Summary
Ever since von Neumann and Morgenstern presented their expected utility theory, the axioms (assumptions) underlying their theory have been intensely debated and tested. Recently, a variety of theories have been presented which model preferences by weakening some of the assumptions of expected utility theory. We describe some of these theories, examine their properties, and provide insights into how they work. Implications for different areas of business research are discussed.
Zusammenfassung
Seit von Neumann und Morgenstern die Erwartungsnutzentheorie vorgestellt haben, werden die dieser Theorie zugrunde liegenden Axiome (Annahmen) intensiv diskutiert. Während man in der Vergangenheit entweder für oder gegen die Theorie war, wurden in letzter Zeit eine Reihe von neuen Ansätzen vorgestellt, die die Erwartungsnutzentheorie durch Abschwächung der ursprünglichen Annahmen erweitern. Nach einer Darstellung der neuen Modelle der erweiterten Erwartungsnutzentheorie werden diese verglichen und bezüglich ihrer Anwendbarkeit in verschiedenen Gebieten der Betriebswirtschaftslehre untersucht.
Similar content being viewed by others
References
Allais M (1953) Le comportement de l'homme rationel devant le risque: Critique des postulats et axiomes de l'école americaine. Econometrica 21:503–546
Allais M (1979) The foundation of a positive theory of choice involving risk and a criticism of the postulates and axioms of the American school. In: Allais M, Hagen O (eds) Expected utility hypotheses and the Allais paradox. Reidel, Dordrecht, pp 27–145
Allais M (1979) The so-called Allais paradox and rational decisions under uncertainty. In: Allais M, Hagen O (eds) Expected utility hypotheses and the Allais paradox. Reidel, Dordrecht, pp 437–699
Becker JL, Sarin RK (1986) Lottery dependent utility. Working Paper, Graduate School of Management, UCLA, Los Angeles
Bell DE (1982) Regret in decision making under uncertainty. Oper Res 30:961–981
Bell DE (1985) Disappointment in decision making under uncertainty. Oper Res 33:1–27
Bell DE, Farquhar PH (1986) Perspectives on utility theory. Oper Res 34:179–183
Bernoulli D (1738, 1954) Specimen theoriae novae de mensura sortis. Comments Acad Sci Imper Petropolitanae 5:175–192, translated by Sommer L (1954) Econometrica 22:23–36
Bolker ED (1966) A simultaneous axiomatization of utility and subjective probability. Philos Sci 34:292–312
Chew SH (1982) A mixture set axiomatization of weighted utility theory. Discussion Paper No 82-4, College of Business and Public Administration, University of Arizona, Tuscon
Chew SH (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
Chew SH (1984) An axiomatization of the rank dependent quasilinear mean generalizing the gini mean and the quasilinear mean. Manuscript, Department of Political Economy, Johns Hopkins University, Baltimore
Chew SH (1985) Implicit-weighted and semi-weighted utility theories, M-estimators, and non-demand revelation of second-price auctions for an uncertain auctioned object. Working Paper No 155, Department of Political Economy, Johns Hopkins University, Baltimore
Chew SH, Karni E, Safra Z (1987) Risk aversion in the theory of expected utility with rank dependent probabilities. J Econ Theory 42:370–381
Chew SH, MacCrimmon KR (1979) Alpha-nu choice theory: A generalization of expected utility theory. Working Paper No. 669, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver
Chew SH, MacCrimmon KR (1979) Alpha utility theory, lottery composition and the Allais paradox. Working Paper No. 686, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver
Chew SH, Waller WS (1986) Empirical tests of weighted utility theory. J Math Psychol 30:55–72
Coombs CH (1975) Portfolio theory and the measurement of risk. In: Kaplan MF, Schwartz SC (eds) Human judgement and decision making processes, Academic Press, New York, pp. 63–85
Curley SP, Yates JF (1985) The center and range of the probability interval as factors affecting ambiguity preferences. Organ Behav Human Dec Proc 36:273–287
Curley SP, Yates JF, Abrams RA (1986) Psychological sources of ambiguity avoidance. Organ Behav Human Dec Proc 38:230–256
Currim IS, Sarin RK (1986) Empirical evaluation of properties and predictive power of prospect theory. Working Paper, Graduate School of Management, UCLA, Los Angeles
Debreu G (1959) Theory of value: An axiomatic analysis of general equilibrium. Yale University Press, New Haven
Dekkel E (1986) An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. J Econ Theory 40:304–318
Dyer JS, Sarin RK (1982) Relative risk aversion. Manag Sci 28:875–886
Einhorn HJ, Hogarth RM (1985) Ambiguity and uncertainty in probabilistic inference. Psychol Rev 92:433–461
Ellsberg D (1961) Risk, ambiguity and the Savage axioms. Q J Econ 75:643–669
Fischhoff B (1983) Predicting frames. J Exp Psychol: Learning, Memory and Cognition 9:103–116
Fishburn PC (1970) Utility theory for decision making. Wiley, New York
Fishburn PC (1978) On Handa's new theory of cardinal utility and the maximization of expected return. J Polit Econ 86:321–324
Fishburn PC (1982) The foundation of expected utility. Reidel, Dordrecht
Fishburn PC (1982) Nontransitive measurable utility. J Math Psychol 26:31–67
Fishburn PC (1983) Transitive measurable utility. J Econ Theory 31:293–317
Fishburn PC (1984) SSB utility theory: An economic perspective. Math Soc Sci 8:63–94
Fishburn PC (1985) Uncertainty aversion and separated effects in decision making under uncertainty. Working Paper, AT & T Bell Laboratories, Murray Hill
Fishburn PC (1986) A new model for decisions under uncertainty. Econ Lett 21:127–130
Fishburn PC (1986) Reconsiderations of decision under uncertainty. Working Paper, AT & T Bell Laboratories, Murray Hill
Fishburn PC (1987) Nonlinear preference and utility theory. John Hopkins University Press, Baltimore
Fishburn PC (1987) Generalizations of expected utility theory: A survey of recent proposals. Working Paper, AT & T Bell Laboratories, Murray Hill
Fishburn PC, Rosenthal RW (1986) Non-cooperative games and nontransitive preferences. Math Soc Sci 12:1–7
Gärdenfors P, Sahlin N-E (1982) Unreliable probabilities, risk taking, and decision making. Synthese 53:361–386
Gärdenfors P, Sahlin N-E (1983) Decision making with unreliable probabilities. Br J Math Stat Psychol 36:240–251
Grether DM, Plott CR (1979) Economic theory of choice and the preference reversal phenomenon. Am Econ Rev 69:623–638
Hagen O (1979) Towards a positive theory of preference under risk. In: Allais M, Hagen O (eds) Expected utility and the Allais paradox. Reidel, Dordrecht, pp 271–302
Handa J (1977) Risk, probabilities and a new theory of cardinal utilities. J Polit Econ 85:97–122
Hazen GB (1986) Subjectively weighted utility. Working Paper No. 86-08, Department of Industrial Engineering and Management Science, Northwestern University, Evanston
Herstein IN, Milnor J (1953) An axiomatic approach to measurable utility. Econometrica 21:291–297
Hogarth RM, Kunreuther H (1985) Ambiguity and insurance decisions. Am Econ Rev 75:386–390
Kahn BE, Sarin RK (1987) Modelling ambiguity in decisions under uncertainty. Working Paper, Graduate School of Management, UCLA, Los Angeles
Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47:263–291
Karmarkar US (1978) Subjectively weighted utility: A descriptive extension of the expected utility model. Organ Behav Human Perform 21:61–72
Karni E, Safra Z (1987) Dynamic consistency in English auctions and expected utility theory. Working Paper, Department of Political Economy, Johns Hopkins University, Baltimore
Karni E, Safra Z (1987) Revelations in auctions and the structure of preferences. Working Paper, Department of Political Economy, Johns Hopkins University, Baltimore
Keeney RL, Raiffa H (1976) Decisions with multiple objectives. Wiley, New York
Keim D (1983) Size related anomalies and stock return seasonality. J Fin Econ 14:13–32
Keller LR (1985) Effects of problem representation on the sure-thing and substitution principle. Manag Sci 31:738–751
Keller LR, Farquhar PH (1987) The measurement of value functions. Working Paper, Graduate School of Management, UC Irvine, Irvine
Keller LR, Sarin RK, Weber M (1986) Empirical investigation of some properties of the perceived riskiness of gambles. Organ Behav Human Dec Proc 38:114–130
Kunreuther H, Ginsberg R, Miller L, Slovic P, Botkan B, Katz N (1978) Disaster insurance protection: Public policy lessons. Wiley, New York
Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement. Academic Press, New York
LaValle IH, Wapman KR (1986) Rolling back decision trees requires the independence axiom. Manag Sei 32:382–385
Lichtenstein S, Slovic P (1971) Reversals of preference between bids and choices in gambling decisions. J Exp Psychol 89:46–55
Loewenstein G (1986) Frames of mind in intertemporal choice. Working Paper, Center for Decision Research, University of Chicago, Chicago
Loomes G (1987) Predicted violations of the invariance principle in choice under uncertainty. Working Paper, Center for Experimental Economics, University of York, York
Loomes G, Sudgen R (1982) Regret theory: An alternative theory of rational choice under uncertainty. Econ J 92: 805–824
Loomes G, Sudgen R (1986) Disappointment and dynamic consistency in choice under uncertainty. Rev Econ Stud LIII:271–282
Luce RD (1981, 1982) Several possible measures of risk. Theory Dec 12:217–228, correction 13:381
Luce RD, Narens L (1985) Classification of concatenation measurement structures according to scale type. J Math Psychol 29:1–72
MacCrimmon KR (1968) Descriptive and normative implications of the decision theory postulate. In: Borch K, Mossin J (eds) Risk and uncertainty. MacMillian, New York, pp 3–23
MacCrimmon KR, Larsson S (1979) Utility theory: Axioms versus ‘paradoxes’. In: Allais M, Hagen O (eds) Expected utility and the Allais paradox. Reidel, Dordrecht, pp 333–409
Machina MJ (1982) ‘Expected utility’ analysis without the independence axion. Econometrica 50:277–323
Machina MJ (1982) A stronger characterization of declining risk aversion. Econometrica 50:1069–1079
Machina MJ (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, Stanford
Machina MJ (1987) Decision making in the presence of risk. Science 236:537–543
Marschak J (1950) Rational behavior, uncertain prospects, and measurable utility. Econometrica 18:111–141
McClelland G, Schulze WH, Coursey D (1987) Valuing risk: A comparison of expected utility theory with models from cognitive psychology. Working Paper, University of Colorado, Boulder
Morris PA (1986) The credibility of probabilities. Paper presented at the ORSA/TIMS meeting. October 1986, Miami Beach
Moskowitz H (1974) Effects of problem representation and feedback on rational behavior in Allais and Morlat-type problems. Dec Sci 5:225–242
Nau RF (1986) A new theory of indeterminate probabilities and utilities. Working Paper No. 8609, Fuqua School of Business, Duke University, Durham
von Neumann J, Morgenstern O (1947) Theory of games and economic behavior. 2nd edn. University Press, Princeton
Pollatsek A, Tversky A (1970) A theory of risk. J Math Psychol 7:540–553
Quiggin J (1982) A theory of anticipated utility. J Econ Behav Organ 3:323–343
Sarin RK (1982) Strength of preference and risky choice. Oper Res 30:982–997
Savage LJ (1954) The foundations of statistics. Wiley, New York
Schmeidler D (1984) Subjective probability and expected utility without additivity. Preprint 84, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis
Schoemaker PJH (1982) The expected utility model: Its variants, purposes, evidence and limitations. J Econ Lit 30: 529–563
Segal U (1984) Non-linear decision weights with the independence axiom. Working Paper, Department of Economics, UCLA, Los Angeles
Segal U (1985) On the axiomatic foundation of prospect theory. Working Paper, Economics Department, University of Pennsylvania, Philadelphia
Segal U (1986) The Ellsberg paradox and risk aversion: An anticipated utility approach. Working Paper No. 362, Department of Economics, UCLA, Los Angeles
Segal U (1986) Some remarks on Quiggin's anticipated utility. Working Paper No. 392, Department of Economics, UCLA, Los Angeles
Shefrin HM, Statman M (1984) Explaining investor preference for cash dividends. J Fin Econ 13:253–282
Shefrin HM, Statman M (1985) The disposition to sell winners too early and ride losers too long: Theory and evidence. J Fin 40:777–790
Slovic P, Tversky A (1974) Who accepts Savage's axiom? Behav Sci 19:368–373
Starmer C, Sugden R (1987) Violations of the sure-thing principle: An experimental test of some competing hypotheses. Working Paper, School of Economic and Social Studies, University of East Anglia, Norwich
Stone BK (1973) A general class of three-parameter risk measures. J Fin 28:657–685
Sudgen R (1986) New developments in the theory of choice under uncertainty. Bull Econ Res 38:1–24
Thaler R (1980) Toward a positive theory of consumer choice. J Econ Behav Organ 1:39–60
Thaler R (1985) Using mental accounting in a theory of consumer choices. Mark Sci 4:199–214
Tversky A, Kahneman D (1981) The framing of decisions and the psychology of choice. Science 211:453–458
Tversky A, Kahneman D (1986) Rational choice and the framing of decisions. J Business 59:S251-S278
Yaari ME (1987) The dual theory of choice under risk. Econometrica 55:95–115
Weber RJ (1982) The Allais paradox Dutch auctions, and alpha-utility theory. Working Paper No. 536, J. L. Kellog Graduate School of Management, Northwestern University, Evanston
Wilhelm J (1986) Zum Verhältnis von Höhenpräferenz und Risikopräferenz. Z betriebswirt Forsch 38:467–492
von Winterfeldt D, Edwards W (1986) Decision analysis and behavioral research. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Weber, M., Camerer, C. Recent developments in modelling preferences under risk. OR Spektrum 9, 129–151 (1987). https://doi.org/10.1007/BF01721094
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01721094