Journal of Risk and Uncertainty

, Volume 5, Issue 4, pp 325–370 | Cite as

Recent developments in modeling preferences: Uncertainty and ambiguity

  • Colin Camerer
  • Martin Weber
Symposium on Risk and Ambiguity

Abstract

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.

Key words

ambiguity uncertainty Ellsberg paradox nonexpected utility 

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References

  1. Anscombe, Francis J. and Robert, Aumann. (1963). “A Definition of Subjective Probability,” Annals of Mathematical Statistics 34, 199–205.Google Scholar
  2. 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.Google Scholar
  3. Aumann, Robert J. (1962). “Utility Theory without the Completeness Axiom,” Econometrica 30, 445–462; 32 (1964), 210–212.Google Scholar
  4. Becker, Gordon M., Morris H. DeGroot, and Jacob Marschak. (1964). “Measuring Utility by a Single-Response Sequential Method,” Behavioral Science 9, 226–232.Google Scholar
  5. Becker, Joao L. and Rakesh K. Sarin. (1990) “Economics of Ambiguity in Probability,” working paper, UCLA Graduate School of Management, May.Google Scholar
  6. Becker, Selwyn W. and Fred O. Brownson. (1964). “What Price Ambiguity? Or the Role of Ambiguity in Decision-Making,” Journal of Political Economy 72, 62–73.Google Scholar
  7. 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.Google Scholar
  8. Bell, David E. (1985). “Disappointment in Decision Making under Uncertainty,” Operations Research 33, 1–27.Google Scholar
  9. Bernasconi, Michele and Graham Loomes. (In press). “Failures of the Reduction Principle in an Ellsberg-Type Problem,” Theory and Decision.Google Scholar
  10. Bewley, Truman F. (1986). “Knightian Decision Theory: Part I,” Cowles Foundation Discussion Paper No. 807, New Haven, CT.Google Scholar
  11. Boiney, Lindsley G. (1990). “Effects of Skewed Probability on Preference under Ambiguity,” working paper, Fuqua School of Business, Duke University.Google Scholar
  12. Brown, Rex V. (1990). “Assessment Uncertainty Technology for Making and Defending Risky Decisions,” Journal of Behavioral Decision Making 3, 213–228.Google Scholar
  13. Buchanan, Bruce G. and Edward H. Shortliffe (eds.). (1984). Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading, MA: Addison-Wesley.Google Scholar
  14. Budner, Stanley. (1963). “Intolerance of Ambiguity as a Personality Variable,” Journal of Personality 30, 29–50.Google Scholar
  15. Brun, Wibecke and Karl Teigen. (1990). “Prediction and Postdiction Inferences in Guessing,” Journal of Behavioral Decision Making 3, 17–28.Google Scholar
  16. Camerer, Colin F. (1992). “Recent Tests of Generalized Utility Theories.” In W. Edwards (ed.), Utility: Measurement, Theory, and Application. Dordrecht, Holland: Kluwer Academic Publishers.Google Scholar
  17. Camerer, Colin F. and Teck-Hua Ho. (1991). “Isolation Effects in Compound Lottery Reduction,” working paper, University of Pennsylvania Department of Decision Sciences.Google Scholar
  18. Camerer, Colin F. and Howard Kunreuther. (1989). “Experimental Markets for Insurance,” Journal of Risk and Uncertainty 2, 265–300.Google Scholar
  19. Casey, Jeff T. and John T. Scholz. (In press). “Boundary Effects of Vague Risk Information on Taxpayer Decisions,” Organizational Behavior and Human Decision Processes.Google Scholar
  20. 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.Google Scholar
  21. Chew, Soo Hong, Edi Karni, and Zvi Safra. (1987). “Risk Aversion in the Theory of Expected Utility with Rank-Dependent Probabilities,” Journal of Economic Theory 42, 370–381.Google Scholar
  22. Chew, Soo Hong and Kenneth R. MacCrimmon. (1979). “Alpha-nu Choice Theory: An Axiomatization of Expected Utility,” Working Paper #669, University of British Columbia Faculty of Commerce.Google Scholar
  23. 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.Google Scholar
  24. Choquet, Gustave. (1953–54). “Theory of Capacities,” Annales de l'Institut Fourier 5, 131–295.Google Scholar
  25. Cohen, Michele, Jean-Yves Jaffray, and Tanois Said. (1985). “Individual Behavior under Risk and under Uncertainty: An Experimental Study,” Theory and Decision 18, 203–228.Google Scholar
  26. Cohen, John, and Mark Hansel. (1959). “Preferences for Different Combinations of Chance and Skill in Gambling,” Nature 183, 841–843.Google Scholar
  27. 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.Google Scholar
  28. 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.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. 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.Google Scholar
  32. Curley, Shawn P., Mark J. Young, and Frank J. Yates. (1989). “Characterizing Physicians' Perceptions of Ambiguity,” Medical Decision Making 9, 116–124.Google Scholar
  33. Dempster, Arthur P. (1967). “Upper and Lower Probabilities Induced by a Multivalued Mapping,” Annals of Mathematical Statistics 38, 325–339.Google Scholar
  34. Dow, James and Sergio R. C. Werlang. (in press). “Excess Volatility of Stock Prices and Knightian Uncertainty,” European Economic Review.Google Scholar
  35. Dow, James and Sergio R. C. Werlang. (in press). “Uncertainty Aversion and the Optimal Choice of Portfolio,” Econometrica.Google Scholar
  36. Dow, James, Vincente Madrigal, and Sergio R. C. Werlang. (1989). “Preferences, Common Knowledge, and Speculative Trade,” working paper, London Business School.Google Scholar
  37. Edwards, Ward (ed.). (1992). Utility: Theories, Measurement, and Applications. Dordrecht, Holland: Kluwer Academic Publishers.Google Scholar
  38. Einhorn, Hillel J. and Robin M. Hogarth. (1985). “Ambiguity and Uncertainty in Probabilistic Inference,” Psychology Review 92, 433–461.Google Scholar
  39. Einhorn, Hillel J. and Robin M. Hogarth. (1986). “Decision Making under Ambiguity,” Journal of Business 59, S225-S250.Google Scholar
  40. Ellsberg, Daniel. (1961). “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, 643–669.Google Scholar
  41. Epstein, Larry G. and Tan Wang. (1992). “Intertemporal Asset Pricing under Knightian Uncertainty,” working paper no. 9211, Department of Economics, University of Toronto.Google Scholar
  42. Fellner, William. (1961). “Distortion of Subjective Probabilities as a Reaction to Uncertainty,” Quarterly Journal of Economics 75, 670–694.Google Scholar
  43. 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.Google Scholar
  44. 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: North-Holland, pp. 1–10.Google Scholar
  45. Fishburn, Peter C. (1970). Utility Theory for Decision Making. New York: Wiley.Google Scholar
  46. Fishburn, Peter C. (1982). The Foundation of Expected Utility Theory. Dordrecht: Reidel.Google Scholar
  47. Fishburn, Peter C. (1983). “Transitive Measurable Utility,” Journal of Economic Theory 31, 293–317.Google Scholar
  48. Fishburn, Peter C. (1986). “A New Model for Decisions under Uncertainty,” Economics Letters 21, 127–130.Google Scholar
  49. Fishburn, Peter C. (1987). “Reconsiderations in the Foundations of Decision under Uncertainty,” Economic Journal 97, 825–841.Google Scholar
  50. 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: Springer-Verlag, 1025.Google Scholar
  51. Fishburn, Peter C. (1988b). Nonlinear Preference and Utility Theory. Baltimore: Johns Hopkins University Press.Google Scholar
  52. Fishburn, Peter C. (1989). “Generalizations of Expected Utility Theories: A Survey of Recent Proposals,” Annals of Operations Research 19, 3–28.Google Scholar
  53. Fishburn, Peter C. (In press). “On the Theory of Ambiguity,” International Journal of Information and Management Science.Google Scholar
  54. Franke, Günter. (1978). “Expected Utility with Ambiguous Probabilities and ‘Irrational Parameters’,” Theory and Decision 9, 267–283.Google Scholar
  55. French, Kenneth R. and James M. Poterba. (1991). “Investor Diversification and International Equity Markets,” American Economic Review Papers and Proceedings.Google Scholar
  56. Frisch, Deborah. (1988). “The Effect of Ambiguity on Judgment and Choice,” Unpublished doctoral dissertation, Department of Psychology, University of Pennsylvania.Google Scholar
  57. Frisch, Deborah and Jonathan, Baron. (1988). “Ambiguity and Rationality,” Journal of Behavioral Decision Making 1, 149–157.Google Scholar
  58. Gardenfors, Peter and Nils-Eric, Sahlin. (1982). “Unreliable Probabilities, Risk Taking, and Decision Making,” Synthese 53, 361–386.Google Scholar
  59. Gigliotti, Gary and Barry Sopher. (1990). “The Testing Principle: A Resolution of the Ellsberg Paradox,” working paper, Department of Economics, Rutgers University.Google Scholar
  60. Gilboa, Itzhak. (1987). “Expected Utility with Purely Subjective Non-Additive Probabilities,” Journal of Mathematical Economics 16, 65–88.Google Scholar
  61. Gilboa, Itzhak. (1988). “A Combination of Expected Utility Theory and Maxmin Decision Criteria,” Journal of Mathematical Psychology 32, 405–420.Google Scholar
  62. Gilboa, Itzhak. (1989a). “Additivizations of Nonadditive Measures,” Mathematics of Operations Research 4, 1–17.Google Scholar
  63. Gilboa, Itzhak. (1989b). “Duality in Non-Additive Expected Utility Theory,” Annals of Operations Research 19, 405–414.Google Scholar
  64. Gilboa, Itzhak and David Schmeidler. (1989). “Maxmin Expected Utility with A Non-Unique Prior,” Journal of Mathematical Economics 18, 141–153.Google Scholar
  65. Gilboa, Itzhak and David Schmeidler. (1991). “Updating Ambiguous Beliefs,” working paper, Department of Managerial Economics and Decision Sciences, Northwestern University.Google Scholar
  66. Good, Irving J. (1950). Probability and the Weighing of Evidence. New York: Hafner's.Google Scholar
  67. 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.), Analysing and Aiding Decision Processes. Amsterdam: North-Holland, 455–467.Google Scholar
  68. Green, Jerry and Bruno Julien. (1988). “Ordinal Independence in Nonlinear Utility Theory,” Journal of Risk and Uncertainty 1, 355–387. (Erratum, 1989, 2, 119.)Google Scholar
  69. 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.Google Scholar
  70. Gul, Faruk. (1991). “A Theory of Disappointment in Decision Making under Uncertainty,” Econometrica 59, 667–683.Google Scholar
  71. 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.Google Scholar
  72. Hazen, Gordon B. (1987). “Subjectively Weighted Linear Utility,” Theory and Decision 23, 261–282.Google Scholar
  73. Hazen, Gordon B. and Jia-Sheng Lee. (1989). “Ambiguity Aversion in the Small and in the Large for Weighted Linear Utility,” Journal of Risk and Uncertainty 4, 177–212.Google Scholar
  74. Heath, Chip and Amos Tversky. (1991). “Preference and Belief: Ambiguity and Competence in Choice under Uncertainty,” Journal of Risk and Uncertainty 4, 5–28.Google Scholar
  75. Hellwig, Martin. (1989). “Asymmetric Information, Financial Markets, and Financial Institutions,” European Economic Review 33, 277–285.Google Scholar
  76. Hodges, J. L. and E. L. Lehmann. (1952). “The Use of Previous Experience in Reaching Statistical Decisions,” Annals of Mathematical Statistics 23, 396–407.Google Scholar
  77. Hogarth, Robin M. (1989). “Ambiguity in Competitive Decision-Making: Some Implications and Tests.” In. P. C. Fishburn and I. LaValle (eds.), Annals of Operations Research 19, 31–50.Google Scholar
  78. Hogarth, Robin M. and Hillel J. Einhorn. (1990). “Venture Theory: A Model of Decision Weights,” Management Science 36, 780–803.Google Scholar
  79. Hogarth, Robin M. and Howard Kunreuther. (1985). “Ambiguity and Insurance Decisions,” American Economic Review Papers and Proceedings 75, 386–390.Google Scholar
  80. Hogarth, Robin M. and Howard Kunreuther. (1989). “Risk, Ambiguity, and Insurance,” Journal of Risk and Uncertainty 2, 5–35.Google Scholar
  81. Hogarth, Robin M. and Howard Kunreuther. (In press). “Pricing Insurance and Warranties: Ambiguity and Correlated Risks,” Geneva Papers on Insurance.Google Scholar
  82. Howard, Ronald A. (1992). “The Cogency of Decision Analysis.” In W. Edwards (ed.), Utility: Theories, Measurement, Applications. Dordrecht, Holland: Kluwer Academic Publishers.Google Scholar
  83. Hurwicz, Leonid. (1951). “Optimality Criteria for Decision Making Under Ignorance,” Cowles Commission Discussion Paper, Statistics 370.Google Scholar
  84. Jaffray, Jean-Yves. (1988). “Choice under Risk and the Security Factor,” Theory and Decision 24, 169–200.Google Scholar
  85. Kahn, Barbara E. and Robert J. Meyer. (1991). “Consumer Multiattribute Judgments under Attribute Weight Uncertainty,” Journal of Consumer Research 17, 508–522.Google Scholar
  86. Kahn, Barbara E. and Rakesh K. Sarin. (1987). “Modelling Ambiguity in Decisions under Uncertainty,” Working Paper no. 163, UCLA Center for Marketing Studies, July.Google Scholar
  87. Kahn, Barbara E. and Rakesh K. Sarin. (1988). “Modelling Ambiguity in Decisions under Uncertainty,” Journal of Consumer Research 15, 265–272.Google Scholar
  88. Kahneman, Daniel, Paul Slovic, and Amos Tversky (eds.). (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.Google Scholar
  89. Karni, Edi. (1985). Decision Making under Uncertainty: The Case of State-Dependent Preferences. Cambridge: Harvard University Press.Google Scholar
  90. Karni, Edi and David Schmeidler. (1990). “Utility Theory with Uncertainty.” In W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, Volume 4. Amsterdam: North-Holland.Google Scholar
  91. Keim, Donald. (1983). “Size Related Anomalies and Stock Return Seasonality,” Journal of Financial Economics 14, 13–32.Google Scholar
  92. Keppe, Hans-Jurgen and Martin Weber. (1991). “Judged Knowledge and Ambiguity Aversion,” working paper no. 277, Christian-Albrechts-Universitat, Kiel, Germany.Google Scholar
  93. Keynes, John Maynard. (1921). A Treatise on Probability. London: Macmillan.Google Scholar
  94. Kischka, P. and C. Puppe. (1990). “Decisions under Risk and Uncertainty: A Survey of Recent Developments,” working paper, Universitaet Karlsruhe, August.Google Scholar
  95. Knetsch, Jack L. (1989). “The Endowment Effect and Evidence of Nonreversible Indifference Curves,” American Economic Review 79, 1277–1284.Google Scholar
  96. Knight, Frank H. (1921). Risk, Uncertainty and Profit. Boston: Houghton Mifflin.Google Scholar
  97. 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.Google Scholar
  98. Koopman, B. (1940). “The Bases of Probability,” Bulletin of the American Mathematical Society 46, 763–774.Google Scholar
  99. 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.Google Scholar
  100. Langer, Ellen J. (1975). “The Illusion of Control,” Journal of Personality and Social Psychology 32, 311–328.Google Scholar
  101. 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.Google Scholar
  102. Lemaire, Jean. (1986). Theorie Mathematique des Assurances. Belgium: Presses Universitaires de Bruxelles.Google Scholar
  103. Levi, Isaac. (1984). Decisions and Revisions. Cambridge: Cambridge University Press.Google Scholar
  104. Loomes, Graham and Robert Sugden. (1986). “Disappointment and Dynamic Consistency in Choice under Uncertainty,” Review of Economic Studies 53, 271–282.Google Scholar
  105. Luce, R. Duncan. (1988). “Rank-Dependent, Subjective Expected Utility Representations,” Journal of Risk and Uncertainty 1, 305–332.Google Scholar
  106. Luce, R. Duncan. (1991). “Rank- and Sign-Dependent Linear Utility Models for Binary Gambles,” Journal of Economic Theory 53, 75–100.Google Scholar
  107. 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.Google Scholar
  108. Luce, R. Duncan and Louis Narens. (1985). “Classification of Concatenation Measurement Structures According to Scale Type,” Journal of Mathematical Psychology 29, 1–72.Google Scholar
  109. MacCrimmon, Kenneth R. (1968). “Descriptive and Normative Implications of the Decision-Theory Postulates.” In K. Borch and J. Mossin (eds.), Risk and Uncertainty. London: MacMillan.Google Scholar
  110. 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.Google Scholar
  111. Machina, Mark J. (1987). “Choice under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1, 121–154.Google Scholar
  112. Machina, Mark J. (1989). “Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty,” Journal of Economic Literature 27, 1622–1668.Google Scholar
  113. Machina, Mark J. and David Schmeidler. (in press). “A More Robust Definition of Subjective Probability,” Econometrica.Google Scholar
  114. Marschak, Jacob. (1975). “Personal Probabilities of Probabilities,” Theory and Decision 6, 121–153.Google Scholar
  115. March, James G. and J. P. Olsen. (1976). Ambiguity and Choice in Organizations. Bergen: Universitetsforlaget.Google Scholar
  116. Milgrom, Paul and Nancy Stokey. (1982). “Information, Trade and Common Knowledge,” Journal of Economic Theory 26, 17–27.Google Scholar
  117. Nakamura, Yutaka. (1990). “Subjective Expected Utility with Non-Additive Probabilities on Finite State Spaces,” Journal of Economic Theory 51, 346–366.Google Scholar
  118. Nau, Robert F. (1988). “Decision Analysis with Indeterminate or Incoherent Probabilities,” working paper, Fuqua School of Business, Duke University.Google Scholar
  119. Nehring, Klaus. (1990). “A Theory of Simultaneous Expected Utility Maximization with Vague Beliefs,” IRU working paper, University of California, Irvine.Google Scholar
  120. von Neumann, John and Oskar Morgenstern. (1947). Theory of Games and Economic Behavior, 2nd ed. Princeton: Princeton University Press.Google Scholar
  121. Pate-Cornell, 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.Google Scholar
  122. Phillipson, Tomas. (1991). “Choice between Observable Risk and Uncertainty,” working paper, Department of Economics, University of Chicago.Google Scholar
  123. Priest, George L. (1987). “The Current Insurance Crisis and Modern Tort Law,” Yale Law Journal 96, 1521–1590.Google Scholar
  124. Quiggin, John. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  125. Raiffa, Howard. (1961). “Risk, Ambiguity, and the Savage Axioms: Comment,” Quarterly Journal of Economics 75, 690–694.Google Scholar
  126. 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.Google Scholar
  127. Ritov, Ilana and Jonathan Baron. (1990). “Reluctance to Vaccinate: Omission Bias and Ambiguity,” Journal of Behavioral Decision Making 3, 263–277.Google Scholar
  128. Roberts, Harry V. (1963). “Risk, Ambiguity, and the Savage Axioms: Comment,” Quarterly Journal of Economics 77, 327–336.Google Scholar
  129. Ross, William T. (1989). “The Effect of Ambiguity on Strategic Marketing Decision Making,” working paper, Wharton School, University of Pennsylvania.Google Scholar
  130. Rothbart, Myron and Mark Snyder. (1970). “Confidence in the Prediction and Postdiction of an Uncertain Outcome,” Canadian Journal of Behavioral Science 2, 38–43.Google Scholar
  131. Samuelson, William and Richard Zeckhauser. (1988). “Status Quo Bias in Decision Making,” Journal of Risk and Uncertainty 1, 7–59.Google Scholar
  132. Sarin, Rakesh K. and Peter Wakker. (1990). “Incorporating Attitudes towards Ambiguity in Savage's Set-up,” working paper, Anderson Graduate School of Management, UCLA.Google Scholar
  133. Sarin, Rakesh K. and Martin Weber. (1989). “The Effect of Ambiguity in Market Setting,” Management Science.Google Scholar
  134. Sarin, Rakesh K. and Robert L. Winkler. (1990). “Ambiguity and Decision Modeling: A Preference-Based Approach,” working paper, Institute of Statistics and Decision Sciences, Duke University, June.Google Scholar
  135. Savage, Leonard J. (1954). The Foundations of Statistics. New York: Wiley.Google Scholar
  136. Schmeidler, David. (1982). “Subjective Probability without Additivity,” working paper, Foerder Institute for Economic Research, Tel Aviv University.Google Scholar
  137. Schmeidler, David. (1986). “Integral Representation without Additivity,” Proceedings of the American Mathematical Society 97, 255–261.Google Scholar
  138. Schmeidler, David. (1989). “Subjective Probability and Expected Utility without Additivity,” Econometrica 57, 571–587.Google Scholar
  139. Schum, David A. (1989). “Knowledge, Probability, and Credibility,” Journal of Behavioral Decision Making 2, 39–62.Google Scholar
  140. Segal, Uzi. (1987a). “The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,” International Economic Review 28, 175–202.Google Scholar
  141. Segal, Uzi. (1987b). “Some Remarks on Quiggin's Anticipated Utility Theory,” Journal of Economic Behavior and Organization 8, 145–154.Google Scholar
  142. Segal, Uzi. (1989). “Anticipated Utility: A Measure Representation Approach,” Annals of Operations Research 19, 359–373.Google Scholar
  143. Shafer, Glenn. (1976). A Mathematical Theory of Evidence. Princeton: Princeton University Press.Google Scholar
  144. Sherman, Roger. (1974). “The Psychological Difference between Ambiguity and Risk,” Quarterly Journal of Economics 88, 166–169.Google Scholar
  145. Simonsen, M. H. and Sergio R. C. Werlang. (1990). “Subadditive Probabilities and Portfolio Inertia,” working paper.Google Scholar
  146. Slovic, Paul and Amos Tversky. (1974). “Who Accepts Savage's Axiom?” Behavioral Science 19, 368–373.Google Scholar
  147. Smith, Cedric A. B. (1961). “Consistency in Statistical Inference and Decision,” Journal of Royal Statistical Society, Series B 23, 1–37.Google Scholar
  148. Smith, Vernon L. (1969). “Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn,” Quarterly Journal of Economics 83, 324–329.Google Scholar
  149. Smithson, Michael. (1989). Ignorance and Uncertainty: Emerging Paradigms. New York: Springer-Verlag.Google Scholar
  150. Spetzler, C. S. and C. A. Stael von Holstein. (1975). “Probability Encoding in Decision Analysis,” Management Science 22, 240–358.Google Scholar
  151. 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.Google Scholar
  152. Taylor, Kimberly A. (1991). “Testing Credit and Blame Attributions as Explanations for Choices under Ambiguity,” working paper, Department of Decision Sciences, University of Pennsylvania.Google Scholar
  153. Tversky, Amos and Daniel Kahneman. (undated). “Can Normative and Descriptive Analyses Be Reconciled?” working paper, Department of Psychology, Standard University.Google Scholar
  154. Tversky, Amos and Daniel Kahneman. (in press). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty.Google Scholar
  155. Viscusi, W. Kip. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264.Google Scholar
  156. Viscusi, W. Kip and Wesley A. Magat. (1991). “Bayesian Decisions with Ambiguous Belief Aversion,” working paper, Department of Economics, Duke University.Google Scholar
  157. Viscusi, W. Kip, Wesley A. Magat, and Joel Huber. (1991). “Communication of Ambiguous Risk Information,” Theory and Decision.Google Scholar
  158. Wakker, Peter. (1984). “Cardinal Coordinate Independence for Expected Utility,” Journal of Mathematical Psychology 28, 110–117.Google Scholar
  159. Wakker, Peter. (1989a). “Continuous Subjective Expected Utility with Non-Additive Probabilities,” Journal of Mathematical Economics 18, 1–27.Google Scholar
  160. Wakker, Peter. (1989b). Additive Representation of Preferences: A New Foundation for Decision Analysis. Dordrecht, Holland: Kluwer Academic Publisher.Google Scholar
  161. Wald, Abraham. (1950). Statistical Decision Functions. New York: John Wiley & Sons.Google Scholar
  162. Weber, Martin. (1987). “Decision Making under Incomplete Information,” European Journal of Operational Research 28, 44–57.Google Scholar
  163. Weber, Martin. (1990). Risikoentscheidungskalkule in der Finanzierungstheorie. Stuttgart: C. E. Poeschel Verlag.Google Scholar
  164. Weber, Martin and Colin Camerer. (1987). “Recent Developments in Modelling Preferences under Risk,” OR Spektrum 9, 129–151.Google Scholar
  165. Willham, Cynthia Fobian, and Jay J. J. Christensen-Szalanski. (In press). “Ambiguity and Liability Negotiations: The Effects of the Negotiators' Role and the Sensitivity Zone,” Organizational Behavior and Human Decision Processes.Google Scholar
  166. Williamson, Oliver E. (1985). The Economic Institutions of Capitalism. New York: Free Press.Google Scholar
  167. Winkler, Robert L. (1991). “Ambiguity, Probability, Preference, and Decision Analysis,” Journal of Risk and Uncertainty 4, 285–297.Google Scholar
  168. Yaari, Menahem E. (1987). “The Dual Theory of Choice under Risk,” Econometrica 55, 95–115.Google Scholar
  169. Yates, J. Frank and Lisa, G. Zukowski. (1976). “Characterization of Ambiguity in Decision Making,” Behavioral Science 21, 19–25.Google Scholar
  170. Yoo, K. R. (1990). “A Theory of the Underpricing of Initial Public Offerings, working paper, Kellogg Graduate School of Management, Northwestern University.Google Scholar
  171. Zadeh, Lofti. (1965). “Fuzzy Sets,” Information and Control 8, 338–353.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Colin Camerer
    • 1
  • Martin Weber
    • 2
  1. 1.Graduate School of BusinessUniversity of ChicagoChicago
  2. 2.Lehrstuhl fur Allg. Betriebswirtschaftslehre und EntscheidungsforschungChristian-Albrechts-UniversitatKielGermany

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