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Continuous Representation of Preferences

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  • Graciela Chichilnisky

Abstract

In this paper we study a utility representation for preferences, and we price its continuity, using a topology for preferences introduced by Chichilnisky (1977). Such utility representations were constructed under restrictive conditions first by Y. Kannai and S. Reiter (1974, 1975). Our results are related more closely to those of Mount and Reiter (1974 and 1975). Starting from restrictive conditions these works have attempted to enlarge the class of preferences that could be continuously represented. The class of preferences studied here is much larger than those considered earlier, and it therefore applies to a wider class of problems. Our preferences include ones which are not necessarily convex or monotone, and which may be locally satiated; furthermore, no completeness of preferences is required. The assumption made by Mount and Reiter (1975) of the existence of an E-threshold is also not required here. These results are possible due to properties of the order topology introduced in Chichilnisky (1977). As we shall now discuss, this topology has quite desirable features for the study of preferences, and these now make it a natural choice for the problem at hand.
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  • Graciela Chichilnisky, 1980. "Continuous Representation of Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 959-963.
    • Handle: RePEc:oup:restud:v:47:y:1980:i:5:p:959-963.
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    File URL: http://hdl.handle.net/10.2307/2296925
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    References listed on IDEAS

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    1. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    2. Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, Elsevier, vol. 15(1), pages 160-173, June.
    3. Mount, Kenneth R. & Reiter, Stanley, 1976. "Construction of a continuous utility function for a class of preferences," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 227-245, December.
    4. HILDENBRAND, Werner, 1970. "On economies with many agents," LIDAM Reprints CORE 61, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Hildenbrand, Werner, 1970. "On economies with many agents," Journal of Economic Theory, Elsevier, vol. 2(2), pages 161-188, June.
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    Cited by:

    1. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 11-16, January.
    2. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    3. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 1-10, January.
    4. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
    5. Sebastián Cea-Echenique & Matías Fuentes, 2020. "On the continuity of the walras correspondence for distributional economies with an infinite dimensional commodity space," Working Papers hal-02430960, HAL.
    6. Cea-Echenique, Sebastián & Fuentes, Matías, 2024. "On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 61-69.

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    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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