A Context-Dependent Model of the Gambling Effect

This paper presents a context-dependent theory of decision under risk. The relevant contextual factor is the presence of a riskless lottery in a preference comparison. The theory only deviates from expected utility if the set of options contains both riskless and risky lotteries. The main motivation for the theory is to explain the gambling effect. Contrary to previous theories of the gambling effect, the present theory is consistent with stochastic dominance. It can, however, violate transitivity. The theory allows for a decomposition of the interaction between risk aversion and gambling aversion and thereby extends the classical Arrow-Pratt measure of risk aversion.

[1]  P. Wakker.  Additive Representations of Preferences: A New Foundation of Decision Analysis , 1988 .

[2]  A.A.J. Marley,et al.  On Elements of Chance , 2000 .

[3]  Peter P. Wakker,et al.  Additive Representations of Preferences , 1989 .

[4]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[5]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[6]  Rakesh K. Sarin,et al.  Lottery dependent utility , 1987 .

[7]  David W Harless,et al.  The predictive utility of generalized expected utility theories , 1994 .

[8]  Robert Sugden,et al.  OBSERVING VIOLATIONS OF TRANSITIVITY BY EXPERIMENTAL METHODS , 1991 .

[9]  Niels Erik Jensen,et al.  An Introduction to Bernoullian Utility Theory: II. Interpretation, Evaluation and Application; A Critical Survey , 1967 .

[10]  C. Starmer.  Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk , 2000 .

[11]  David E. Bell,et al.  Regret in Decision Making under Uncertainty , 1982, Oper. Res..

[12]  P. Fishburn.  Nontransitive measurable utility , 1982 .

[13]  A. Tversky,et al.  Context-dependent preferences , 1993 .

[14]  B. Sopher,et al.  A test of generalized expected utility theory , 1993 .

[15]  Graham Loomes,et al.  The myth of the HYE , 1995 .

[16]  R. A. Lakshmi-Ratan,et al.  An aggregate contextual choice model for estimating demand for new products from a laboratory choice experiment , 1992 .

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

[18]  Joel Huber,et al.  Market Boundaries and Product Choice: Illustrating Attraction and Substitution Effects , 1983 .

[19]  Steven J. Humphrey.  More mixed results on boundary effects , 1998 .

[20]  P. Fishburn.  Nontransitive preferences in decision theory , 1991 .

[21]  D. H. Wedell,et al.  Distinguishing Among Models of Contextually Induced Preference Reversals , 1991 .

[22]  Robert Sugden,et al.  Why be Consistent? A Critical Analysis of Consistency Requirements in Choice Theory , 1985 .

[23]  A. Tversky.  Additivity, utility, and subjective probability , 1967 .

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

[25]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[26]  A. Tversky,et al.  Choice in Context: Tradeoff Contrast and Extremeness Aversion , 1992 .

[27]  P. Wakker,et al.  A Criticism of Healthy-years Equivalents , 1996, Medical decision making : an international journal of the Society for Medical Decision Making.

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

[29]  A. Mehrez,et al.  Economics, health and health economics: HYEs versus QALYs , 1993 .

[30]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[31]  Ulrich Schmidt,et al.  Lottery Dependent Utility: a Reexamination , 2001 .

[32]  R. Sugden,et al.  Regret Theory: An alternative theory of rational choice under uncertainty Review of Economic Studies , 1982 .

[33]  Hans Jørgen Jacobsen,et al.  Testing the Intransitivity Explanation of the Allais Paradox , 1999 .

[34]  A. A. J. Marley,et al.  Context dependent probabilistic choice models based on measures of binary advantage , 1991 .

[35]  Paul Anand,et al.  Are the preference axioms really rational? , 1987 .

[36]  William S. Neilson.  Some mixed results on boundary effects , 1992 .

[37]  P. Fishburn.  Transitive measurable utility , 1983 .

[38]  Jean-Yves Jaffray,et al.  Certainty effect versus probability distortion: An experimental analysis of decision making under risk. , 1988 .

[39]  Rakesh K. Sarin,et al.  RELATIVE RISK AVERSION. , 1982 .

[40]  Colin Camerer.  Recent Tests of Generalizations of Expected Utility Theory , 1992 .

[41]  Niels-Erik Jensen.  An Introduction to Bernoullian Utility Theory: I. Utility Functions , 1967 .

[42]  R. Sugden,et al.  Violations of the independence axion in common ratio problems: An experimental test of some competing hypotheses , 1989 .

[43]  R. Luce.  Semiorders and a Theory of Utility Discrimination , 1956 .

[44]  J. Conlisk.  The utility of gambling , 1993 .

[45]  Christopher P. Puto,et al.  Adding Asymmetrically Dominated Alternatives: Violations of Regularity & the Similarity Hypothesis. , 1981 .

[46]  Ulrich Schmidt,et al.  A Measurement of the Certainty Effect. , 1998, Journal of mathematical psychology.

[47]  Mark R. McCord,et al.  Lottery Equivalents: Reduction of the Certainty Effect Problem in Utility Assessment , 1986 .

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

[49]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[50]  Peter C. Fisi-Iburn.  Nontransitive preferences in decision theory , 1991 .

[51]  A. Mehrez,et al.  Quality-adjusted Life Years, Utility Theory, and Healthy-years Equivalents , 1989, Medical decision making : an international journal of the Society for Medical Decision Making.

[52]  Peter C. Fishburn,et al.  A simple model for the utility of gambling , 1980 .

[53]  Robert Sugden,et al.  An Axiomatic Foundation for Regret Theory , 1993 .

[54]  P. Farquhar.  State of the Art—Utility Assessment Methods , 1984 .

[55]  C. Starmer,et al.  Testing New Theories of Choice under Uncertainty using the Common Consequence Effect , 1992 .