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A new equity condition for infinite utility streams and the possibility of being Paretian

Author

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  • Asheim, Geir B.

    (Dept. of Economics, University of Oslo)

  • Tungodden, Bertil

    (Department of Economics, Norwegian School of Economics and Business Administration)

Abstract

We investigate the properties of a new equity condition, "Hammond Equity for the Future" (HEF), capturing the following ethical intuition: A sacrifice by the present generation leading to a uniform gain for all future generations cannot lead to a less desirable utility stream if the present remains better off than the future. Since HEF is a weak condition when compared to other consequentialist equity conditions, it is of interest to establish whether it to a greater extent can be combined with Paretian conditions. We show that this is not the case: HEF is not compatible with the "Strong Pareto" condition when social preferences are upper semi-continuous in the sup norm topology. If we impose that the social preferences are complete, transitive and continuous in the sup norm topology, and satisfy an "Independent future" condition, then HEF cannot even be combined with the "Weak Pareto" condition.

Suggested Citation

  • Asheim, Geir B. & Tungodden, Bertil, 2005. "A new equity condition for infinite utility streams and the possibility of being Paretian," Memorandum 08/2005, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2005_008
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    References listed on IDEAS

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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. Alcantud, José Carlos R., 2012. "Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto," Journal of Economic Theory, Elsevier, vol. 147(1), pages 353-363.
    3. 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.
    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. Banerjee, Kuntal, 2006. "On the equity-efficiency trade off in aggregating infinite utility streams," Economics Letters, Elsevier, vol. 93(1), pages 63-67, October.
    6. Geir Asheim & Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2010. "Infinite-horizon choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 1-21, April.
    7. Asheim, Geir B. & Mitra, Tapan, 2010. "Sustainability and discounted utilitarianism in models of economic growth," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 148-169, March.
    8. 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.
    9. Walter Bossert & Kotaro Suzumura, 2011. "Multi-profile intergenerational social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 493-509, September.
    10. Dubey, Ram Sewak & Mitra, Tapan, 2014. "On construction of equitable social welfare orders on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 53-60.
    11. Ram Sewak Dubey & Tapan Mitra, 2015. "On social welfare functions on infinite utility streams satisfying Hammond Equity and Weak Pareto axioms: a complete characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 169-180, October.
    12. 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.
    13. 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.
    14. Alcantud, José Carlos R. & García-Sanz, María D., 2009. "A comment on "Intergenerational equity: sup, inf, lim sup, and lim inf"," MPRA Paper 14763, University Library of Munich, Germany.
    15. Ram Dubey & Tapan Mitra, 2014. "Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 591-602, October.
    16. 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.
    17. Alcantud, José C.R. & García-Sanz, María D., 2010. "Paretian evaluation of infinite utility streams: An egalitarian criterion," Economics Letters, Elsevier, vol. 106(3), pages 209-211, March.
    18. Dubey, Ram Sewak & Laguzzi, Giorgio, 2021. "Equitable preference relations on infinite utility streams," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    19. 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.
    20. Dubey, Ram Sewak, 2016. "On construction of social welfare orders satisfying Hammond equity and Weak Pareto axioms," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 119-124.

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    More about this item

    Keywords

    Intergenerational equity; Pareto condition;

    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
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development

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