Find out how to access previewonly content
Recent developments in modeling preferences: Uncertainty and ambiguity
 Colin Camerer,
 Martin Weber
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In subjective expected utility (SEU), the decision weights people attach to events are their beliefs about the likelihood of events. Much empirical evidence, inspired by Ellsberg (1961) and others, shows that people prefer to bet on events they know more about, even when their beliefs are held constant. (They are averse to ambiguity, or uncertainty about probability.) We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU.
Thanks to Jonathan Baron, James Dow, Peter Fishburn, Itzhak Gilboa, Gordon Hazen, Howard Kunreuther, Tomas Phillipson, David Schmeidler, Amos Tversky, the editor, and several anonymous referees for corrections and helpful comments. Camerer's contribution to this work was supported by the National Science Foundation, grant no. SES 8809299. Weber's contribution was supported by the Deutsche Forschungsgemeinschaft, grant no. WE 993/51.
 Anscombe, Francis J. and Robert, Aumann. (1963). “A Definition of Subjective Probability,” Annals of Mathematical Statistics 34, 199–205.
 Asch, David A., James P. Patton, and John C. Hershey. (1990). “Knowing for the Sake of Knowing: The Value of Prognostic Information,” Medical Decision Making 10, 47–57.
 Aumann, Robert J. (1962). “Utility Theory without the Completeness Axiom,” Econometrica 30, 445–462; 32 (1964), 210–212.
 Becker, Gordon M., Morris H. DeGroot, and Jacob Marschak. (1964). “Measuring Utility by a SingleResponse Sequential Method,” Behavioral Science 9, 226–232.
 Becker, Joao L. and Rakesh K. Sarin. (1990) “Economics of Ambiguity in Probability,” working paper, UCLA Graduate School of Management, May.
 Becker, Selwyn W. and Fred O. Brownson. (1964). “What Price Ambiguity? Or the Role of Ambiguity in DecisionMaking,” Journal of Political Economy 72, 62–73.
 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.
 Bell, David E. (1985). “Disappointment in Decision Making under Uncertainty,” Operations Research 33, 1–27.
 Bernasconi, Michele and Graham Loomes. (In press). “Failures of the Reduction Principle in an EllsbergType Problem,” Theory and Decision.
 Bewley, Truman F. (1986). “Knightian Decision Theory: Part I,” Cowles Foundation Discussion Paper No. 807, New Haven, CT.
 Boiney, Lindsley G. (1990). “Effects of Skewed Probability on Preference under Ambiguity,” working paper, Fuqua School of Business, Duke University.
 Brown, Rex V. (1990). “Assessment Uncertainty Technology for Making and Defending Risky Decisions,” Journal of Behavioral Decision Making 3, 213–228.
 Buchanan, Bruce G. and Edward H. Shortliffe (eds.). (1984). RuleBased Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading, MA: AddisonWesley.
 Budner, Stanley. (1963). “Intolerance of Ambiguity as a Personality Variable,” Journal of Personality 30, 29–50.
 Brun, Wibecke and Karl Teigen. (1990). “Prediction and Postdiction Inferences in Guessing,” Journal of Behavioral Decision Making 3, 17–28.
 Camerer, Colin F. (1992). “Recent Tests of Generalized Utility Theories.” In W. Edwards (ed.), Utility: Measurement, Theory, and Application. Dordrecht, Holland: Kluwer Academic Publishers.
 Camerer, Colin F. and TeckHua Ho. (1991). “Isolation Effects in Compound Lottery Reduction,” working paper, University of Pennsylvania Department of Decision Sciences.
 Camerer, Colin F. and Howard Kunreuther. (1989). “Experimental Markets for Insurance,” Journal of Risk and Uncertainty 2, 265–300.
 Casey, Jeff T. and John T. Scholz. (In press). “Boundary Effects of Vague Risk Information on Taxpayer Decisions,” Organizational Behavior and Human Decision Processes.
 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.
 Chew, Soo Hong, Edi Karni, and Zvi Safra. (1987). “Risk Aversion in the Theory of Expected Utility with RankDependent Probabilities,” Journal of Economic Theory 42, 370–381.
 Chew, Soo Hong and Kenneth R. MacCrimmon. (1979). “Alphanu Choice Theory: An Axiomatization of Expected Utility,” Working Paper #669, University of British Columbia Faculty of Commerce.
 Chipman, John S. (1960). “Stochastic Choice and Subjective Probability.” In D. Willner (ed.), Decisions, Values and Groups, Volume I. Oxford, England: Pergamon Press, pp. 70–95.
 Choquet, Gustave. (1953–54). “Theory of Capacities,” Annales de l'Institut Fourier 5, 131–295.
 Cohen, Michele, JeanYves Jaffray, and Tanois Said. (1985). “Individual Behavior under Risk and under Uncertainty: An Experimental Study,” Theory and Decision 18, 203–228.
 Cohen, John, and Mark Hansel. (1959). “Preferences for Different Combinations of Chance and Skill in Gambling,” Nature 183, 841–843.
 Coombs, Clyde H. and P. E. Lehner. (1981). “Evaluation of Two Alternative Models for a Theory of Risk: I. Are Moments of Distributions Useful in Assessing Risk?” Journal of Experimental Psychology: Human Perception and Performance 7, 1110–1123.
 Curley, Shawn P., Stephen A. Eraker, and Frank J. Yates. (1984). “An Investigation of Patient's Reactions to Therapeutic Uncertainty,” Medical Decision Making 4, 501–511.
 Curley, Shawn P. and Frank J. Yates. (1985). “The Center and Range of the Probability Interval as Factors Affecting Ambiguity Preferences,” Organizational Behavior and Human Decision Processes 36, 272–287.
 Curley, Shawn P. and Frank J. Yates. (1989). “An Empirical Evaluation of Descriptive Models of Ambiguity Reactions in Choice Situations,” Journal of Mathematical Psychology 33, 397–427.
 Curley, Shawn P., Frank J. Yates and R.A. Abrams. (1986). “Psychological Sources of Ambiguity Avoidance,” Organizational Behavior and Human Decision Processes 38, 230–256.
 Curley, Shawn P., Mark J. Young, and Frank J. Yates. (1989). “Characterizing Physicians' Perceptions of Ambiguity,” Medical Decision Making 9, 116–124.
 Dempster, Arthur P. (1967). “Upper and Lower Probabilities Induced by a Multivalued Mapping,” Annals of Mathematical Statistics 38, 325–339.
 Dow, James and Sergio R. C. Werlang. (in press). “Excess Volatility of Stock Prices and Knightian Uncertainty,” European Economic Review.
 Dow, James and Sergio R. C. Werlang. (in press). “Uncertainty Aversion and the Optimal Choice of Portfolio,” Econometrica.
 Dow, James, Vincente Madrigal, and Sergio R. C. Werlang. (1989). “Preferences, Common Knowledge, and Speculative Trade,” working paper, London Business School.
 Edwards, Ward (ed.). (1992). Utility: Theories, Measurement, and Applications. Dordrecht, Holland: Kluwer Academic Publishers.
 Einhorn, Hillel J. and Robin M. Hogarth. (1985). “Ambiguity and Uncertainty in Probabilistic Inference,” Psychology Review 92, 433–461.
 Einhorn, Hillel J. and Robin M. Hogarth. (1986). “Decision Making under Ambiguity,” Journal of Business 59, S225S250.
 Ellsberg, Daniel. (1961). “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, 643–669.
 Epstein, Larry G. and Tan Wang. (1992). “Intertemporal Asset Pricing under Knightian Uncertainty,” working paper no. 9211, Department of Economics, University of Toronto.
 Fellner, William. (1961). “Distortion of Subjective Probabilities as a Reaction to Uncertainty,” Quarterly Journal of Economics 75, 670–694.
 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 H.E. Kyburg and H.E. Smokler, H.E. (eds.). (1964). Studies in Subjective Probability. New York: Wiley, 93–158.
 de Finetti, Bruno. (1977). “Probabilities of Probabilities: A Real Problem or a Misunderstanding?” In A. Aykac and C. Brumat (eds.), New Directions in the Application of Bayesian Methods. Amsterdam: NorthHolland, pp. 1–10.
 Fishburn, Peter C. (1970). Utility Theory for Decision Making. New York: Wiley.
 Fishburn, Peter C. (1982). The Foundation of Expected Utility Theory. Dordrecht: Reidel.
 Fishburn, Peter C. (1983). “Transitive Measurable Utility,” Journal of Economic Theory 31, 293–317.
 Fishburn, Peter C. (1986). “A New Model for Decisions under Uncertainty,” Economics Letters 21, 127–130.
 Fishburn, Peter C. (1987). “Reconsiderations in the Foundations of Decision under Uncertainty,” Economic Journal 97, 825–841.
 Fishburn, Peter C. (1988a). “Uncertainty Aversion and Separated Effects in Decision Making under Uncertainty,” In J. Kacprzyk and M. Fedrizzi (eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Berlin: SpringerVerlag, 1025.
 Fishburn, Peter C. (1988b). Nonlinear Preference and Utility Theory. Baltimore: Johns Hopkins University Press.
 Fishburn, Peter C. (1989). “Generalizations of Expected Utility Theories: A Survey of Recent Proposals,” Annals of Operations Research 19, 3–28.
 Fishburn, Peter C. (In press). “On the Theory of Ambiguity,” International Journal of Information and Management Science.
 Franke, Günter. (1978). “Expected Utility with Ambiguous Probabilities and ‘Irrational Parameters’,” Theory and Decision 9, 267–283.
 French, Kenneth R. and James M. Poterba. (1991). “Investor Diversification and International Equity Markets,” American Economic Review Papers and Proceedings.
 Frisch, Deborah. (1988). “The Effect of Ambiguity on Judgment and Choice,” Unpublished doctoral dissertation, Department of Psychology, University of Pennsylvania.
 Frisch, Deborah and Jonathan, Baron. (1988). “Ambiguity and Rationality,” Journal of Behavioral Decision Making 1, 149–157.
 Gardenfors, Peter and NilsEric, Sahlin. (1982). “Unreliable Probabilities, Risk Taking, and Decision Making,” Synthese 53, 361–386.
 Gigliotti, Gary and Barry Sopher. (1990). “The Testing Principle: A Resolution of the Ellsberg Paradox,” working paper, Department of Economics, Rutgers University.
 Gilboa, Itzhak. (1987). “Expected Utility with Purely Subjective NonAdditive Probabilities,” Journal of Mathematical Economics 16, 65–88.
 Gilboa, Itzhak. (1988). “A Combination of Expected Utility Theory and Maxmin Decision Criteria,” Journal of Mathematical Psychology 32, 405–420.
 Gilboa, Itzhak. (1989a). “Additivizations of Nonadditive Measures,” Mathematics of Operations Research 4, 1–17.
 Gilboa, Itzhak. (1989b). “Duality in NonAdditive Expected Utility Theory,” Annals of Operations Research 19, 405–414.
 Gilboa, Itzhak and David Schmeidler. (1989). “Maxmin Expected Utility with A NonUnique Prior,” Journal of Mathematical Economics 18, 141–153.
 Gilboa, Itzhak and David Schmeidler. (1991). “Updating Ambiguous Beliefs,” working paper, Department of Managerial Economics and Decision Sciences, Northwestern University.
 Good, Irving J. (1950). Probability and the Weighing of Evidence. New York: Hafner's.
 Goldsmith, Robert W. and NilsEric Sahlin. (1983). “The Role of SecondOrder Probabilities in Decision Making.” In. P. Humphreys, O. Svenson and A. Vari (eds.), Analysing and Aiding Decision Processes. Amsterdam: NorthHolland, 455–467.
 Green, Jerry and Bruno Julien. (1988). “Ordinal Independence in Nonlinear Utility Theory,” Journal of Risk and Uncertainty 1, 355–387. (Erratum, 1989, 2, 119.)
 Grossman, Sanford J. and Oliver D. Hart. (1986). “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration,” Journal of Political Economy 94, 691–719.
 Gul, Faruk. (1991). “A Theory of Disappointment in Decision Making under Uncertainty,” Econometrica 59, 667–683.
 Hamm, Robert M. and H. Bursztajn. (1979). “A Medical Version of a Decision Paradox: Is it Still a Paradox?” Presented at the First Annual Meeting of the Society for Medical Decision Making, Cincinnati OH, September 11.
 Hazen, Gordon B. (1987). “Subjectively Weighted Linear Utility,” Theory and Decision 23, 261–282.
 Hazen, Gordon B. and JiaSheng Lee. (1989). “Ambiguity Aversion in the Small and in the Large for Weighted Linear Utility,” Journal of Risk and Uncertainty 4, 177–212.
 Heath, Chip and Amos Tversky. (1991). “Preference and Belief: Ambiguity and Competence in Choice under Uncertainty,” Journal of Risk and Uncertainty 4, 5–28.
 Hellwig, Martin. (1989). “Asymmetric Information, Financial Markets, and Financial Institutions,” European Economic Review 33, 277–285.
 Hodges, J. L. and E. L. Lehmann. (1952). “The Use of Previous Experience in Reaching Statistical Decisions,” Annals of Mathematical Statistics 23, 396–407.
 Hogarth, Robin M. (1989). “Ambiguity in Competitive DecisionMaking: Some Implications and Tests.” In. P. C. Fishburn and I. LaValle (eds.), Annals of Operations Research 19, 31–50.
 Hogarth, Robin M. and Hillel J. Einhorn. (1990). “Venture Theory: A Model of Decision Weights,” Management Science 36, 780–803.
 Hogarth, Robin M. and Howard Kunreuther. (1985). “Ambiguity and Insurance Decisions,” American Economic Review Papers and Proceedings 75, 386–390.
 Hogarth, Robin M. and Howard Kunreuther. (1989). “Risk, Ambiguity, and Insurance,” Journal of Risk and Uncertainty 2, 5–35.
 Hogarth, Robin M. and Howard Kunreuther. (In press). “Pricing Insurance and Warranties: Ambiguity and Correlated Risks,” Geneva Papers on Insurance.
 Howard, Ronald A. (1992). “The Cogency of Decision Analysis.” In W. Edwards (ed.), Utility: Theories, Measurement, Applications. Dordrecht, Holland: Kluwer Academic Publishers.
 Hurwicz, Leonid. (1951). “Optimality Criteria for Decision Making Under Ignorance,” Cowles Commission Discussion Paper, Statistics 370.
 Jaffray, JeanYves. (1988). “Choice under Risk and the Security Factor,” Theory and Decision 24, 169–200.
 Kahn, Barbara E. and Robert J. Meyer. (1991). “Consumer Multiattribute Judgments under Attribute Weight Uncertainty,” Journal of Consumer Research 17, 508–522.
 Kahn, Barbara E. and Rakesh K. Sarin. (1987). “Modelling Ambiguity in Decisions under Uncertainty,” Working Paper no. 163, UCLA Center for Marketing Studies, July.
 Kahn, Barbara E. and Rakesh K. Sarin. (1988). “Modelling Ambiguity in Decisions under Uncertainty,” Journal of Consumer Research 15, 265–272.
 Kahneman, Daniel, Paul Slovic, and Amos Tversky (eds.). (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.
 Karni, Edi. (1985). Decision Making under Uncertainty: The Case of StateDependent Preferences. Cambridge: Harvard University Press.
 Karni, Edi and David Schmeidler. (1990). “Utility Theory with Uncertainty.” In W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, Volume 4. Amsterdam: NorthHolland.
 Keim, Donald. (1983). “Size Related Anomalies and Stock Return Seasonality,” Journal of Financial Economics 14, 13–32.
 Keppe, HansJurgen and Martin Weber. (1991). “Judged Knowledge and Ambiguity Aversion,” working paper no. 277, ChristianAlbrechtsUniversitat, Kiel, Germany.
 Keynes, John Maynard. (1921). A Treatise on Probability. London: Macmillan.
 Kischka, P. and C. Puppe. (1990). “Decisions under Risk and Uncertainty: A Survey of Recent Developments,” working paper, Universitaet Karlsruhe, August.
 Knetsch, Jack L. (1989). “The Endowment Effect and Evidence of Nonreversible Indifference Curves,” American Economic Review 79, 1277–1284.
 Knight, Frank H. (1921). Risk, Uncertainty and Profit. Boston: Houghton Mifflin.
 Koh, Francis and Terry Walter. (1989). “A Direct Test of Rock's Model of the Pricing of Unseasoned Issues,” Journal of Financial Economics 23, 251–272.
 Koopman, B. (1940). “The Bases of Probability,” Bulletin of the American Mathematical Society 46, 763–774.
 Kunreuther, Howard, Jacqueline Meszaros, Robin M. Hogarth, and Mark Spranca. (1991). “Ambiguity and Underwriter Decision Processes,” working paper, Department of Decision Sciences, University of Pennsylvania.
 Langer, Ellen J. (1975). “The Illusion of Control,” Journal of Personality and Social Psychology 32, 311–328.
 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.
 Lemaire, Jean. (1986). Theorie Mathematique des Assurances. Belgium: Presses Universitaires de Bruxelles.
 Levi, Isaac. (1984). Decisions and Revisions. Cambridge: Cambridge University Press.
 Loomes, Graham and Robert Sugden. (1986). “Disappointment and Dynamic Consistency in Choice under Uncertainty,” Review of Economic Studies 53, 271–282.
 Luce, R. Duncan. (1988). “RankDependent, Subjective Expected Utility Representations,” Journal of Risk and Uncertainty 1, 305–332.
 Luce, R. Duncan. (1991). “Rank and SignDependent Linear Utility Models for Binary Gambles,” Journal of Economic Theory 53, 75–100.
 Luce, R. Duncan and Peter C. Fishburn. (1991). “Rank and SignDependent Linear Utility Models for Finite FirstOrder Gambles,” Journal of Risk and Uncertainty 4, 29–59.
 Luce, R. Duncan and Louis Narens. (1985). “Classification of Concatenation Measurement Structures According to Scale Type,” Journal of Mathematical Psychology 29, 1–72.
 MacCrimmon, Kenneth R. (1968). “Descriptive and Normative Implications of the DecisionTheory Postulates.” In K. Borch and J. Mossin (eds.), Risk and Uncertainty. London: MacMillan.
 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, pp. 333–409.
 Machina, Mark J. (1987). “Choice under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1, 121–154.
 Machina, Mark J. (1989). “Dynamic Consistency and NonExpected Utility Models of Choice Under Uncertainty,” Journal of Economic Literature 27, 1622–1668.
 Machina, Mark J. and David Schmeidler. (in press). “A More Robust Definition of Subjective Probability,” Econometrica.
 Marschak, Jacob. (1975). “Personal Probabilities of Probabilities,” Theory and Decision 6, 121–153.
 March, James G. and J. P. Olsen. (1976). Ambiguity and Choice in Organizations. Bergen: Universitetsforlaget.
 Milgrom, Paul and Nancy Stokey. (1982). “Information, Trade and Common Knowledge,” Journal of Economic Theory 26, 17–27.
 Nakamura, Yutaka. (1990). “Subjective Expected Utility with NonAdditive Probabilities on Finite State Spaces,” Journal of Economic Theory 51, 346–366.
 Nau, Robert F. (1988). “Decision Analysis with Indeterminate or Incoherent Probabilities,” working paper, Fuqua School of Business, Duke University.
 Nehring, Klaus. (1990). “A Theory of Simultaneous Expected Utility Maximization with Vague Beliefs,” IRU working paper, University of California, Irvine.
 von Neumann, John and Oskar Morgenstern. (1947). Theory of Games and Economic Behavior, 2nd ed. Princeton: Princeton University Press.
 PateCornell, M. Elizabeth. (1987). “Risk Analysis and the Relevance of Uncertainty in Nuclear Safety Decisions.” In E. E. Bailey (ed.), Public Regulation: New Perspectives on Institutions and Policies. Cambridge, MA: MIT Press, pp. 227–253.
 Phillipson, Tomas. (1991). “Choice between Observable Risk and Uncertainty,” working paper, Department of Economics, University of Chicago.
 Priest, George L. (1987). “The Current Insurance Crisis and Modern Tort Law,” Yale Law Journal 96, 1521–1590.
 Quiggin, John. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.
 Raiffa, Howard. (1961). “Risk, Ambiguity, and the Savage Axioms: Comment,” Quarterly Journal of Economics 75, 690–694.
 Ramsey, Frank. (1931). “Truth and Probability.” In The Foundations of Mathematics and Other Logical Essays, London: Routledge and Kegan Paul, pp. 156–198. Reprinted in H. E. Kyburg and H. E. Smokler (eds.). (1964). Studies in Subjective Probability. New York: Wiley, pp. 61–92.
 Ritov, Ilana and Jonathan Baron. (1990). “Reluctance to Vaccinate: Omission Bias and Ambiguity,” Journal of Behavioral Decision Making 3, 263–277.
 Roberts, Harry V. (1963). “Risk, Ambiguity, and the Savage Axioms: Comment,” Quarterly Journal of Economics 77, 327–336.
 Ross, William T. (1989). “The Effect of Ambiguity on Strategic Marketing Decision Making,” working paper, Wharton School, University of Pennsylvania.
 Rothbart, Myron and Mark Snyder. (1970). “Confidence in the Prediction and Postdiction of an Uncertain Outcome,” Canadian Journal of Behavioral Science 2, 38–43.
 Samuelson, William and Richard Zeckhauser. (1988). “Status Quo Bias in Decision Making,” Journal of Risk and Uncertainty 1, 7–59.
 Sarin, Rakesh K. and Peter Wakker. (1990). “Incorporating Attitudes towards Ambiguity in Savage's Setup,” working paper, Anderson Graduate School of Management, UCLA.
 Sarin, Rakesh K. and Martin Weber. (1989). “The Effect of Ambiguity in Market Setting,” Management Science.
 Sarin, Rakesh K. and Robert L. Winkler. (1990). “Ambiguity and Decision Modeling: A PreferenceBased Approach,” working paper, Institute of Statistics and Decision Sciences, Duke University, June.
 Savage, Leonard J. (1954). The Foundations of Statistics. New York: Wiley.
 Schmeidler, David. (1982). “Subjective Probability without Additivity,” working paper, Foerder Institute for Economic Research, Tel Aviv University.
 Schmeidler, David. (1986). “Integral Representation without Additivity,” Proceedings of the American Mathematical Society 97, 255–261.
 Schmeidler, David. (1989). “Subjective Probability and Expected Utility without Additivity,” Econometrica 57, 571–587.
 Schum, David A. (1989). “Knowledge, Probability, and Credibility,” Journal of Behavioral Decision Making 2, 39–62.
 Segal, Uzi. (1987a). “The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,” International Economic Review 28, 175–202.
 Segal, Uzi. (1987b). “Some Remarks on Quiggin's Anticipated Utility Theory,” Journal of Economic Behavior and Organization 8, 145–154.
 Segal, Uzi. (1989). “Anticipated Utility: A Measure Representation Approach,” Annals of Operations Research 19, 359–373.
 Shafer, Glenn. (1976). A Mathematical Theory of Evidence. Princeton: Princeton University Press.
 Sherman, Roger. (1974). “The Psychological Difference between Ambiguity and Risk,” Quarterly Journal of Economics 88, 166–169.
 Simonsen, M. H. and Sergio R. C. Werlang. (1990). “Subadditive Probabilities and Portfolio Inertia,” working paper.
 Slovic, Paul and Amos Tversky. (1974). “Who Accepts Savage's Axiom?” Behavioral Science 19, 368–373.
 Smith, Cedric A. B. (1961). “Consistency in Statistical Inference and Decision,” Journal of Royal Statistical Society, Series B 23, 1–37.
 Smith, Vernon L. (1969). “Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn,” Quarterly Journal of Economics 83, 324–329.
 Smithson, Michael. (1989). Ignorance and Uncertainty: Emerging Paradigms. New York: SpringerVerlag.
 Spetzler, C. S. and C. A. Stael von Holstein. (1975). “Probability Encoding in Decision Analysis,” Management Science 22, 240–358.
 Strull, William M., Bernard Lo, and Gerald Charles. (1984). “Do Patients Want to Participate in Medical Decision Making?” Journal of the American Medical Association 252, 2990–2994.
 Taylor, Kimberly A. (1991). “Testing Credit and Blame Attributions as Explanations for Choices under Ambiguity,” working paper, Department of Decision Sciences, University of Pennsylvania.
 Tversky, Amos and Daniel Kahneman. (undated). “Can Normative and Descriptive Analyses Be Reconciled?” working paper, Department of Psychology, Standard University.
 Tversky, Amos and Daniel Kahneman. (in press). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty.
 Viscusi, W. Kip. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264.
 Viscusi, W. Kip and Wesley A. Magat. (1991). “Bayesian Decisions with Ambiguous Belief Aversion,” working paper, Department of Economics, Duke University.
 Viscusi, W. Kip, Wesley A. Magat, and Joel Huber. (1991). “Communication of Ambiguous Risk Information,” Theory and Decision.
 Wakker, Peter. (1984). “Cardinal Coordinate Independence for Expected Utility,” Journal of Mathematical Psychology 28, 110–117.
 Wakker, Peter. (1989a). “Continuous Subjective Expected Utility with NonAdditive Probabilities,” Journal of Mathematical Economics 18, 1–27.
 Wakker, Peter. (1989b). Additive Representation of Preferences: A New Foundation for Decision Analysis. Dordrecht, Holland: Kluwer Academic Publisher.
 Wald, Abraham. (1950). Statistical Decision Functions. New York: John Wiley & Sons.
 Weber, Martin. (1987). “Decision Making under Incomplete Information,” European Journal of Operational Research 28, 44–57.
 Weber, Martin. (1990). Risikoentscheidungskalkule in der Finanzierungstheorie. Stuttgart: C. E. Poeschel Verlag.
 Weber, Martin and Colin Camerer. (1987). “Recent Developments in Modelling Preferences under Risk,” OR Spektrum 9, 129–151.
 Willham, Cynthia Fobian, and Jay J. J. ChristensenSzalanski. (In press). “Ambiguity and Liability Negotiations: The Effects of the Negotiators' Role and the Sensitivity Zone,” Organizational Behavior and Human Decision Processes.
 Williamson, Oliver E. (1985). The Economic Institutions of Capitalism. New York: Free Press.
 Winkler, Robert L. (1991). “Ambiguity, Probability, Preference, and Decision Analysis,” Journal of Risk and Uncertainty 4, 285–297.
 Yaari, Menahem E. (1987). “The Dual Theory of Choice under Risk,” Econometrica 55, 95–115.
 Yates, J. Frank and Lisa, G. Zukowski. (1976). “Characterization of Ambiguity in Decision Making,” Behavioral Science 21, 19–25.
 Yoo, K. R. (1990). “A Theory of the Underpricing of Initial Public Offerings, working paper, Kellogg Graduate School of Management, Northwestern University.
 Zadeh, Lofti. (1965). “Fuzzy Sets,” Information and Control 8, 338–353.
 Title
 Recent developments in modeling preferences: Uncertainty and ambiguity
 Journal

Journal of Risk and Uncertainty
Volume 5, Issue 4 , pp 325370
 Cover Date
 19921001
 DOI
 10.1007/BF00122575
 Print ISSN
 08955646
 Online ISSN
 15730476
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 ambiguity
 uncertainty
 Ellsberg paradox
 nonexpected utility
 Industry Sectors
 Authors

 Colin Camerer ^{(1)}
 Martin Weber ^{(2)}
 Author Affiliations

 1. Graduate School of Business, University of Chicago, 60637, Chicago, IL
 2. Lehrstuhl fur Allg. Betriebswirtschaftslehre und Entscheidungsforschung, ChristianAlbrechtsUniversitat, Olshausenstr. 2040, 2300, Kiel, Germany