On the Intuition of Rank-Dependent Utility

Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rank-dependence and comonotonicity. It has been suggested that these concepts are technical tools that have no intuitive or empirical content. This paper describes such contents. As a result, rank-dependence and comonotonicity become natural concepts upon which preference conditions, empirical tests, and improvements in utility measurement can be based. Further, a new derivation of the rank-dependent models is obtained. It is not based on observable preference axioms or on empirical data, but naturally follows from the intuitive perspective assumed. We think that the popularity of the rank-dependent theories is mainly due to the natural concepts used in these theories.

[1]  P. Wakker Separating marginal utility and probabilistic risk aversion , 1994 .

[2]  M. Abdellaoui A Genuine Rank-Dependent Generalization of the Von Neumann-Morgenstern Expected Utility Theorem , 2002 .

[3]  Daniel Kahneman,et al.  Advances in prospect theory: Cumulative representation of , 1992 .

[4]  Michèle Cohen,et al.  Security level, potential level, expected utility: A three-criteria decision model under risk , 1992 .

[5]  R. Duncan Luce,et al.  The ongoing dialog between empirical science and measurement theory , 1996 .

[6]  W. Viscusi,et al.  Alarmist Decisions with Divergent Risk Information , 1997 .

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

[8]  Ben Shneiderman,et al.  Between hope and fear , 1997, CACM.

[9]  R. Luce Coalescing, Event Commutativity, and Theories of Utility , 1998 .

[10]  A. Röell Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty , 1987 .

[11]  P. Wakker,et al.  Revealed Likelihood and Knightian Uncertainty , 1998 .

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

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

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

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

[16]  M. Birnbaum The nonadditivity of personality impressions. , 1974, Journal of experimental psychology.

[17]  W. Edwards The prediction of decisions among bets. , 1955, Journal of experimental psychology.

[18]  A. Tversky,et al.  An axiomatization of cumulative prospect theory , 1993 .

[19]  J. Jaffray Choice under risk and the security factor: An axiomatic model , 1988 .

[20]  E. Weber From Subjective Probabilities to Decision Weights: The Effect of Asymmetric Loss Functions on the Evaluation of Uncertain Outcomes and Events , 1994 .

[21]  Lola L. Lopes Risk and Distributional Inequality. , 1984 .

[22]  U. Ebert Measurement of Inequality: An Attempt at Unification and Generalization , 1988 .

[23]  Eric J. Johnson,et al.  Bias in utility assessments: further evidence and explanations , 1989 .

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

[25]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

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

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

[28]  Edi Karni,et al.  Rank-Dependent Probabilities , 1990 .

[29]  Rakesh K. Sarin,et al.  Prospect Versus Utility , 1989 .

[30]  Steven J. Kachelmeier,et al.  Examining Risk Preferences under High Monetary Incentives: Experimental Evidence from the People's Republic of China , 1992 .

[31]  M. Allais,et al.  Fondements d'une theorie positive des choix comportant un risque et critique des postulats et axiomes de l'ecole americaine , 1959 .

[32]  John Quiggin,et al.  Risk Perception And The Analysis Of Risk Attitudes , 1981 .

[33]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

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

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

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

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

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

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

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

[41]  M. Yaari The Dual Theory of Choice under Risk , 1987 .

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

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

[44]  Lola L. Lopes,et al.  The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory. , 1999, Journal of mathematical psychology.

[45]  Michael H. Birnbaum,et al.  Violations of Branch Independence in Choices between Gambles , 1996 .

[46]  Itzhak Gilboa,et al.  Expectation and Variation in Multi-Period Decisions , 1989 .

[47]  David E. Bell,et al.  Disappointment in Decision Making Under Uncertainty , 1985, Oper. Res..

[48]  Larry G. Epstein Advances in Economic Theory: Behavior under risk: recent developments in theory and applications , 1993 .

[49]  Larry G. Epstein A definition of uncertainty aversion , 1999 .

[50]  Itzhak Gilboa,et al.  A combination of expected utility and maxmin decision criteria , 1988 .

[51]  P. Fishburn,et al.  On Handa's "New Theory of Cardinal Utility" and the Maximization of Expected Return , 1978, Journal of Political Economy.

[52]  S. Chew Axiomatic utility theories with the betweenness property , 1989 .

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

[54]  Uday S. Karmarkar,et al.  Subjectively weighted utility: A descriptive extension of the expected utility model , 1978 .

[55]  Kenneth J. Arrow,et al.  Studies in Resource Allocation Processes: Appendix: An optimality criterion for decision-making under ignorance , 1977 .

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

[57]  W. Fellner Distortion of Subjective Probabilities as a Reaction to Uncertainty , 1961 .

[58]  John A. Weymark,et al.  GENERALIZED GIN 1 INEQUALITY INDICES , 2001 .

[59]  M. Birnbaum,et al.  Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence , 1998 .

[60]  M. Yaari Convexity in the Theory of Choice under Risk , 1965 .

[61]  Zvi Safra,et al.  Constant Risk Aversion , 1998 .

[62]  Roger E. Backhouse,et al.  If Mathematics is Informal, Then Perhaps we Should Accept That Economics Must be Informal Too , 1998 .

[63]  R. Luce,et al.  When Four Distinct Ways to Measure Utility Are the Same , 1996 .

[64]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

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

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

[67]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

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

[69]  Lola L. Lopes,et al.  [Advances in Experimental Social Psychology] Advances in Experimental Social Psychology Volume 20 Volume 20 || Between Hope and Fear: The Psychology of Risk , 1987 .

[70]  Jonathan Shalev,et al.  Loss Aversion in a Multi-Period Model , 1997 .

[71]  H. Jeffreys A Treatise on Probability , 1922, Nature.

[72]  Edi Karni,et al.  Utility theory with uncertainty , 1991 .