Lottery Dependent Utility: a Reexamination

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science.

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

[2]  Eddie Dekel.  An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom , 1986 .

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

[4]  John Conlisk,et al.  Three Variants on the Allais Example , 1989 .

[5]  Larry G. Epstein,et al.  MIXTURE SYMMETRY AND QUADRATIC UTILITY , 1991 .

[6]  John H. Kagel,et al.  Testing between alternative models of choice under uncertainty: Some initial results , 1990 .

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

[8]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[9]  Bruno Jullien,et al.  Ordinal independence in nonlinear utility theory , 1988 .

[10]  Jean-Michel Grandmont,et al.  Continuity properties of a von Neumann-Morgenstern utility , 1972 .

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

[12]  Uzi Segal,et al.  The measure representation: A correction , 1993 .

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

[14]  Faruk Gul.  A Theory of Disappointment Aversion , 1991 .

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

[16]  J. Hey,et al.  INVESTIGATING GENERALIZATIONS OF EXPECTED UTILITY THEORY USING EXPERIMENTAL DATA , 1994, Experiments in Economics.

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

[18]  Larry G. Epstein,et al.  A unifying approach to axiomatic non-expected utility theories , 1989 .

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

[20]  David W Harless,et al.  Predictions about indifference curves inside the unit triangle: A test of variants of expected utility theory , 1992 .

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

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

[23]  C. Ferguson.  The Theory of Multidimensional Utility Analysis in Relation to Multiple-Goal Business Behavior: A Synthesis , 1965 .

[24]  Peter C. Fishburn,et al.  A Study of Lexicographic Expected Utility , 1971 .

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

[26]  William S. Neilson.  A mixed fan hypothesis and its implications for behavior toward risk , 1992 .

[27]  W. Viscusi.  Prospective reference theory: Toward an explanation of the paradoxes , 1989 .

[28]  Jean-Yves Jaffray,et al.  Preponderence of the Certainty Effect Over Probability Distortion in Decision Making Under Risk , 1988 .

[29]  Uzi Segal.  Anticipated utility: A measure representation approach , 1989 .

[30]  Samir Essid,et al.  Choice under risk with certainty and potential effects: A general axiomatic model , 1997 .

[31]  Peter P. Wakker,et al.  The Axiomatic Basis of Anticipated Utility: A Clarification , 1994 .

[32]  Clemens Puppe.  Distorted Probabilities and Choice under Risk , 1991 .

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

[34]  G. Debreu.  Mathematical Economics: Continuity properties of Paretian utility , 1964 .

[35]  M. Machina.  "Expected Utility" Analysis without the Independence Axiom , 1982 .