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Von Neumann-Morgenstern Utilities and Cardinal Preferences

Listed author(s):
  • Graciela Chichilnisky

    (Department of Economics, International Affairs Building, Columbia University, New York, New York 10027)

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 do 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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File URL: http://dx.doi.org/10.1287/moor.10.4.633
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Article provided by INFORMS in its journal Mathematics of Operations Research.

Volume (Year): 10 (1985)
Issue (Month): 4 (November)
Pages: 633-641

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Handle: RePEc:inm:ormoor:v:10:y:1985:i:4:p:633-641
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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, Oxford University Press, vol. 97(2), pages 337-352.
  3. Graciela Chichilnisky, 1980. "Continuous Representation of Preferences," Review of Economic Studies, Oxford University Press, vol. 47(5), pages 959-963.
  4. 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.
  5. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  6. 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.
  7. Graciela Chichilnisky, 1981. "Existence and Characterization of Optimal Growth Paths Including Models with Non-Convexities in Utilities and Technologies," Review of Economic Studies, Oxford University Press, vol. 48(1), pages 51-61.
  8. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
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