Abstract
Recently, a number of generalizations of the expected utility (EU) model have been proposed. In order to make such generalizations useful, it is necessary that they should yield sharp comparative static results, like those obtained using EU theory. In this article, rank dependent expected utility (RDEU) theory, a generalization of EU theory based on the concept of probability weighting, is examined. A number of methods of extending results from EU to RDEU are considered. It is shown that a major class of comparative static results can be extended to the RDEU model, but not to the case of general smooth preferences. This is because RDEU maintains the separation between probabilities and utilities that is abandoned in the general case.
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Allais, Maurice. (1987). The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function: The (U, θ) model—A General Overview. Paris: Centre National de la Recherche Scientifique.
Arrow, Kenneth and R. Lind. (1970). “Uncertainty and the Evaluation of Public Investment Decisions,” American Economic Review 60, 364–378.
Bertsekas, D. (1974). “Necessary and Sufficient conditions for the Existence of an Optimal Portfolio,” Journal of Economic Theory 8, 235–247.
Chew, Soo-Hoong. (1983). “A Generalisation of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox,” Econometrica 51, 1065–1092.
Chew, Soo-Hoong, Edi, Karni, and Zvi, Safra. (1987). “Risk Aversion in the Theory of Expected Utility with Rank Dependent Preferences,” Journal of Economic Theory 42, 370–381.
Chew, Soo-Hoong, Larry, Epstein, and Itzhak, Zilcha. (1988). “A Correspondence Theorem Between Expected Utility and Smooth Utility,” Journal of Economic Theory 46, 186–193.
Coes, Donald. (1977). “Firm Output and Changes in Uncertainty,” American Economic Review 67, 249–251.
Diamond, P., and Joseph, Stiglitz. (1974). “Increases in Risk and Risk Aversion,” Journal of Economic Theory 8, 337–360.
Feder, Gershon. (1977). “The Impact of Uncertainty in a Class of Objective Functions,” Journal of Economic Theory 16, 504–512.
Friedman, Milton and L.J. Savage. (1948). “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56, 279–304.
Gilboa, Itzhak. (1987). “Expected Utility with Purely Subjective Non-Additive Probabilities,” Journal of mathematical Economics 16, 65–88.
Hildreth, K. (1974). “Ventures, Bets and Initial Prospects.” In M. Balch, D. McFadden, and S. Wu (eds.), Essays on Economic Behaviour under Uncertainty. Amsterdam: North-Holland.
Kahneman, Daniel and Amos, Tversky. (1979). “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, 263–291.
Karmarkar, Uday. (1978). “Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model,” Organisational Behavior and Human Preference 21, 61–72.
Karni, Edi and Zvi, Safra. (1987). “Preference Reversal' and the Observability of Preferences by Experimental Methods,” Econometrica 55, 675–685.
Lintner, J. (1965). “The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics 47, 13–37.
Machina, Mark. (1982). “Expected Utility' Analysis Without the Independence Axion,” Econometrica 50, 277–323.
Machina, Mark. (1983). “The Economic Theory of Individual Behavior Toward Risk: Theory, Evidence and New Directions,” Technical Report No. 433, Center for Research on Organizational Efficiency, Stanford University.
Machina, Mark. (1984). “Temporal Risk and the Nature of Induced Preferences,” Journal of Economic Theory 33, 199–231.
Machina, Mark. (1989). “Comparative Statics and Non-Expected Utility Preferences,” Journal of Economic Theory 47, 393–405.
Meyer, Jack and Michael, Ormiston. (1989). “Deterministic Transformation of Random Variables and the Comparative Statics of Risk,” Journal of Risk and Uncertainty 2, 179–188.
Newbery, D. an J. Stiglitz. (1981). The Theory of Commodity Price Stabilisation—A Study in the Economics of Risk. Oxford: Oxford University Press.
Quiggin, John. (1981). “Risk Perception and Risk Aversion among Australian Farmers,” Australian Journal of Agricultural Economics 25, 160–169.
Quiggin, John. (1982a). “A theory of Anticipated Utility,” Journal of Economic Behavior and Organisation 3, 323–343.
Quiggin, John. (1982b). “A Note on the Existence of a Competitive Optimum,” Economic Record 55, 174–176.
Quiggin, John. (1985). “Anticipated Utility, Subjectively Weighted Utility and the Allais Paradox,” Organisational Behavior and Human Performance 35, 94–101.
Quiggin, John. (1986). “Anticipated Utility: Some Developments in the Economic Theory of Uncertainty”. Unpublished Ph.D. thesis, University of New England.
Quiggin, John. (1988). “Increasing Risk: Another Definition”, paper presented at 4th Conference on Foundations of Utility Research, Budapest.
Quiggin, John. (1990). “On the Optimal Design of Lotteries”. Economica, forthcoming.
Rothschild, Michael and Joseph Stiglitz. (1971). “Increasing Risk: II. Its Economic Consequences”,, Journal of Economic Theory 3, 66–84.
Sandmo, Agnar. (1970). “The effect of Uncertainty on Savings Decisions”, Review of Economic Studies 37, 353–360.
Sandmo, Agnar. (1971). “The Competitive Firm Under Output Price Uncertainty,” American Economic Review 61, 65–73.
Schmeidler, David. (1989). “Subjective Probability and Expected Utility Without Additivity,” Econometrica 57, 571–587.
Segal, Uzi. (1987). “Some Remarks on Quiggin's Anticipated Utility,” Journal of Economic Behavior and Organisation 8, 145–154.
Segal, Uzi. (1989). “Anticipated Utility: A Measure Representation Approach,” Annals of Operations Research 19, 359–374.
Sharpe, J. (1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance 19, 425–442.
Smith, Adam. (1776, 1976). The Wealth of Nations, 1976 ed. Oxford: Clarendon.
Tobin, James. (1969). “Comment on Borch and Feldstein,” Review of Economic Studies 36, 13–14.
Tversky, Amos and Daniel Kahneman. (1990). “Cumulative Prospect Theory: An Analysis of Attitudes Towards Uncertainty and Value”, paper presented at the 5th International Conference on the Foundations and Applications of Utility, Risk and Decision Theories, Duke University, June 9–13.
Viscusi, Kip. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264.
von Neumann, John and Oskar Morgenstern. (1994). Theory of Games and Economic Behavior: Princeton, NJ: Princeton University Press.
Yaari, Menahem. (1987). “The Dual Theory of Choice Under Risk,” Econometrica 55, 95–115.
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Quiggin, J. Comparative statics for rank-dependent expected utility theory. J Risk Uncertainty 4, 339–350 (1991). https://doi.org/10.1007/BF00056160
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DOI: https://doi.org/10.1007/BF00056160