Chichilnisky, Graciela (1985): Von Neuman- Morgenstern utilities and cardinal preferences. Published in: Mathematical Operations Research , Vol. 10, (November 1985): pp. 288-296.
Download (2012Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Von Neuman- Morgenstern utilities and cardinal preferences|
|Keywords:||preferences; cardinal preferences; aggregation; von Neumann; Morgenstern; Morgenstern utilities; unanimity; utilities|
|Subjects:||C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||04. Apr 2008 06:34|
|Last Modified:||12. Feb 2013 13:01|
ARROW, K. J. (1963) Social choice and individual values (2nd ed.) Cowles Foundation for Research Economics, monograph 12, yale University, New Haven.
BESSAGA, C. AND PELCZYNSKY, A. (1975). Selected Topics in Infinite Dimensional Topology. Polska Akademia Nauk, Instytyt Matema Eyczny, Warszawa.
BLACK, D. (Feb. 1948). On the rationale of group decision-making, J. Political Economy 56, 23-24.
Chichilnisky, G . (Jan. 1980) "Social Choice and the Topology of Spaces of Preferences", Advances in Mathematics. 27, 19-32.
Chichilnisky, G . (1980) "Continuous Representation of Preferences", Review of Economic Studies 47 959-963.
Chichilnisky, G . (1981) Existence and Characterization of Optimal Growth Paths in Models with Non-Convexities in Utilities and Technologies. Rev. Econ. Studies 48 51-61.
Chichilnisky, G . (1981) "The Structural Instability of Decisive Majority Rules", Journal of Mathematical Economics 9 207-221.
Chichilnisky, G . (1982b) "The Topological Equivalence of the Pareto Condition and the Existence of a Dictator", Journal of Mathematical Economics 9 223-233.
Chichilnisky, G . (1982a) "Social Aggregation Rules and Continuity", Quarterly Journal of Economics, 337-352.
Chichilnisky, G . and G . Heal (1979a) "Necessary and Sufficient Conditions for the Existence of Social Choice Rules. The Economic Workshop, Columbia University, Aug. 1979, J. Econ. Theory, 31 68-87.
d'Aspremont, C. and Gevers, L. (June 1977). Equity and the Informational Basis of Collective Choice. Rev. Economic Studies 44 199-207.
N. DUNFORD AND J. SCHWARTZ, "Linear Operators," Interscience, New York, 1963.
FISHBURN, P.C. (1970). Utility theory for decision making. Publications in Operations Research No. 18, Wiley, New York.
KALAI, E. AND SCHMEIDLER, D. (Sep. 1977). Aggregation Procedure for Cardinal Preferences, Econometrica 45 1431-1438.
KUIPER, N.H. (1971). Varieties Hilbertiennes, Aspects Geometriques. Sem. Math. Sup., Les Presses de l'Universite de Montreal.
Sen, A .K . (1970) Collective Choice and Social Welfare. Oliver and Boyd, Edinburgh.
Sen, A.K. (1975). Intertemporal Comparisons of Welfare. mimeo.
Spanier, E . (1966) Algebraic Topology (McGraw-Hill, New York) .
von Neumann, J. and Morgenstern, D. (1967). Theory of Games and Economic Behavior. Wiley, New York.