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On the leximin and utilitarian overtaking criteria with extended anonymity

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  • Kohei Kamaga

    ()

  • Takashi Kojima

    ()

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.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 35 (2010)
Issue (Month): 3 (September)
Pages: 377-392

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Handle: RePEc:spr:sochwe:v:35:y:2010:i:3:p:377-392

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References

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  1. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer, vol. 35(3), pages 393-414, 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.
  3. Luc LAUWERS, 2009. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Center for Economic Studies - Discussion papers ces09.05, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  4. 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.
  5. FLEURBAEY, Marc & MICHEL, Philippe, 1997. "Intertemporal equity and the extension of the Ramsey criterion," CORE Discussion Papers 1997004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Asheim, Geir B. & Mitra, Tapan & Tungodden, Bertil, 2006. "Sustainable recursive social welfare functions," Memorandum 18/2006, Oslo University, Department of Economics.
  7. 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.
  8. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
  9. Kohei Kamaga & Takashi Kojima, 2010. "On the leximin and utilitarian overtaking criteria with extended anonymity," Social Choice and Welfare, Springer, vol. 35(3), pages 377-392, September.
  10. Geir Asheim & Bertil Tungodden, 2004. "Resolving distributional conflicts between generations," Economic Theory, Springer, vol. 24(1), pages 221-230, 07.
  11. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-56, July.
  12. Zame, William R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
  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. 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.
  15. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
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Citations

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Cited by:
  1. Geir B. Asheim & Kuntal Banerjee, 2009. "Fixed-step anonymous overtaking and catching-up," Working Papers 09001, Department of Economics, College of Business, Florida Atlantic University.
  2. Geir B. , ASHEIM & Claude, DASPREMONT & Kuntal, BANERJEE, 2008. "Generalized time-invariant overtaking," Discussion Papers (ECON - Département des Sciences Economiques) 2008039, Université catholique de Louvain, Département des Sciences Economiques.
  3. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer, vol. 35(3), pages 393-414, September.
  4. Kohei Kamaga & Takashi Kojima, 2010. "On the leximin and utilitarian overtaking criteria with extended anonymity," Social Choice and Welfare, Springer, vol. 35(3), pages 377-392, September.
  5. Luc LAUWERS, 2010. "Intergenerational equity, efficiency and constructability," Center for Economic Studies - Discussion papers ces10.22, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  6. Geir B. Asheim & Stéphane Zuber, 2011. "A Complete and Strongly Anonymous Leximin Relation on Infinite Streams," CESifo Working Paper Series 3578, CESifo Group Munich.
  7. Susumu Cato, 2009. "Characterizing the Nash social welfare relation for infinite utility streams: a note," Economics Bulletin, AccessEcon, vol. 29(3), pages 2372-2379.

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