Skip to main content
SpringerLink
Log in

Ambiguity-Aversion and Non-Additive Probability:

experimental evidence, models and applications

  • Chapter
Uncertain Decisions

Abstract

In the last 40 years the leading theories of choice in economics and psychology under uncertainty has been the subjective expected utility theory (SEU) of Savage (1954) (and earlier, Ramsey, DeFinetti, et al). Empirical violations and philosophical doubts have led to reexaminations of SEU, particularly in the last ten years. In these notes I will review some of the empirical evidence (which is mostly experimental), sketch some details of alternative models that have been proposed, and describe a few interesting applications to problems in game theory and economics. A fuller treatment is given in Camerer and Weber (1992), from which these notes plagiarize heavily.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anscombe, Francis J.; Aumann, Robert J. (1963). “A Definition of Subjective Probability”, Annals of Mathematical Statistics, 34, 199–205.

    Article  Google Scholar 

  • Asch, David A.; Patton, James P.; Hershey, John C. (1990). “Knowing for the sake of knowing: The value of prognostic information”. Medical Decision Making, 10, 47–57.

    Article  Google Scholar 

  • Becker, Selwyn W.; Brownson, Fred O. (1964). “What Price Ambiguity? Or the Role of Ambiguity in Decision-Making”, Journal of Political Economy, 72, 62–73

    Article  Google Scholar 

  • Begley, Thomas M.; and David P. Boyd. (1987). “Psychological characteristics associated with performance in entrepreneurial firms and smaller businesses”. Journal of Business Venturing, 2, 79–93.

    Article  Google Scholar 

  • Bernasconi, Michele; Loomes, Graham, (in press). Failures of the Reduction Principle in an Ellsberg-type Problem. Theory and Decision, 32, 77–100.

    Google Scholar 

  • Bewley, Truman F. (1986). “Knightian Decision Theory: Part I”, Cowles Foundation Discussion Paper No. 807, New Haven, CT.

    Google Scholar 

  • Buchanan, Bruce G., and Shortliffe, Edward H. (Eds.) (1984). Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading, Mass.: Addison-Wesley.

    Google Scholar 

  • Brun, Wibecke, and Karl Teigen (1990). “Prediction and postdiction inferences in guessing”. Journal of Behavioral Decision Making, 3, 17–28.

    Article  Google Scholar 

  • Camerer, Colin F. (1992). Recent tests of generalized utility theories. In W. Edwards (Ed.), Utility: Measurement, Theory, and Application. Cambridge: Cambridge University Press.

    Google Scholar 

  • Camerer, Colin F. and Risto Karjalainen (1994). “Ambiguity-aversion and Nonadditive Beliefs in Non-cooperative Games: Experimental Evidence” in B. Munier & M. Machina (eds.) Models and Experiments on Risk and Rationality, Dordrecht: Kluwer Academic Publishers, 325–358.

    Google Scholar 

  • Camerer, Colin F., and Howard Kunreuther. (1989). “Experimental markets for insurance”. Journal of Risk and Uncertainty, 2, 265–300.

    Google Scholar 

  • Camerer, Colin F. and Martin Weber. (1992). “Recent developments in modeling preferences: Uncertainty and ambiguity”, Journal of Risk and Uncertainty, 5, 325–370.

    Article  Google Scholar 

  • Chew, Soo Hong. (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.

    Article  Google Scholar 

  • Chew, Soo Hong, and MacCrimmon, Kenneth R (1979). Alpha-nu choice theory: An axiomatization of expected utility. University of British Columbia Faculty of Commerce working paper #669.

    Google Scholar 

  • Chipman, John S (1960). “Stochastic choice and subjective probability”. In D. Willner (Ed.) Decisions, Values and Groups, Volume I. Oxford, England: Pergamon Press,, 70–95.

    Google Scholar 

  • Choquet, Gerard. (1953–4). “Theory of capacities”. Annales de l’Institut Fourier 5, 131–295.

    Article  Google Scholar 

  • Cohen, Michele; Jaffray, Jean-Yves; Said, T.(1985). “Individual behavior under risk and under uncertainty: An experimental study”, Theory and Decision, 18, 203–228

    Article  Google Scholar 

  • Cohen, John, and Mark Hansel(1959). “Preferences for different combinations of chance and skill in gambling”. Nature, 183, 841–843

    Article  Google Scholar 

  • Curley, Shawn P.; Eraker, Stephen A.; and J. Frank Yates (1984). “An investigation of patient’s reactions to therapeutic uncertainty”. Medical Decision Making, 4, 501–511.

    Article  Google Scholar 

  • Curley, Shawn P.; Yates, J. Frank (1985). “The Center and Range of the Probability Interval as Factors Affecting Ambiguity Preferences”, Organizational Behavior and Human Decision Processes, 36, 272–287

    Article  Google Scholar 

  • Curley, Shawn P.; Yates, J. Frank. (1989) “An empirical evaluation of descriptive models of ambiguity reactions in choice situations”. Journal of Mathematical Psychology, 33, 397–427.

    Article  Google Scholar 

  • Curley, Shawn P.; Yates, J. Frank; Abrams, R.A. (1986). “Psychological Sources of Ambiguity Avoidance”, Organizational Behavior and Human Decision Processes, 38, 230–256

    Article  Google Scholar 

  • Curley, Shawn P.; Young, Mark J.; and J. Frank Yates (1989). “Characterizing physicians’ perceptions of ambiguity”. Medical Decision Making, 9, 116–124.

    Article  Google Scholar 

  • Dempster, Arthur P. (1967). “Upper and lower probabilities induced by a multivalued mapping”. Annals of Mathematical Statistics, 38, 325–339.

    Article  Google Scholar 

  • Dow, James, and Sergio R. C. Werlang. (1992). “Uncertainty Aversion, risk aversion, and the Optimal Choice of Portfolio”. Econometrica, 60, 1992, 197–204.

    Article  Google Scholar 

  • Dow, James, and Sergio R. C. Werlang. (1994). “Nash equilibrium under Knightian uncertainty: Breaking down backward induction”, Journal of Economic Theory, 64, 305–324.

    Article  Google Scholar 

  • Dow, James; Madrigal, Vincente; and Sergio R. C. Werlang. (1989). Preferences, common knowledge, and speculative trade. Fundacao Getulio Vargas working paper.

    Google Scholar 

  • Einhorn, Hillel J., and Robin M. Hogarth (1985). “Ambiguity and uncertainty in probabilistic inference”. Psychological Review, 92, 433–461.

    Article  Google Scholar 

  • Einhorn, Hillel J., and Robin M. Hogarth (1986). “Decision making under ambiguity”. Journal of Business, 59, S225–S250.

    Article  Google Scholar 

  • Ellsberg, Daniel. (1961). “Risk, ambiguity, and the savage Axioms”, Quarterly Journal of Economics, 75, 643–669

    Article  Google Scholar 

  • Fellner, William. (1961) “Distortion of subjective probabilities as a reaction to uncertainty”. Quarterly Journal of Economics, 75, 670–694.

    Article  Google Scholar 

  • de Finetti, Bruno. (1937). “La prevision: ses lois logiques, ses sources sources subjectives”, Annales de l’Institut Henri Poincare, 7, 1–68. English translation in Kyburg, H.E.; Smokier, H.E. (1964 Ed.), Studies in Subjective Probability, New York, Wiley Publisher, 93-158

    Google Scholar 

  • de Finetti, Bruno (1977). “Probabilities of probabilities: A real problem or a misunderstanding?” In A. Aykac & C. Brumat (Eds.), New Directions in the Application of Bayesian Methods. Amsterdam, North-Holland, pp. 1–10.

    Google Scholar 

  • Fox, Craig and Tversky, Amos (1995). “Comparative ignorance and ambiguity”, Quarterly Journal of Economics. 13(1), 5–17.

    Google Scholar 

  • Frisch, Deborah, and Jonathan Baron. (1988). “Ambiguity and rationality”. Journal of Behavioral Decision Making, 1, 149–157.

    Article  Google Scholar 

  • Gardenfors, Peter; and Sahlin, Nils-Eric (1982). “Unreliable probabilities, risk taking, and decision making”. Synthese 53, 361–386.

    Article  Google Scholar 

  • Ghirardato, Paolo. (1994) Coping with ignorance: Unforeseen contingencies and non-additive uncertainty. California Institute of Technology working paper.

    Google Scholar 

  • Gigliotti, Gary, and Sopher, Barry. (1990). The testing principle: A resolution of the Ellsberg paradox. Rutgers University Department of Economics working paper.

    Google Scholar 

  • Gilboa, Itzhak (1987). “Expected utility with purely subjective non-additive probabilities”, Journal of Mathematical Economics, 16, 65–88.

    Article  Google Scholar 

  • Gilboa, Itzhak (1988). “A combination of expected utility theory and maxmin decision criteria”. Journal of Mathematical Psychology, 32, 405–420.

    Article  Google Scholar 

  • Gilboa, Itzhak (1989). “Duality in non-additive expected utility theory”. Annals of Operations Research, 19, 405–414.

    Article  Google Scholar 

  • Gilboa, Itzhak, and David Schmeidler (1989). “Maxmin Expected Utility with A Non-Unique Prior”. Journal of Mathematical Economics, 18, 141–153.

    Article  Google Scholar 

  • Gilboa, Itzhak, and David Schmeidler(1993). Updating ambiguous beliefs. Journey of Economic Theory, 59(1), 33–49.

    Article  Google Scholar 

  • Goldsmith, Robert W., and Nils-Eric Sahlin. (1983). The role of second-order probabilities in decision making. In P. Humphreys, O. Svenson, and A. Vari (Eds.), Analysiing and Aiding Decision Processes. Amsterdam: North-Holland, pp. 455–467.

    Chapter  Google Scholar 

  • Hamm,Robert M., and H. Bursztajn. (1979) A medical version of a decision theory paradox: Is it still a paradox? Presented at the First Annual Meeting of the Society for Medical Decision Making, Cincinnati OH, September 11, 1979.

    Google Scholar 

  • Hazen, Gordon (1987). “Subjectively weighted linear utility”. Theory and Decision, 23, 261–282.

    Article  Google Scholar 

  • Heath, Chip, and Amos Tversky. (1991). “Preference and belief: Ambiguity and competence in choice under uncertainty”. Journal of Risk and Uncertainty, 4, 5–28.

    Article  Google Scholar 

  • Hodges, J. L.; Lehmann, E. L. (1952). “The Use of Previous Experience in Reaching Statistical Decisions”. Annals of Mathematical Statistics, 23, 396–407.

    Article  Google Scholar 

  • Hogarth, Robin M.; Einhorn, Hillel J. (1990). “Venture Theory: A Model of Decision Weights”, Management Science, 36, 780–803.

    Article  Google Scholar 

  • Hogarth, Robin M., and Howard Kunreuther. (1989). “Risk, ambiguity, and insurance”. Journal of Risk and Uncertainty, 2, 5–35.

    Article  Google Scholar 

  • Kahn, Barbara E.; Sarin, Rakesh K. (1988). “Modeling ambiguity in decisions under uncertainty”. Journal of Consumer Research, 15, 265–272.

    Article  Google Scholar 

  • Keppe, Hans-Jurgen and Martin Weber. (1995). “Judged knowledge and ambiguity aversion”, Theory and Decision, 51–77.

    Google Scholar 

  • Keynes, John Maynard. (1921). A Treatise on Probability. London: Macmillan.

    Google Scholar 

  • Knight, Frank H. (1921). Risk, Uncertainty and Profit, Boston, New York, Houghton Mifflin

    Google Scholar 

  • Kreps, David; Milgrom, Paul; Roberts, John; and Robert Wilson Jr. (1982). “Rational cooperation in the finitely repeated prisoners’ dilemma”. Journal of Economic Theory, 27, 245–252.

    Article  Google Scholar 

  • Langer, Ellen J. (1975). “The Illusion of Control”. Journal of Personality and Social Psychology, 32, 311–328.

    Article  Google Scholar 

  • Larson, James R., Jr. (1980). “Exploring the External Validity of a Subjectively Weighted Utility Model of Decision Making”. Organizational Behavior and Human Performance, 26, 293–304

    Article  Google Scholar 

  • Levi, Isaac. (1984). Decisions and Revisions. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Loewenstein, George. (1994). Curiosity.

    Google Scholar 

  • Luce, R. Duncan, and Peter C. Fishburn. (1991). “Rank-and sign-dependent linear utility models for finite first-order gambles”. Journal of Risk and Uncertainty, 4, 29–59.

    Article  Google Scholar 

  • MacCrimmon, Kenneth R. (1968). Descriptive and normative implications of the decision-theory postulates. In K. Borch & J. Mossin (Eds.), Risk and Uncertainty. London: MacMillan.

    Google Scholar 

  • MacCrimmon, Kenneth R. and Stig Larsson. (1979) Utility theory: Axioms versus ‘paradoxes’. In M. Allais and O. Hagen (Eds.), Expected Utility and the Allais Paradox. Dordrecht, Holland: D. Reidel Publishing Co., 333–409.

    Google Scholar 

  • Marschak, Jacob (1975). “Personal probabilities of probabilities”. Theory and Decision, 6, 121–153.

    Article  Google Scholar 

  • Milgrom, Paul, and Nancy Stokey. (1982). “Information, trade and common knowledge”. Journal of Economic Theory, 26, 17–27.

    Article  Google Scholar 

  • Nau, Robert F. (1988). Decision Analysis with Indeterminate or Incoherent Probabilities, Working Paper, Fuqua School of Business, Duke University, Durham.

    Google Scholar 

  • Nehring, Klaus. (1992). Foundations for the theory of rational choice with vague priors. In J. Geweke (Ed.), Decision Making Under Risk and Uncertainty. Dordrecht: Kluwer, 231–242.

    Chapter  Google Scholar 

  • Nehring, Klaus. (1994) “On the interpretation of Sarin and Wakker’s ‘A simple axiomatization of nonadditive expected utility’”. Econometrica, 62, 935–938.

    Article  Google Scholar 

  • von Neumann, John; Morgenstern, Oskar. (1947). Theory of Games and Economic Behavior, 2nd ed. Univ. Press, Princeton

    Google Scholar 

  • Plott, Charles. (1995). The discovered preference hypothesis, mimeo.

    Google Scholar 

  • Ritov, liana, and Jonathan Baron. (1990). “Reluctance to vaccinate: Omission bias and ambiguity”. Journal of Behavioral Decision Making, 3, 263–277.

    Article  Google Scholar 

  • Rothbart, Myron, and Mark Snyder. (1970). “Confidence in the prediction and postdiction of an uncertain outcome”. Canadian Journal of Behavioral Science, 2, 38–43.

    Article  Google Scholar 

  • Sarin, Rakesh K., and Peter Wakker. (1992). “A simple axiomatization of nonadditive expected utility”. Econometrica, 60, 1255–1272.

    Article  Google Scholar 

  • Sarin, Rakesh K.; Weber, Martin(1993). “The Effect of Ambiguity in Market Setting”, Management Science. 39, 602–615.

    Article  Google Scholar 

  • Sarin, Rakesh K., and Robert L. Winkler. (1992) “Ambiguity and decision modeling: A preference-based approach”. Journal of Risk and Uncertainty, 5, 389–407.

    Article  Google Scholar 

  • Savage, Leonard J.(1954). The Foundations of Statistics, Wiley, New York

    Google Scholar 

  • Schmeidler, David. (1982). Subjective probability without additivity. Foerder Institute for Economic Research, Tel Aviv University, working paper.

    Google Scholar 

  • Schmeidler, David. (1986). “Integral representation without additivity”. Proceedings of the American Mathematical Society, 97, 255–261.

    Article  Google Scholar 

  • Schmeidler, David (1989). “Subjective probability and expected utility without additivity”, Econometrica, 57, 571–587

    Article  Google Scholar 

  • Schum, David A. (1989). “Knowledge, probability, and credibility”. Journal of Behavioral Decision Making, 2, 39–62.

    Article  Google Scholar 

  • Segal, Uzi(1987). “The Ellsberg paradox and risk aversion: An anticipated utility approach”, International Economic Review, 28, 175–202.

    Google Scholar 

  • Shafer, Glenn. (1976). A Mathematical Theory of Evidence, Princeton: Princeton University Press.

    Google Scholar 

  • Sherman, Roger. (1974). “The psychological difference between ambiguity and risk”. Quarterly Journal of Economics, 88, 166–169.

    Article  Google Scholar 

  • Slovic, Paul; Tversky, Amos (1974). “Who Accepts Savage’s Axiom?”, Behavioral Science, 19, 368–373.

    Article  Google Scholar 

  • Strull, William M.; Lo, Bernard; and Gerald Charles. (1984) “Do patients want to participate in medical decision making?” Journal of the American Medical Association 252, 2990–2994.

    Article  Google Scholar 

  • Taylor, Kimberly A. (1991). Testing credit and blame attributions as explanations for choices under ambiguity. University of Pennsylvania Department of Decision Sciences working paper.

    Google Scholar 

  • Tversky, Amos, and Daniel Kahneman. (1992). Advances in prospect theory: Cumulative representations of uncertainty. Journal of Risk and Uncertainty, 5, 297–323.

    Article  Google Scholar 

  • Viscusi, W. Kip. (1989) “Prospective reference theory: Toward an explanation of the paradoxes”. Journal of Risk and Uncertainty 2, 235–264.

    Article  Google Scholar 

  • Viscusi, W. Kip, Wesley A. Magat, and Joel Huber. (1991). Communication of ambiguous risk information, mimeo.

    Google Scholar 

  • Wakker, Peter. (1989). “Continuous subjective expected utility with non-additive probabilities”. Journal of Mathematical Economics 18, 1–27.

    Article  Google Scholar 

  • Weber, Martin(1987). “Decision making under incomplete information”, European Journal of Operational Research, 28, 44–57.

    Google Scholar 

  • Weber, Martin; Camerer, Colin (1987). “Recent developments in modelling preferences under risk”, OR Spektrum, 9, 129–151.

    Article  Google Scholar 

  • Yates, J. Frank; Zukowski, Lisa G. (1976). “Characterization of ambiguity in decision making”, Behavioral Science, 21, 19–25.

    Article  Google Scholar 

Download references

Authors
  1. Colin Camerer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Siena, Italy

    Luigi Luini

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Camerer, C. (1999). Ambiguity-Aversion and Non-Additive Probability:. In: Luini, L. (eds) Uncertain Decisions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5083-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5083-9_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7312-4

  • Online ISBN: 978-1-4615-5083-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation