Belief and Preference in Decision Under Uncertainty

Most decisions in life are gambles. Should I speed up or slow down as I approach the yellow traffic light ahead? Should I invest in the stock market or in treasury bills? Should I undergo surgery or radiation therapy to treat my tumor? From mundane choices rendered with scarcely a moment's reflection to urgent decisions founded on careful deliberation, we seldom know in advance and with certainty what the consequences of our choices will be. Thus, most decisions require not only an assessment of the attractiveness of potential consequences, but also some appraisal of their likelihood of occurrence. Virtually all decision theorists agree that values and beliefs jointly influence willingness to act under uncertainty. However, there is considerable disagreement about how to measure values and beliefs, and howto model their influence on decisions. Our purpose in this chapter is to bring into sharper focus the role of values and beliefs in decision under uncertainty and contrast some recent developments in the descriptive modeling of choice under uncertainty with the classical normative model.

[1]  Derek J. Koehler,et al.  A Strength Model of Probability Judgments for Tournaments , 1996 .

[2]  H. Markowitz.  The Utility of Wealth , 1952, Journal of Political Economy.

[3]  Shawn P. Curley,et al.  The center and range of the probability interval as factors affecting ambiguity preferences , 1985 .

[4]  A. Tversky,et al.  Heuristics and Biases: Unpacking, Repacking, and Anchoring: Advances in Support Theory , 2002 .

[5]  D. Ellsberg,et al.  Risk, ambiguity, and decision , 2001 .

[6]  Lyle Brenner,et al.  Focus, repacking, and the judgment of grouped hypotheses , 1999 .

[7]  R. Luce.  Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches , 2000 .

[8]  P. Wakker,et al.  Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown , 1996 .

[9]  Richard Gonzalez,et al.  Nonlinear Decision Weights in Choice Under Uncertainty , 1999 .

[10]  Peter P. Wakker,et al.  Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility , 2001, Manag. Sci..

[11]  Roland Michelitsch,et al.  Experimental tests of the endowment effect , 1996 .

[12]  D. Krantz,et al.  A Note on Superadditive Probability Judgment , 1999 .

[13]  R. Hogarth,et al.  Decision Making under Ambiguity , 1986 .

[14]  R. M. Hogarth,et al.  Ambiguity and competitive decision making: Some implications and tests , 1989 .

[15]  A. Garnham,et al.  Thinking and Reasoning , 1994 .

[16]  L. J. Savage,et al.  The Foundation of Statistics , 1956 .

[17]  Martin Weber,et al.  Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries , 1995 .

[18]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .

[19]  Colin Camerer,et al.  Recent developments in modeling preferences: Uncertainty and ambiguity , 1992 .

[20]  A. Tversky,et al.  Preference and belief: Ambiguity and competence in choice under uncertainty , 1991 .

[21]  Richard Gonzalez,et al.  On the Shape of the Probability Weighting Function , 1999, Cognitive Psychology.

[22]  H. Raiffa,et al.  The Foundations of Decision under Uncertainty: An Elementary Exposition , 1964 .

[23]  Peter P Wakkar.  On the composition of risk preference and belief. , 2004, Psychological review.

[24]  Richard Gonzalez,et al.  Curvature of the Probability Weighting Function , 1996 .

[25]  James Bowen,et al.  Satisficing when buying information , 1992 .

[26]  Peter C. Fishburn,et al.  Reconsiderations in the Foundations of Decision under Uncertainty , 1987 .

[27]  K. Taylor.  Testing credit and blame attributions as explanation for choices under ambiguity , 1995 .

[28]  D. Prelec.  The Probability Weighting Function , 1998 .

[29]  A. Tversky,et al.  Risk Attitudes and Decision Weights , 1995 .

[30]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[31]  Craig R. Fox,et al.  Partition Priming in Judgment Under Uncertainty , 2003, Psychological science.

[32]  J. R. Larson,et al.  Exploring the external validity of a subjectively weighted utility model of decision making , 1980 .

[33]  K. Vind.  A foundation for statistics , 2003 .

[34]  J. L. Pinto,et al.  A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis , 2000 .

[35]  M. Rabin.  Risk Aversion and Expected Utility Theory: A Calibration Theorem , 2000 .

[36]  Eric J. Johnson,et al.  Framing, probability distortions, and insurance decisions , 1993 .

[37]  F. Ramsey.  The Foundations of Mathematics and Other Logical Essays , 2001 .

[38]  Harry V. Roberts,et al.  Risk, Ambiguity, and the Savage Axioms: Comment , 1963 .

[39]  P. Fishburn,et al.  TWO‐PIECE VON NEUMANN‐MORGENSTERN UTILITY FUNCTIONS* , 1979 .

[40]  Martin Weber,et al.  Judged knowledge and ambiguity aversion , 1995 .

[41]  Rakesh K. Sarin,et al.  Modeling Ambiguity in Decisions Under Uncertainty , 1988 .

[42]  Craig R. Fox,et al.  Ambiguity Aversion, Comparative Ignorance, and Decision Context , 2002 .

[43]  Martin Weber,et al.  What Determines the Shape of the Probability Weighting Function Under Uncertainty? , 1998, Manag. Sci..

[44]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[45]  A. Tversky,et al.  Options traders exhibit subadditive decision weights , 1996 .

[46]  Richard Gonzalez,et al.  Dominance Violations and Event Splitting in Decision under Uncertainty * , 2002 .

[47]  Christopher K. Hsee,et al.  Money, Kisses, and Electric Shocks: On the Affective Psychology of Risk , 2001, Psychological science.

[48]  P. Fishburn,et al.  Rank- and sign-dependent linear utility models for finite first-order gambles , 1991 .

[49]  A. Tversky,et al.  Choices, Values, and Frames , 2000 .

[50]  K. MacCrimmon,et al.  Utility Theory: Axioms Versus ‘Paradoxes’ , 1979 .

[51]  Howard Kunreuther,et al.  Risk, ambiguity, and insurance , 1989 .

[52]  Rakesh K. Sarin,et al.  Effects of ambiguity in market experiments , 1993 .

[53]  Peter Ayton,et al.  How to Be IncoherentandSeductive: Bookmakers' Odds and Support Theory☆☆☆ , 1997 .

[54]  Edi Karni,et al.  On the Determination of Subjective Probability by Choices , 2000 .

[55]  W. Edwards,et al.  Decision Analysis and Behavioral Research , 1986 .

[56]  P. Wakker.  Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle , 2001 .

[57]  John S. Chipman,et al.  Stochastic Choice and Subjective Probability , 1960 .

[58]  Wibecke Brun,et al.  Prediction and postdiction preferences in guessing , 1990 .

[59]  M. Abdellaoui.  Parameter-Free Elicitation of Utility and Probability Weighting Functions , 2000 .

[60]  Rakesh K. Sarin,et al.  Comparative Ignorance and the Ellsberg Paradox , 2001 .

[61]  A. Tversky,et al.  Contingent weighting in judgment and choice , 1988 .

[62]  B. D. Finetti.  La prévision : ses lois logiques, ses sources subjectives , 1937 .

[63]  S. Becker,et al.  What Price Ambiguity? or the Role of Ambiguity in Decision-Making , 1964, Journal of Political Economy.

[64]  James A. Wise,et al.  Subjective probability and decision strategy , 1969 .

[65]  Ward Edwards,et al.  Dynamic Decision Theory and Probabilistic Information Processings1 , 1962 .

[66]  C. Fox.  Strength of Evidence, Judged Probability, and Choice Under Uncertainty , 1999, Cognitive Psychology.

[67]  Craig R. Fox,et al.  Ambiguity Aversion and Comparative Ignorance , 1995 .

[68]  J. Frank Yates,et al.  Characterization of Ambiguity in Decision Making. , 1976 .

[69]  J. Baron.  Thinking and deciding, 3rd ed. , 2000 .

[70]  A. Tversky,et al.  A Belief-Based Account of Decision Under Uncertainty , 1998 .

[71]  Jonathan Baron,et al.  Ambiguity and rationality , 1988 .

[72]  D. Kahneman,et al.  Experimental Tests of the Endowment Effect and the Coase Theorem , 1990, Journal of Political Economy.

[73]  V. Smith,et al.  Experimental tests of the endowment effect , 1996 .

[74]  G. Shafer.  Savage revisited , 1990 .

[75]  Colin Camerer,et al.  Violations of the betweenness axiom and nonlinearity in probability , 1994 .

[76]  P. Schoemaker,et al.  Prospect theory's reflection hypothesis: A critical examination , 1980 .

[77]  John W. Payne,et al.  Note-Further Tests of Aspiration Level Effects in Risky Choice Behavior , 1981 .

[78]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[79]  I. Gilboa.  Expected utility with purely subjective non-additive probabilities , 1987 .

[80]  Jean-Yves Jaffray,et al.  Individual behavior under risk and under uncertainty: An experimental study , 1985 .

[81]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[82]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[83]  C. Fox,et al.  Forecasting Trial Outcomes: Lawyers Assign Higher Probability to Possibilities That Are Described in Greater Detail , 2002, Law and human behavior.

[84]  D A Redelmeier,et al.  Probability judgement in medicine: discounting unspecified possibilities. , 1995, Medical decision making : an international journal of the Society for Medical Decision Making.

[85]  J. March,et al.  Managerial perspectives on risk and risk taking , 1987 .

[86]  A. Tversky.  Utility theory and additivity analysis of risky choices. , 1967, Journal of experimental psychology.

[87]  A. Tversky,et al.  Weighing Risk and Uncertainty , 1995 .

[88]  D. Schmeidler,et al.  A More Robust Definition of Subjective Probability , 1992 .

[89]  A. Tversky,et al.  Loss Aversion in Riskless Choice: A Reference-Dependent Model , 1991 .

[90]  R. Hogarth,et al.  Venture Theory: A Model of Decision Weights , 1990 .

[91]  Martin Weber,et al.  Willingness-to-pay and willingness-to-accept for risky and ambiguous lotteries , 1995 .

[92]  D. Koehler,et al.  Probability judgment in three-category classification learning. , 2000, Journal of Experimental Psychology. Learning, Memory and Cognition.

[93]  Howard Kunreuther,et al.  Ambiguity and underwriter decision processes , 1995 .

[94]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[95]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[96]  F. Knight.  The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[97]  The Relation Between Probability and Evidence Judgment: An Extension of Support Theory , 2001 .

[98]  Shawn P. Curley,et al.  An empirical evaluation of descriptive models of ambiguity reactions in choice situations , 1989 .

[99]  J. Quiggin.  A theory of anticipated utility , 1982 .

[100]  M. G. Preston,et al.  An experimental study of the auction-value of an uncertain outcome. , 1948, The American journal of psychology.

[101]  A. Tversky,et al.  Who accepts Savage's axiom? , 1974 .

[102]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[103]  B. Fischhoff,et al.  Fault Trees: Sensitivity of Estimated Failure Probabilities to Problem Representation , 2005 .

[104]  G. Gigliotti.  The Testing Principle: Inductive Reasoning and the Ellsberg Paradox , 1996 .

[105]  K. Teigen.  Subjective sampling distributions and the additivity of estimates , 1974 .

[106]  K. MacCrimmon.  DESCRIPTIVE AND NORMATIVE IMPLICATIONS OF THE DECISION THEORY POSTULATES. A SUMMARY OF EXPERIMENTAL RESULTS WITH BUSINESS EXECUTIVES , 1966 .

[107]  M. Allais.  Le comportement de l'homme rationnel devant le risque : critique des postulats et axiomes de l'ecole americaine , 1953 .