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14 - Extensions of the Subjective Expected Utility Model

Published online by Cambridge University Press:  05 June 2012

Robert F. Nau
Affiliation:
Fuqua School of Business, Duke University
Ralph F. Miles Jr.
Affiliation:
California Institute of Technology
Detlof von Winterfeldt
Affiliation:
University of Southern California
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Summary

ABSTRACT. The subjective expected utility (SEU) model rests on very strong assumptions about the consistency of decision making across a wide range of situations. The descriptive validity of these assumptions has been extensively challenged by behavioral psychologists during the last few decades, and the normative validity of the assumptions has also been reappraised by many statisticians, philosophers, and economists, motivating the development of more general utility theories and decision models. These generalized models are characterized by features such as imprecise probabilities, nonlinearly weighted probabilities, source-dependent risk attitudes, and state-dependent utilities, permitting the pattern of the decision maker's behavior to change with the decision context and to perhaps satisfy the usual SEU assumptions only locally. Recent research in the emerging field of neuroeconomics sheds light on the physiological basis of decision making, the nature of preferences and beliefs, and interpersonal differences in decision competence. These findings do not necessarily invalidate the use of SEU-based decision analysis tools, but they suggest that care needs to be taken to structure preferences and to assess beliefs and risk attitudes in a manner that is appropriate for the decision and also for the decision maker.

The SEU model and its assumptions

The subjective expected utility (SEU) model provides the conceptual and computational framework that is most often used to analyze decisions under uncertainty. In the SEU model, uncertainty about the future is represented by a set of states of the world, which are mutually exclusive and exhaustive events.

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Advances in Decision Analysis
From Foundations to Applications
, pp. 253 - 278
Publisher: Cambridge University Press
Print publication year: 2007

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References

Allais, M. (1953). Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Américaine. Econometrica, 21, 503–546.CrossRefGoogle Scholar
Anscombe, F., and Aumann, R. (1963). A Definition of Subjective Probability. Annals of Mathematical Statistics, 34, 199–205.CrossRefGoogle Scholar
Arrow, K. (1951). An Extension of the Basic Theorems of Classical Welfare Economics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press.Google Scholar
Arrow, K. (1953/1964). The Role of Securities in the Optimal Allocation of Risk-Bearing. Quarterly Journal of Economics, 31, 91–96.Google Scholar
Aumann, R. (1971). Letter to L. J. Savage. Reprinted in Drèze, J. (1987). Essays on Economic Decision Under Uncertainty. London: Cambridge University Press.Google Scholar
Bechara, A., Damasio, A., Damasio, H., and Anderson, S. (1994). Insensitivity to Future Consequences Following Damage to Human Prefrontal Cortex. Cognition, 50, 7–15.CrossRefGoogle ScholarPubMed
Bechara, A., Damasio, H., Damasio, A., and Lee, G. (1999). Different Contributions of the Human Amygdala and Ventromedial Prefrontal Cortex to Decision-Making. J. Neuroscience, 19, 473–481.CrossRefGoogle ScholarPubMed
Becker, J., and Sarin, R. (1987). Lottery Dependent Utility. Management Science, 33, 1367–1382.CrossRefGoogle Scholar
Bell, D. (1982). Regret in Decision Making under Uncertainty. Operations Research, 30, 961–981.CrossRefGoogle Scholar
Bell, D. (1985). Disappointment in Decision Making under Uncertainty. Operations Research, 33, 1–27.CrossRefGoogle Scholar
Bernoulli, D. (1738). Specimen Theoriae Novae de Mensura Sortis. Commentarii Academiae Scientiarum Imperialis Petropolitanae, 5, 175–192. Translation by L. Sommer (1954) Exposition of a New Theory on the Measurement of Risk. Econometrica, 22, 23–36.Google Scholar
Bewley, T. (1986). Knightian Decision Theory Part I. Cowles Foundation Discussion Paper No. 807. Reprinted in (2002). Decisions in Economics and Finance, 25, 79–110.CrossRef
Bleichrodt, H., and Pinto, J. (2000). A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis. Management Science, 46, 1485–1496.CrossRefGoogle Scholar
Bleichrodt, H., Pinto, J., and Wakker, P. (2001). Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility. Management Science, 47, 1498–1514.CrossRefGoogle Scholar
Camerer, C., Loewenstein, G., and Prelec, D. (2004a). Neuroeconomics: How Neuroscience Can Inform Economics. Journal of Economic Literature, XⅬIII, 9–64.Google Scholar
Camerer, C., Loewenstein, G., and Prelec, D. (2004b). Neuroeconomics: Why Economics Needs Brains. Scandinavian Journal of Economics, 106, 555–579.CrossRefGoogle Scholar
Chew, S. H. (1983). A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox. Econometrica, 51, 1065–1092.Google Scholar
Chew, S. H. and Sagi, J. (2006). Small Worlds: Modeling Attitudes Toward Sources of Uncertainty. Working paper, University of California at Berkeley.
Chew, S. H., and Wakker, P. (1996). The Comonotonic Sure-Thing Principle. Journal of Risk and Uncertainty, 12, 5–27.Google Scholar
Chew, S. H., Karni, E. and Safra, Z. (1987). Risk Aversion in the Theory of Expected Utility with Rank Dependent Probabilities. Journal of Economic Theory, 42, 370–381.Google Scholar
CNRS. (1953). Econometrie, Paris, 12–17 Mai 1952. Colloques Internationaux, 40, Centre National de la Recherche Scientifique, Paris.
Damasio, A. (1994). Descartes' Error: Emotion, Reason, and the Human Brain. New York: Putnam.Google Scholar
Damasio, A. (2003). Looking For Spinoza: Joy, Sorrow, and the Feeling Brain. Orlando: Harcourt.Google Scholar
Finetti, B. (1974). Theory of Probability, Vol. 1. New York: Wiley.Google Scholar
Debreu, G. (1959). Theory of Value. New Haven: Cowles Foundation.Google Scholar
Degroot, M. (1970). Optimal Statistical Decisions. New York: McGraw-Hill.Google Scholar
Diecidue, E., and Wakker, P. (2001). On the Intuition of Rank-Dependent Utility. Journal of Risk and Uncertainty, 23, 281–298.CrossRefGoogle Scholar
Dorris, M., and Glimcher, P. (2004) Activity in Posterior Parietal Cortex is Correlated with the Subjective Desirability of an Action. Neuron, 44, 365–378.CrossRefGoogle ScholarPubMed
Drèze, J. (1970). Market Allocation Under Uncertainty. European Economic Review, 2, 133–165.CrossRefGoogle Scholar
Drèze, J. (1987). Essays on Economic Decision Under Uncertainty. London: Cambridge University Press.CrossRefGoogle Scholar
Eisenberger, R., and Weber, M. (1995). Willingness-to-Pay and Willingness-to-Accept for Risky and Ambiguous Lotteries. Journal of Risk and Uncertainty, 10, 223–233.CrossRefGoogle Scholar
Ellsberg, D. (1961). Risk, Ambiguity and the Savage Axioms. Quarterly Journal of Economics, 75, 643–669.CrossRefGoogle Scholar
Ergin, H., and Gul, F. (2004). A Subjective Theory of Compound Lotteries. Working paper, MIT.
Fishburn, P. (1970). Utility Theory for Decision Making. New York: WileyCrossRefGoogle Scholar
Fishburn, P. (1982). Nontransitive Measurable Utility. Journal of Mathematical Psychology, 26, 31–67.CrossRefGoogle Scholar
Fishburn, P. and Wakker, P. (1995). The Invention of the Independence Condition for Preferences. Management Science, 41, 1130–1144.CrossRefGoogle Scholar
Gilboa, I., and Schmeidler, D. (1989). Maxmin Expected Utility with Nonunique Prior. Journal of Mathematical Economics, 18, 141–153.CrossRefGoogle Scholar
Glimcher, P. (2002). Decisions, Decisions, Decisions: Choosing a Neurobiological Theory of Choice. Neuron, 36, 323–332.CrossRefGoogle Scholar
Glimcher, P., and Rustichini, A. (2004). Neuroeconomics: The Concilience of Brain and Decision. Science, 306, 447–452.CrossRefGoogle Scholar
Glimcher, P. (2003). Decisions, Uncertainty, and the Brain: The Science of NeuroEconomics. Cambridge, MA and London: MIT Press.Google Scholar
Hacking, I. (1967). Slightly More Realistic Personal Probability. Philosophy of Science, 34, 311–325.CrossRefGoogle Scholar
Hirshleifer, J. (1965). Investment Decision under Uncertainty: Choice-Theoretic Approaches. Quarterly Journal of Economics, 74, 509–536.CrossRefGoogle Scholar
Hsu, M., Bhatt, M., Adolphs, R., Tranel, D., and Camerer, C. (2005). Neural Systems Responding to Degrees of Uncertainty in Human Decision-Making. Science, 310, 1680–1683.CrossRefGoogle ScholarPubMed
Huettel, S., Stowe, J., Gordon, E., Warner, B., and Platt, M. (2006). Neural Signatures of Economic Preferences for Risk and Ambiguity. Neuron, 49, 765–775.CrossRefGoogle ScholarPubMed
Kadane, J. B., and Winkler, R. L. (1988). Separating Probability Elicitation from Utilities. Journal of the American Statistical Association, 83, 357–363.CrossRefGoogle Scholar
Kahneman, D. and Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
Karni, E. (1985). Decision-Making under Uncertainty: The Case of State-Dependent Preferences. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Karni, E. (1996). Probabilities and Beliefs. Journal of Risk and Uncertainty, 13, 249–262.CrossRefGoogle Scholar
Karni, E. and Mongin, P. (2000) On the Determination of Subjective Probabilities by Choices. Management Science, 46, 233–248.CrossRefGoogle Scholar
Karni, E., Schmeidler, D., and Vind, K. (1983). On State Dependent Preferences and Subjective Probabilities. Econometrica, 51, 1021–1031.CrossRefGoogle Scholar
Karni, E., and Schmeidler, D. (1993). On the Uniqueness of Subjective Probabilities. Economic Theory, 3, 267–277.Google Scholar
Klibanoff, P., Marinacci, M., and Mukerji, S. (2005). A Smooth Model of Decision Making Under Ambiguity. Econometrica, 73, 1849–1892.CrossRefGoogle Scholar
Knight, F. (1921). Risk, Uncertainty, and Profit. New York: Houghton Mifflin.Google Scholar
Koopman, B. (1940). Axioms and Algebra of Intuitive Probability. Annals of Mathematics, 41, 269–292.CrossRefGoogle Scholar
Kreps, D. (1988). Notes on the Theory of Choice. Boulder: Westview Press.Google Scholar
Kyburg, H. (1974). The Logical Foundations of Statistical Inference. Dordrecht: Reidel.CrossRefGoogle Scholar
Levi, I. (1980). The Enterprise of Knowledge. Cambridge, MA: MIT Press.Google Scholar
Loomes, G., and Sugden, R. (1982). Regret Theory: An Alternative Theory of Rational Choice under Uncertainty. Economic Journal, 92, 805–824.CrossRefGoogle Scholar
Luce, R. D. (2000). Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Mahwah, NJ: Erlbaum.Google Scholar
Luce, R. D., and Fishburn, P. (1991). Rank-and Sign-Dependent Linear Utility Models for Finite First-Order Gambles. Journal of Risk and Uncertainty, 4, 29–59.CrossRefGoogle Scholar
Luce, R. D., and Narens, L. (1985). Classification of Concatenation Measurement Structures According to Scale Type. Journal of Mathematical Psychology, 29, 1–72.CrossRefGoogle Scholar
Luce, R. D., and Manders, K. (1988). Rank-Dependent Subjective Expected-Utility Representations. Journal of Risk and Uncertainty, 1, 305–332.CrossRefGoogle Scholar
Machina, M. (1982). Expected Utility without the Independence Axiom. Econometrica, 50, 227–323.CrossRefGoogle Scholar
Machina, M. (2005). ‘Expected Utility/Subjective Probability’ Analysis without the Sure-Thing Principle or Probabilistic Sophistication. Economic Theory, 26, 1–62.CrossRefGoogle Scholar
Machina, M. and Schmeidler, D. (1992). A More Robust Definition of Subjective Probability. Econometrica, 60, 745–780.CrossRefGoogle Scholar
Moskowitz, H., Preckel, P. and Yang, A. (1993). Decision Analysis with Incomplete Utility and Probability Information. Operations Research, 41, 864–879.CrossRefGoogle Scholar
Nau, R. (1989). Decision Analysis with Indeterminate or Incoherent Probabilities. Annals of Operations Research, 19, 375–403.CrossRefGoogle Scholar
Nau, R. (1992). Indeterminate Probabilities on Finite Sets. Annals of Statistics, 20, 1737–1767.CrossRefGoogle Scholar
Nau, R. (1995). Coherent Decision Analysis with Inseparable Probabilities and Utilities. Journal of Risk and Uncertainty, 10, 71–91.CrossRefGoogle Scholar
Nau, R. (2001a). De Finetti Was Right: Probability Does Not Exist. Theory and Decision, 59, 89–124.CrossRefGoogle Scholar
Nau, R. (2001b). Uncertainty Aversion with Second-Order Probabilities and Utilities. Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications. Web site: http://www.sipta.org/isipta01/proceedings/063.html
Nau, R. (2003). A Generalization of Pratt-Arrow Measure to Non-Expected-Utility Preferences and Inseparable Probability and Utility. Management Science, 49, 1089–1104.CrossRefGoogle Scholar
Nau, R. (2006a). Uncertainty Aversion with Second-Order Utilities and Probabilities. Management Science, 52, 136–145.CrossRefGoogle Scholar
Nau, R. (2006b). The Shape of Incomplete Preferences. Annals of Statistics 34, 5, 155–164.CrossRefGoogle Scholar
Nau, R. and McCardle, K. (1991). Arbitrage, Rationality, and Equilibrium. Theory and Decision, 31, 199–240.CrossRefGoogle Scholar
Pinker, S. (1997). How the Mind Works. New York: Norton.Google Scholar
Pinker, S. (2002). The Blank Slate: the Modern Denial of Human Nature. New York: Viking.Google Scholar
Platt, M. and Glimcher, P. (1999). Neural Correlates of Decision Variables in Parietal Cortex. Nature 400, 233–238.CrossRefGoogle ScholarPubMed
Prelec, D. (1998). The Probability Weighting Function. Econometrica, 66, 497–527.CrossRefGoogle Scholar
Prelec, D., and Loewenstein, G. (1998). The Red and the Black: Mental Accounting of Savings and Debt. Marketing Science, 17, 4–28.CrossRefGoogle Scholar
Quiggin, J. (1982). A Theory of Anticipated Utility. Journal of Economic Behaviour and Organization, 3, 323–343.CrossRefGoogle Scholar
Rios Insua, D. (1990). Sensitivity Analysis in Multiobjective Decision Making. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Rios Insua, D. (1992). On the Foundations of Decision Making Under Partial Information. Theory and Decision, 33, 83–100.CrossRefGoogle Scholar
Rios Insua, D., and Ruggeri, F. (2000). Robust Decision Analysis. New York: Springer-Verlag.Google Scholar
Rubin, H. (1987). A Weak System of Axioms for “Rational” Behavior and the Non-Separability of Utility from Prior. Statistics and Decisions, 5, 47–58.Google Scholar
Rubinstein, M. (1976). The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets. Journal of Finance, 31, 551–571.CrossRefGoogle Scholar
Savage, L. (1954). The Foundations of Statistics. New York: Wiley.Google Scholar
Schervish, M., Seidenfeld, T., and Kadane, J. (1990). State-Dependent Utilities. Journal of the American Statistical Association, 85, 840–847.CrossRefGoogle Scholar
Schmeidler, D. (1989). Subjective Probability and Expected Utility without Additivity. Econometrica, 57, 571–587.CrossRefGoogle Scholar
Schmidt, U. (2004). Alternatives to Expected Utility: Formal Theories. In Barberà, S., Hammond, P., and Seidl, C., Handbook of Utility Theory, Vol. 2. Dordrecht: Kluwer.CrossRefGoogle Scholar
Segal, U. (1989). Anticipated Utility: A Measure Representation Approach. Annals of Operations Research, 19, 359–373.CrossRefGoogle Scholar
Shafer, G. (1986). Savage Revisited (including comments). Statistical Science, 1, 463–501.CrossRefGoogle Scholar
Shiv, B., Loewenstein, G., Bechara, A., Damasio, H., and Damasio, A. (2005). Investment Behavior and the Negative Side of Emotion. Psychological Science, 16, 435–439.Google ScholarPubMed
Smith, C. (1961). Consistency in Statistical Inference and Decision. Journal of the Royal Statistical Society B, 23, 1–25.Google Scholar
Smith, J., and Nau, R. (1995). Valuing Risky Projects: Option Pricing Theory and Decision Analysis. Management Science, 41, 795–816.CrossRefGoogle Scholar
Starmer, C. (2000). Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk. Journal of Economic Literature, XXXVIII, 332–82.CrossRefGoogle Scholar
Stigler, G. (1950). The Development of Utility Theory: I; II. Journal of Political Economy, 58, 307–327;373–396.CrossRefGoogle Scholar
Sugden, R. (2004). Alternatives to Expected Utility: Foundations. In Barberà, S., Hammond, P., and Seidl, C., Handbook of Utility Theory, Vol. 2. Dordrecht: Kluwer.CrossRefGoogle Scholar
Tversky, A., and Fox, C. (1995). Weighing Risk and Uncertainty. Psychological Review, 102, 269–283.CrossRefGoogle Scholar
Tversky, A., and Kahneman, D. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5, 297–323.CrossRefGoogle Scholar
Kuilen, G., and Wakker, P. (2006). Learning in the Allais Paradox. Journal of Risk and Uncertainty, 33, 155–164.CrossRefGoogle Scholar
Neumann, J., and Morgenstern, O. (1947). Theory of Games and Economic Behavior. Princeton: Princeton University Press.Google Scholar
Wakker, P. (1989). Additive Representations of Preferences: A New Foundation for Decision Analysis. Dordrecht: Kluwer.CrossRefGoogle Scholar
Wakker, P. (1991). Additive Representations on Rank-Ordered Sets. I. The Algebraic Approach. Journal of Mathematical Psychology, 35, 501–531.CrossRefGoogle Scholar
Wakker, P. (1996) The Sure-Thing Principle and the Comonotonic Sure-Thing Principle: An Axiomatic Analysis. Journal of Mathematical Economics, 25, 213–227.CrossRefGoogle Scholar
Wakker, P. (2006). Annotated References on Decisions and Uncertainty. Web site: http://www1.fee.uva.nl/creed/wakker/refs/rfrncs.htm. Accessed 11/14/06.
Wakker, P., and Tversky, A. (1993). An Axiomatization of Cumulative Prospect Theory. Journal of Risk and Uncertainty, 7, 147–176.CrossRefGoogle Scholar
Wakker, P., and Zank, H. (1999). State Dependent Expected Utility for Savage's State Space. Mathematics of Operations Research, 24, 8–34.CrossRefGoogle Scholar
Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. London: Chapman & Hall.CrossRefGoogle Scholar
Wu, G., and Gonzalez, R. (1996). Curvature of the Probability Weighting Function. Management Science, 42, 1676–1690.CrossRefGoogle Scholar
Yaari, M. (1969). Some Remarks on Measures of Risk Aversion and Their Uses. Journal of Economic Theory, 1, 315–329.CrossRefGoogle Scholar
Yaari, M. (1987). The Dual Theory of Choice under Risk. Econometrica, 55, 95–115.CrossRefGoogle Scholar

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