Incremental Preference Elicitation for Decision Making Under Risk with the Rank-Dependent Utility Model

This work concerns decision making under risk with the rank-dependent utility model (RDU), a generalization of expected utility providing enhanced descriptive possibilities. We introduce a new incremental decision procedure, involving monotone regression spline functions to model both components of RDU, namely the probability weighting function and the utility function. First, assuming the utility function is known, we propose an elicitation procedure that incrementally collects preference information in order to progressively specify the probability weighting function until the optimal choice can be identified. Then, we present two elicitation procedures for the construction of a utility function as a monotone spline. Finally, numerical tests are provided to show the practical efficiency of the proposed methods.

[1]  Eyke Hüllermeier,et al.  Pairwise Preference Learning and Ranking , 2003, ECML.

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

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

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

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

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

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

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

[9]  Jean-Yves Jaffray,et al.  Dynamic decision making without expected utility: An operational approach , 2006, Eur. J. Oper. Res..

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

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

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

[13]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[14]  I. Gilboa.  Theory Of Decision Under Uncertainty , 2009 .

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

[16]  Greg Hines,et al.  Preference elicitation for risky prospects , 2010, AAMAS.

[17]  D. Bernoulli.  Exposition of a New Theory on the Measurement of Risk , 1954 .

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

[19]  Patrice Perny,et al.  Incremental Elicitation of Choquet Capacities for Multicriteria Decision Making , 2014, ECAI.

[20]  Peter P. Wakker,et al.  Under stochastic dominance Choquet-expected utility and anticipated utility are identical , 1990 .

[21]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

[22]  Peter P. Wakker,et al.  On the Intuition of Rank-Dependent Utility , 2000 .

[23]  Vicenç Torra,et al.  Learning Aggregation Operators for Preference Modeling , 2010, Preference Learning.

[24]  Ariel D. Procaccia,et al.  Strategyproof Classification with Shared Inputs , 2009, IJCAI.

[25]  Stephan Freytag.  An Introduction To Splines For Use In Computer Graphics And Geometric Modeling , 2016 .

[26]  J. Prashker,et al.  Violations of Expected Utility Theory in Route-Choice Stated Preferences: Certainty Effect and Inflation of Small Probabilities , 2004 .

[27]  J. Quiggin.  Generalized expected utility theory : the rank-dependent model , 1994 .

[28]  M. Marchesi,et al.  Journal of economic behavior and organization: special issue on heterogeneous interacting agents in financial markets , 2002 .

[29]  Craig Boutilier,et al.  Constraint-based optimization and utility elicitation using the minimax decision criterion , 2006, Artif. Intell..

[30]  C. S. Hong,et al.  Risk aversion in the theory of expected utility with rank dependent probabilities , 1987 .

[31]  Daniel R. Cavagnaro,et al.  Discriminating among probability weighting functions using adaptive design optimization , 2013, Journal of risk and uncertainty.

[32]  Patrice Perny,et al.  Sequential Decision Making with Rank Dependent Utility: A Minimax Regret Approach , 2012, AAAI.

[33]  Eyke Hüllermeier,et al.  Learning monotone nonlinear models using the Choquet integral , 2011, Machine Learning.

[34]  Alain Chateauneuf,et al.  Risk seeking with diminishing marginal utility in a non-expected utility model , 1994 .

[35]  Craig Boutilier,et al.  Minimax regret based elicitation of generalized additive utilities , 2007, UAI.

[36]  Craig Boutilier,et al.  Decision-theoretic elicitation of generalized additive utilities , 2012 .

[37]  J. Schreiber.  Foundations Of Statistics , 2016 .