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Intergenerational equity and an explicit construction of welfare criteria

Author

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  • Sakai, Toyotaka
  • 坂井, 豊貴
  • サカイ, トヨタカ

Abstract

Ranking infinite utility streams includes many impossibility results, most involving certain Pareto, anonymity, or continuity requirements. We introduce the concept of the future agreement extension, a method that explicitly extends orderings on finite time horizon to an infinite time horizon. The future agreement extension of given orderings is quasi-transitive, complete, and pairwisely continuous. Furthermore, it is a subrelation of any other pairwisely continuous extension of the orderings. In case of anonymous and strongly Paretian orderings, their future agreement extension is variable step anonymous and strongly Paretian. Characterizations of the future agreement extensions of the utilitarian and leximin orderings are obtained as applications.

Suggested Citation

  • Sakai, Toyotaka & 坂井, 豊貴 & サカイ, トヨタカ, 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.
    • Handle: RePEc:hit:piecis:395
    Note: August 19, 2008
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    Cited by:

    1. 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.
    2. Pivato, Marcus & Fleurbaey, Marc, 2024. "Intergenerational equity and infinite-population ethics: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    3. repec:fal:wpaper:08004 is not listed on IDEAS
    4. repec:fal:wpaper:09001 is not listed on IDEAS
    5. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    6. 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.
    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, March.
    8. 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.
    9. Sakai, Toyotaka, 2010. "A characterization and an impossibility of finite length anonymity for infinite generations," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 877-883, September.
    10. Jonsson, Adam & Voorneveld, Mark, 2018. "The limit of discounted utilitarianism," Theoretical Economics, Econometric Society, vol. 13(1), January.
    11. 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.
    12. Asier Estevan & Roberto Maura & Óscar Valero, 2023. "Quasi-Metrics for Possibility Results: Intergenerational Preferences and Continuity," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    13. 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.
    14. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    15. 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.
    16. Geir B. Asheim & Kohei Kamaga & Stéphane Zuber, 2025. "Exploring infinite population utilitarianism under strong anonymity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(1), pages 39-85, August.
    17. 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.
    18. Marcus Pivato, 2023. "Cesàro average utilitarianism in relativistic spacetime," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(4), pages 733-761, November.

    More about this item

    Keywords

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D60 - Microeconomics - - Welfare Economics - - - General

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