principle," Global COE Hi-Stat Discussion Paper Series gd09-078, Institute of Economic Research, Hitotsubashi University.
    3. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    4. Robert D. Cairns & Stellio Del Campo & Vincent Martinet, 2016. "Sustainability of an economy relying on two reproducible assets," Working Papers 2016/03, INRA, Economie Publique.
    5. 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.
    6. repec:wly:econjl:v:126:y:2016:i:597:p:2173-2196 is not listed on IDEAS
    7. Ngo Van Long & Vincent Martinet, 2016. "How to Take Rights Seriously: A New Approach to the Intertemporal Evaluation of Social Alternatives," CIRANO Working Papers 2016s-60, CIRANO.

    More about this item

    Keywords

    intergenerational equity; lexicographic maximin;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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