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The non-existence of a utility function and the structure of non-representable preference relations

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  • Beardon, Alan F.
  • Candeal, Juan C.
  • Herden, Gerhard
  • Indurain, Esteban
  • Mehta, Ghanshyam B.

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  • Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    • Handle: RePEc:eee:mateco:v:37:y:2002:i:1:p:17-38
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    References listed on IDEAS

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    1. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "Lexicographic decomposition of chains and the concept of a planar chain," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 95-104, April.
    2. Kelly, Jerry S, 1971. "The Continuous Representation of a Social Preference Ordering," Econometrica, Econometric Society, vol. 39(3), pages 593-597, May.
    3. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    4. Saposnik, Rubin, 1975. "Social Choice with Continuous Expression of Individual Preferences," Econometrica, Econometric Society, vol. 43(4), pages 683-690, July.
    5. Vohra, Ranjit, 1995. "The Souslin Hypothesis and Continuous Utility Functions: A Remark," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 537-540, May.
    6. 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.
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    Cited by:

    1. Knoblauch, Vicki, 2016. "Elections generate all binary relations on infinite sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 105-108.
    2. J. Alcantud & G. Bosi & M. Campión & J. Candeal & E. Induráin & C. Rodríguez-Palmero, 2008. "Continuous Utility Functions Through Scales," Theory and Decision, Springer, vol. 64(4), pages 479-494, June.
    3. Herden, G. & Mehta, G. B., 2004. "The Debreu Gap Lemma and some generalizations," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 747-769, November.
    4. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    5. Abrísqueta, Francisco J. & Candeal, Juan C. & Induráin, Esteban & Zudaire, Margarita, 2009. "Scott-Suppes representability of semiorders: Internal conditions," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 245-261, March.
    6. Rizza, Davide, 2015. "Nonstandard utilities for lexicographically decomposable orderings," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 105-109.
    7. Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, University Library of Munich, Germany.
    8. Dubra Juan & Echenique Federico, 2001. "Monotone Preferences over Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-18, December.
    9. Denis Bouyssou & Marc Pirlot, 2021. "Unit representation of semiorders II: The general case," Post-Print hal-02918017, HAL.
    10. Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1591-1598, March.
    11. Tapan Mitra & M. Ozbek, 2013. "On representation of monotone preference orders in a sequence space," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 473-487, September.
    12. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "Lexicographic decomposition of chains and the concept of a planar chain," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 95-104, April.
    13. Caserta, A. & Giarlotta, A. & Watson, S., 2008. "Debreu-like properties of utility representations," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1161-1179, December.
    14. Lumley, Thomas & Gillen, Daniel L., 2016. "Characterising transitive two-sample tests," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 118-123.
    15. Knoblauch, Vicki, 2023. "Lexicographic preference representation: Intrinsic length of linear orders on infinite sets," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    16. Campion, Maria J. & Candeal, Juan C. & Indurain, Esteban, 2006. "The existence of utility functions for weakly continuous preferences on a Banach space," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 227-237, March.
    17. Banerjee, Kuntal & Mitra, Tapan, 2018. "On Wold’s approach to representation of preferences," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 65-74.

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