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On the extension of a preorder under translation invariance

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  • Mabrouk, Mohamed

Abstract

This paper proves the existence, for any preorder on a real vector space satisfying translation invariance, of a complete preorder extending the preorder and satisfying translation invariance. As application, the existence of a translation-invariant complete preorder on infinite utility streams satisfying strong Pareto and fixed-step anonymity, is established.

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  • Mabrouk, Mohamed, 2009. "On the extension of a preorder under translation invariance," MPRA Paper 15407, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15407
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    References listed on IDEAS

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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. Mohamed Ben Ridha Mabrouk, 2011. "Translation invariance when utility streams are infinite and unbounded," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(4), pages 317-329, December.
    3. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541, Elsevier.
    4. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
    5. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    6. 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.
    7. 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.
    8. Jörgen W. Weibull, 1985. "Discounted-Value Representations of Temporal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 244-250, May.
    9. Tapan Mitra & Kaushik Basu, 2007. "On the Existence of Paretian Social Welfare Quasi-Orderings for Infinite Utility Streams with Extended Anonymity," International Economic Association Series, in: John Roemer & Kotaro Suzumura (ed.), Intergenerational Equity and Sustainability, chapter 6, pages 85-99, Palgrave Macmillan.
    10. , R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    11. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    12. Prasanta K. Pattanaik & Koichi Tadenuma & Yongsheng Xu & Naoki Yoshihara (ed.), 2008. "Rational Choice and Social Welfare," Studies in Choice and Welfare, Springer, number 978-3-540-79832-3, December.
    13. Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
    14. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    15. repec:bla:econom:v:43:y:1976:i:172:p:381-90 is not listed on IDEAS
    16. Kuntal Banerjee, 2006. "On the Extension of the Utilitarian and Suppes–Sen Social Welfare Relations to Infinite Utility Streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 327-339, October.
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    More about this item

    Keywords

    Szpilrajn theorem; translation invariance;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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