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Continuity and equity with infinite horizons

Author

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  • Luc Lauwers

    (Monitoraat ETEW, KU Leuven, Dekenstraat 2, B-3000 Leuven, Belgium)

Abstract

In an infinite dimensional space, e.g. the set of infinite utility streams, there is no natural topology and the content of continuity is manipulable. Different desirable properties induce different topologies. We consider three properties: effectiveness. l1-summability and equity. In view of effectivity, the product topology is the most favourable one. The strict topology is the largest topology for which all the continuous linear maps are l1-summable. However, both topologies are myopic and conflict with the principle of equity. In case equity is desirable, the sup topology comes forward.

Suggested Citation

  • Luc Lauwers, 1997. "Continuity and equity with infinite horizons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 345-356.
    • Handle: RePEc:spr:sochwe:v:14:y:1997:i:2:p:345-356
    Note: Received: 15 April 1993 / Accepted: 22 April 1996
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    Cited by:

    1. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    2. Toyotaka Sakai, 2006. "Equitable Intergenerational Preferences on Restricted Domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 41-54, August.
    3. Bastianello, Lorenzo, 2017. "A topological approach to delay aversion," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 1-12.
    4. Jonsson, Adam & Voorneveld, Mark, 2014. "Utilitarianism for infinite utility streams: summable differences and finite averages," SSE/EFI Working Paper Series in Economics and Finance 747, Stockholm School of Economics, revised 15 Apr 2014.
    5. 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.
    6. Asheim, Geir B. & Kamaga, Kohei & Zuber, Stéphane, 2022. "Maximal sensitivity under Strong Anonymity," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    7. Asheim, Geir B. & Buchholz, Wolfgang & Tungodden, Bertil, 2001. "Justifying Sustainability," Journal of Environmental Economics and Management, Elsevier, vol. 41(3), pages 252-268, May.
    8. repec:ebl:ecbull:v:4:y:2003:i:26:p:1-5 is not listed on IDEAS
    9. Chiaki Hara & Tomoichi Shinotsuka & Kotaro Suzumura & Yongsheng Xu, 2008. "Continuity and egalitarianism in the evaluation of infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 179-191, August.
    10. Asier Estevan & Roberto Maura & Oscar Valero, 2024. "Intergenerational Preferences and Continuity: Reconciling Order and Topology," Papers 2402.01699, arXiv.org.
    11. Toyotaka Sakai, 2003. "Intergenerational preferences and sensitivity to the present," Economics Bulletin, AccessEcon, vol. 4(26), pages 1-5.
    12. Christopher Chambers, 2009. "Intergenerational equity: sup, inf, lim sup, and lim inf," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 243-252, February.
    13. Adam Jonsson & Mark Voorneveld, 2015. "Utilitarianism on infinite utility streams: summable differences and finite averages," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 19-31, April.
    14. 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.
    15. Susumu Cato, 2009. "Characterizing the Nash social welfare relation for infinite utility streams: a note," Economics Bulletin, AccessEcon, vol. 29(3), pages 2372-2379.
    16. Lauwers, Luc, 1998. "Intertemporal objective functions: Strong pareto versus anonymity," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 37-55, January.
    17. Banerjee, Kuntal & Mitra, Tapan, 2004. "On the Continuity of Ethical Social Welfare Orders," Working Papers 04-16, Cornell University, Center for Analytic Economics.
    18. Alcantud, José Carlos R. & Dubey, Ram Sewak, 2014. "Ordering infinite utility streams: Efficiency, continuity, and no impatience," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 33-40.
    19. 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.
    20. 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.

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