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On the leximin and utilitarian overtaking criteria with extended anonymity

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  • Kamaga, Kohei
  • Kojima, Takashi

Abstract

This paper studies the extensions of the infinte-horizon variants of the leximin principle and utilitarianism on the set of infinite utility streams. We especially examine those extensions which satisfy the axiom of Preference-continuity (or Consistency) and the extended anonymity axiom called Q-Anonymity. We formulate new extended leximin and utilitarian social welfare relations (SWRs), called Q-W-leximin SWR and Q-overtaking criterion respectively, and show that Weak Preference-continuity (or Weak Consistency) and Q-Anonymity together with Strong Pareto and Hammond Equity (resp. Partial Unit Comparability) characterize all SWRs that include the Q-W-leximin SWR (resp. the Q-overtaking criterion) as a subrelation. We also show that there exists no SWR satisfying Strong Pareto, Strong Preference-continuity (or Strong Consistency) and Q-Anonymity.

Suggested Citation

  • Kamaga, Kohei & Kojima, Takashi, 2008. "On the leximin and utilitarian overtaking criteria with extended anonymity," PIE/CIS Discussion Paper 392, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:piecis:392
    Note: First version, December 18, 2007; Current version, August 21, 2008
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    File URL: http://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/15915/pie_dp392.pdf
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    References listed on IDEAS

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    1. 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.
    2. Asheim, Geir B. & Buchholz, Wolfgang & Tungodden, Bertil, 2001. "Justifying Sustainability," Journal of Environmental Economics and Management, Elsevier, vol. 41(3), pages 252-268, May.
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    4. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    5. 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.
    6. 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.
    7. Geir Asheim & Tapan Mitra & Bertil Tungodden, 2012. "Sustainable recursive social welfare functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 267-292, February.
    8. Zame, William R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Banerjee, Kuntal & Mitra, Tapan, 2004. "On the Continuity of Ethical Social Welfare Orders," Working Papers 04-16, Cornell University, Center for Analytic Economics.
    14. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    15. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
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    Cited by:

    1. Jonsson, Adam & Voorneveld, Mark, 2018. "The limit of discounted utilitarianism," Theoretical Economics, Econometric Society, vol. 13(1), January.
    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. 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.
    4. 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.
    5. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    6. 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.
    7. Luc Lauwers, 2012. "Intergenerational equity, efficiency, and constructibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 227-242, February.
    8. Susumu Cato, 2020. "Quasi-stationary social welfare functions," Theory and Decision, Springer, vol. 89(1), pages 85-106, July.
    9. Susumu Cato, 2019. "The possibility of Paretian anonymous decision-making with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 587-601, December.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Susumu Cato, 2009. "Characterizing the Nash social welfare relation for infinite utility streams: a note," Economics Bulletin, AccessEcon, vol. 29(3), pages 2372-2379.

    More about this item

    Keywords

    Q-Anonymity; Preference-continuity; Consistency; Leximin; Utilitarianism; Overtaking criterion;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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