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Recent developments in modelling preferences under risk

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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.

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References

  1. 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

    Google Scholar 

  2. 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

    Google Scholar 

  3. 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

    Google Scholar 

  4. Becker JL, Sarin RK (1986) Lottery dependent utility. Working Paper, Graduate School of Management, UCLA, Los Angeles

    Google Scholar 

  5. Bell DE (1982) Regret in decision making under uncertainty. Oper Res 30:961–981

    Google Scholar 

  6. Bell DE (1985) Disappointment in decision making under uncertainty. Oper Res 33:1–27

    Google Scholar 

  7. Bell DE, Farquhar PH (1986) Perspectives on utility theory. Oper Res 34:179–183

    Google Scholar 

  8. 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

    Google Scholar 

  9. Bolker ED (1966) A simultaneous axiomatization of utility and subjective probability. Philos Sci 34:292–312

    Google Scholar 

  10. 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

    Google Scholar 

  11. 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

    Google Scholar 

  12. 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

    Google Scholar 

  13. 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

    Google Scholar 

  14. 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

    Google Scholar 

  15. 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

    Google Scholar 

  16. 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

    Google Scholar 

  17. Chew SH, Waller WS (1986) Empirical tests of weighted utility theory. J Math Psychol 30:55–72

    Google Scholar 

  18. 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

    Google Scholar 

  19. 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

    Google Scholar 

  20. Curley SP, Yates JF, Abrams RA (1986) Psychological sources of ambiguity avoidance. Organ Behav Human Dec Proc 38:230–256

    Google Scholar 

  21. Currim IS, Sarin RK (1986) Empirical evaluation of properties and predictive power of prospect theory. Working Paper, Graduate School of Management, UCLA, Los Angeles

    Google Scholar 

  22. Debreu G (1959) Theory of value: An axiomatic analysis of general equilibrium. Yale University Press, New Haven

    Google Scholar 

  23. Dekkel E (1986) An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. J Econ Theory 40:304–318

    Google Scholar 

  24. Dyer JS, Sarin RK (1982) Relative risk aversion. Manag Sci 28:875–886

    Google Scholar 

  25. Einhorn HJ, Hogarth RM (1985) Ambiguity and uncertainty in probabilistic inference. Psychol Rev 92:433–461

    Google Scholar 

  26. Ellsberg D (1961) Risk, ambiguity and the Savage axioms. Q J Econ 75:643–669

    Google Scholar 

  27. Fischhoff B (1983) Predicting frames. J Exp Psychol: Learning, Memory and Cognition 9:103–116

    Google Scholar 

  28. Fishburn PC (1970) Utility theory for decision making. Wiley, New York

    Google Scholar 

  29. Fishburn PC (1978) On Handa's new theory of cardinal utility and the maximization of expected return. J Polit Econ 86:321–324

    Google Scholar 

  30. Fishburn PC (1982) The foundation of expected utility. Reidel, Dordrecht

    Google Scholar 

  31. Fishburn PC (1982) Nontransitive measurable utility. J Math Psychol 26:31–67

    Google Scholar 

  32. Fishburn PC (1983) Transitive measurable utility. J Econ Theory 31:293–317

    Google Scholar 

  33. Fishburn PC (1984) SSB utility theory: An economic perspective. Math Soc Sci 8:63–94

    Google Scholar 

  34. Fishburn PC (1985) Uncertainty aversion and separated effects in decision making under uncertainty. Working Paper, AT & T Bell Laboratories, Murray Hill

    Google Scholar 

  35. Fishburn PC (1986) A new model for decisions under uncertainty. Econ Lett 21:127–130

    Google Scholar 

  36. Fishburn PC (1986) Reconsiderations of decision under uncertainty. Working Paper, AT & T Bell Laboratories, Murray Hill

    Google Scholar 

  37. Fishburn PC (1987) Nonlinear preference and utility theory. John Hopkins University Press, Baltimore

    Google Scholar 

  38. Fishburn PC (1987) Generalizations of expected utility theory: A survey of recent proposals. Working Paper, AT & T Bell Laboratories, Murray Hill

    Google Scholar 

  39. Fishburn PC, Rosenthal RW (1986) Non-cooperative games and nontransitive preferences. Math Soc Sci 12:1–7

    Google Scholar 

  40. Gärdenfors P, Sahlin N-E (1982) Unreliable probabilities, risk taking, and decision making. Synthese 53:361–386

    Google Scholar 

  41. Gärdenfors P, Sahlin N-E (1983) Decision making with unreliable probabilities. Br J Math Stat Psychol 36:240–251

    Google Scholar 

  42. Grether DM, Plott CR (1979) Economic theory of choice and the preference reversal phenomenon. Am Econ Rev 69:623–638

    Google Scholar 

  43. 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

    Google Scholar 

  44. Handa J (1977) Risk, probabilities and a new theory of cardinal utilities. J Polit Econ 85:97–122

    Google Scholar 

  45. Hazen GB (1986) Subjectively weighted utility. Working Paper No. 86-08, Department of Industrial Engineering and Management Science, Northwestern University, Evanston

    Google Scholar 

  46. Herstein IN, Milnor J (1953) An axiomatic approach to measurable utility. Econometrica 21:291–297

    Google Scholar 

  47. Hogarth RM, Kunreuther H (1985) Ambiguity and insurance decisions. Am Econ Rev 75:386–390

    Google Scholar 

  48. Kahn BE, Sarin RK (1987) Modelling ambiguity in decisions under uncertainty. Working Paper, Graduate School of Management, UCLA, Los Angeles

    Google Scholar 

  49. Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47:263–291

    Google Scholar 

  50. Karmarkar US (1978) Subjectively weighted utility: A descriptive extension of the expected utility model. Organ Behav Human Perform 21:61–72

    Google Scholar 

  51. Karni E, Safra Z (1987) Dynamic consistency in English auctions and expected utility theory. Working Paper, Department of Political Economy, Johns Hopkins University, Baltimore

    Google Scholar 

  52. Karni E, Safra Z (1987) Revelations in auctions and the structure of preferences. Working Paper, Department of Political Economy, Johns Hopkins University, Baltimore

    Google Scholar 

  53. Keeney RL, Raiffa H (1976) Decisions with multiple objectives. Wiley, New York

    Google Scholar 

  54. Keim D (1983) Size related anomalies and stock return seasonality. J Fin Econ 14:13–32

    Google Scholar 

  55. Keller LR (1985) Effects of problem representation on the sure-thing and substitution principle. Manag Sci 31:738–751

    Google Scholar 

  56. Keller LR, Farquhar PH (1987) The measurement of value functions. Working Paper, Graduate School of Management, UC Irvine, Irvine

    Google Scholar 

  57. 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

    Google Scholar 

  58. Kunreuther H, Ginsberg R, Miller L, Slovic P, Botkan B, Katz N (1978) Disaster insurance protection: Public policy lessons. Wiley, New York

    Google Scholar 

  59. Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement. Academic Press, New York

    Google Scholar 

  60. LaValle IH, Wapman KR (1986) Rolling back decision trees requires the independence axiom. Manag Sei 32:382–385

    Google Scholar 

  61. Lichtenstein S, Slovic P (1971) Reversals of preference between bids and choices in gambling decisions. J Exp Psychol 89:46–55

    Google Scholar 

  62. Loewenstein G (1986) Frames of mind in intertemporal choice. Working Paper, Center for Decision Research, University of Chicago, Chicago

    Google Scholar 

  63. Loomes G (1987) Predicted violations of the invariance principle in choice under uncertainty. Working Paper, Center for Experimental Economics, University of York, York

    Google Scholar 

  64. Loomes G, Sudgen R (1982) Regret theory: An alternative theory of rational choice under uncertainty. Econ J 92: 805–824

    Google Scholar 

  65. Loomes G, Sudgen R (1986) Disappointment and dynamic consistency in choice under uncertainty. Rev Econ Stud LIII:271–282

    Google Scholar 

  66. Luce RD (1981, 1982) Several possible measures of risk. Theory Dec 12:217–228, correction 13:381

    Google Scholar 

  67. Luce RD, Narens L (1985) Classification of concatenation measurement structures according to scale type. J Math Psychol 29:1–72

    Google Scholar 

  68. 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

    Google Scholar 

  69. 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

    Google Scholar 

  70. Machina MJ (1982) ‘Expected utility’ analysis without the independence axion. Econometrica 50:277–323

    Google Scholar 

  71. Machina MJ (1982) A stronger characterization of declining risk aversion. Econometrica 50:1069–1079

    Google Scholar 

  72. 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

    Google Scholar 

  73. Machina MJ (1987) Decision making in the presence of risk. Science 236:537–543

    Google Scholar 

  74. Marschak J (1950) Rational behavior, uncertain prospects, and measurable utility. Econometrica 18:111–141

    Google Scholar 

  75. 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

    Google Scholar 

  76. Morris PA (1986) The credibility of probabilities. Paper presented at the ORSA/TIMS meeting. October 1986, Miami Beach

  77. Moskowitz H (1974) Effects of problem representation and feedback on rational behavior in Allais and Morlat-type problems. Dec Sci 5:225–242

    Google Scholar 

  78. Nau RF (1986) A new theory of indeterminate probabilities and utilities. Working Paper No. 8609, Fuqua School of Business, Duke University, Durham

    Google Scholar 

  79. von Neumann J, Morgenstern O (1947) Theory of games and economic behavior. 2nd edn. University Press, Princeton

    Google Scholar 

  80. Pollatsek A, Tversky A (1970) A theory of risk. J Math Psychol 7:540–553

    Google Scholar 

  81. Quiggin J (1982) A theory of anticipated utility. J Econ Behav Organ 3:323–343

    Google Scholar 

  82. Sarin RK (1982) Strength of preference and risky choice. Oper Res 30:982–997

    Google Scholar 

  83. Savage LJ (1954) The foundations of statistics. Wiley, New York

    Google Scholar 

  84. Schmeidler D (1984) Subjective probability and expected utility without additivity. Preprint 84, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis

    Google Scholar 

  85. Schoemaker PJH (1982) The expected utility model: Its variants, purposes, evidence and limitations. J Econ Lit 30: 529–563

    Google Scholar 

  86. Segal U (1984) Non-linear decision weights with the independence axiom. Working Paper, Department of Economics, UCLA, Los Angeles

    Google Scholar 

  87. Segal U (1985) On the axiomatic foundation of prospect theory. Working Paper, Economics Department, University of Pennsylvania, Philadelphia

    Google Scholar 

  88. Segal U (1986) The Ellsberg paradox and risk aversion: An anticipated utility approach. Working Paper No. 362, Department of Economics, UCLA, Los Angeles

    Google Scholar 

  89. Segal U (1986) Some remarks on Quiggin's anticipated utility. Working Paper No. 392, Department of Economics, UCLA, Los Angeles

    Google Scholar 

  90. Shefrin HM, Statman M (1984) Explaining investor preference for cash dividends. J Fin Econ 13:253–282

    Google Scholar 

  91. 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

    Google Scholar 

  92. Slovic P, Tversky A (1974) Who accepts Savage's axiom? Behav Sci 19:368–373

    Google Scholar 

  93. 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

    Google Scholar 

  94. Stone BK (1973) A general class of three-parameter risk measures. J Fin 28:657–685

    Google Scholar 

  95. Sudgen R (1986) New developments in the theory of choice under uncertainty. Bull Econ Res 38:1–24

    Google Scholar 

  96. Thaler R (1980) Toward a positive theory of consumer choice. J Econ Behav Organ 1:39–60

    Google Scholar 

  97. Thaler R (1985) Using mental accounting in a theory of consumer choices. Mark Sci 4:199–214

    Google Scholar 

  98. Tversky A, Kahneman D (1981) The framing of decisions and the psychology of choice. Science 211:453–458

    Google Scholar 

  99. Tversky A, Kahneman D (1986) Rational choice and the framing of decisions. J Business 59:S251-S278

    Google Scholar 

  100. Yaari ME (1987) The dual theory of choice under risk. Econometrica 55:95–115

    Google Scholar 

  101. 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

    Google Scholar 

  102. Wilhelm J (1986) Zum Verhältnis von Höhenpräferenz und Risikopräferenz. Z betriebswirt Forsch 38:467–492

    Google Scholar 

  103. von Winterfeldt D, Edwards W (1986) Decision analysis and behavioral research. Cambridge University Press, Cambridge

    Google Scholar 

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Weber, M., Camerer, C. Recent developments in modelling preferences under risk. OR Spektrum 9, 129–151 (1987). https://doi.org/10.1007/BF01721094

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