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Von Neuman- Morgenstern utilities and cardinal preferences

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  • Chichilnisky, Graciela

Abstract

We study the aggregation of preferences when intensities are taken into account: the aggregation of cardinal preferences, and also of von Neumann-Morgenstern utilities for choices under uncertainty. We show that with a finite number of choices there exist no continuous anonymous aggregation rules that respect unanimity, for such preferences or utilities. With infinitely many (discrete sets of) choices, such rules for exist and they are constructed here. However, their existence is not robust: each is a limit of rules that do not respect unanimity. Both results are for a finite number of individuals. The results are obtained by studying the global topological structure of spaces of cardinal preferences and of von Neumann-Morgenstern utilities. With a finite number of choices, these spaces are proven to be noncontractible. With infinitely many choices, on the other hand, they are proven to be contractible.

Suggested Citation

  • Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:8090
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    File URL: https://mpra.ub.uni-muenchen.de/8090/1/MPRA_paper_8090.pdf
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    References listed on IDEAS

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    1. Kalai, Ehud & Schmeidler, David, 1977. "Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture," Econometrica, Econometric Society, vol. 45(6), pages 1431-1438, September.
    2. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    3. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    4. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
    5. Graciela Chichilnisky, 1981. "Existence and Characterization of Optimal Growth Paths Including Models with Non-Convexities in Utilities and Technologies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 51-61.
    6. Graciela Chichilnisky, 1980. "Continuous Representation of Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 959-963.
    7. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
    8. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    2. Dhillon, Amrita & Mertens, Jean-Francois, 1997. "An impossibility theorem with von Neumann-Morgenstern preferences," Economics Letters, Elsevier, vol. 56(3), pages 305-309, November.
    3. Tilman Börgers & Yan-Min Choo, 2017. "Revealed Relative Utilitarianism," CESifo Working Paper Series 6613, CESifo.
    4. 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.
    5. Benítez-Fernández, Amalia & Ruiz, Francisco, 2020. "A Meta-Goal Programming approach to cardinal preferences aggregation in multicriteria problems," Omega, Elsevier, vol. 94(C).

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    More about this item

    Keywords

    preferences; cardinal preferences; aggregation; von Neumann; Morgenstern; Morgenstern utilities; unanimity; utilities;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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