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On the leximin and utilitarian overtaking criteria with extended anonymity

  • Kamaga, Kohei
  • Kojima, Takashi

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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Paper provided by Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University in its series PIE/CIS Discussion Paper with number 392.

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Length: 21 p.
Date of creation: Aug 2008
Date of revision:
Handle: RePEc:hit:piecis:392
Note: First version, December 18, 2007; Current version, August 21, 2008
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  1. 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.
  2. Zame, William R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
  3. 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.
  4. Banerjee, Kuntal & Mitra, Tapan, 2004. "On the Continuity of Ethical Social Welfare Orders," Working Papers 04-16, Cornell University, Center for Analytic Economics.
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  6. 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.
  7. Geir Asheim & Tapan Mitra & Bertil Tungodden, 2012. "Sustainable recursive social welfare functions," Economic Theory, Springer, vol. 49(2), pages 267-292, February.
  8. 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.
  9. Sakai, Toyotaka, 2008. "Intergenerational equity and an explicit construction of welfare criteria," PIE/CIS Discussion Paper 395, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  10. 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.
  11. 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.
  12. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
  13. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-56, July.
  14. Geir Asheim & Bertil Tungodden, 2004. "Resolving distributional conflicts between generations," Economic Theory, Springer, vol. 24(1), pages 221-230, 07.
  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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