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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8090.

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Date of creation: 1985
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Handle: RePEc:pra:mprapa:8090

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Keywords: preferences; cardinal preferences; aggregation; von Neumann; Morgenstern; Morgenstern utilities; unanimity; utilities;

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References

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  1. Chichilnisky, Graciela, 1981. "Existence and Characterization of Optimal Growth Paths Including Models with Non-Convexities in Utilities and Technologies," Review of Economic Studies, Wiley Blackwell, vol. 48(1), pages 51-61, January.
  2. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
  3. 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.
  4. 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 1431-38, September.
  5. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  6. Chichilnisky, Graciela & Heal, Geoffrey, 1979. "Necessary and sufficient conditions for a resolution of the social choice paradox," MPRA Paper 8495, University Library of Munich, Germany, revised 20 Oct 1981.
  7. Chichilnisky, Graciela, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, MIT Press, vol. 97(2), pages 337-52, May.
  8. Chichilnisky, Graciela, 1980. "Continuous representation of preference," MPRA Paper 8042, University Library of Munich, Germany.
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Cited by:
  1. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer, vol. 13(1), pages 1-10, January.
  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. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.

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