Noisy Preferences in Risky Choice: A Cautionary Note

We examine the effects of multiple sources of noise in risky decision making. Noise in the parameters that characterize an individual’s preferences can combine with noise in the response process to distort observed choice proportions. Thus, underlying preferences that conform to expected value maximization can appear to show systematic risk aversion or risk seeking. Similarly, core preferences that are consistent with expected utility theory, when perturbed by such noise, can appear to display nonlinear probability weighting. For this reason, modal choices cannot be used simplistically to infer underlying preferences. Quantitative model fits that do not allow for both sorts of noise can lead to wrong conclusions.

[1]  Ryan K. Jessup,et al.  Feedback Produces Divergence From Prospect Theory in Descriptive Choice , 2008, Psychological science.

[2]  G. Loewenstein,et al.  Time Discounting and Time Preference: A Critical Review , 2002 .

[3]  Ian Krajbich,et al.  Visual fixations and the computation and comparison of value in simple choice , 2010, Nature Neuroscience.

[4]  N. Wilcox Stochastically more risk averse: A contextual theory of stochastic discrete choice under risk , 2011 .

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

[6]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[7]  Graham Loomes,et al.  Boundedly rational expected utility theory , 2017, Journal of Risk and Uncertainty.

[8]  Charles A. Holt,et al.  Risk Aversion and Incentive Effects: New Data without Order Effects , 2005 .

[9]  Clintin P Davis-Stober,et al.  QTest: Quantitative Testing of Theories of Binary Choice. , 2014, Decisions.

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

[11]  Graham Loomes,et al.  Testing the ‘standard’ model of stochastic choice under risk , 2012 .

[12]  Sudeep Bhatia,et al.  Associations and the accumulation of preference. , 2013, Psychological review.

[13]  C. Davis-Stober,et al.  Behavioral variability of choices versus structural inconsistency of preferences. , 2012, Psychological review.

[14]  M. Birnbaum,et al.  Testing a class of models that includes majority rule and regret theories: Transitivity, recycling, and restricted branch independence. , 2015 .

[15]  Nick Chater,et al.  Salience driven value integration explains decision biases and preference reversal , 2012, Proceedings of the National Academy of Sciences.

[16]  Daniel M. Oppenheimer,et al.  Information processing as a paradigm for decision making. , 2015, Annual review of psychology.

[17]  J. Busemeyer,et al.  Extending the Bounds of Rationality: Evidence and Theories of Preferential Choice , 2006 .

[18]  Florian Heiss,et al.  Discrete Choice Methods with Simulation , 2016 .

[19]  J. Yellott The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution , 1977 .

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

[21]  Pavlo R. Blavatskyy,et al.  Models of Stochastic Choice and Decision Theories: Why Both are Important for Analyzing Decisions , 2008 .

[22]  Morten I. Lau,et al.  Eliciting Risk and Time Preferences , 2008 .

[23]  Jeffrey P. Bahra,et al.  Separating response variability from structural inconsistency to test models of risky decision making , 2012, Judgment and Decision Making.

[24]  Antonio Rangel,et al.  Neural computations associated with goal-directed choice , 2010, Current Opinion in Neurobiology.

[25]  R. Hertwig,et al.  Who Dares, Who Errs? Disentangling Cognitive and Motivational Roots of Age Differences in Decisions Under Risk , 2017, Psychological science.

[26]  Robert Sugden,et al.  Incorporating a stochastic element into decision theories , 1995 .

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

[28]  G. Charness,et al.  Strong Evidence for Gender Differences in Risk Taking , 2012 .

[29]  Marius Usher,et al.  Extending a biologically inspired model of choice: multi-alternatives, nonlinearity and value-based multidimensional choice , 2007, Philosophical Transactions of the Royal Society B: Biological Sciences.

[30]  R. Sugden,et al.  Testing Different Stochastic Specificationsof Risky Choice , 1998 .

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

[32]  Andrew Heathcote,et al.  The multiattribute linear ballistic accumulator model of context effects in multialternative choice. , 2014, Psychological review.

[33]  M. Birnbaum,et al.  New Paradoxes of Risky Decision Making , 2022 .

[34]  Andreas Glöckner,et al.  Cognitive models of risky choice: Parameter stability and predictive accuracy of prospect theory , 2012, Cognition.

[35]  Michel Regenwetter,et al.  Choice, preference, and utility: Probabilistic and deterministic representations , 2016 .

[36]  J. Rieskamp The probabilistic nature of preferential choice. , 2008, Journal of experimental psychology. Learning, memory, and cognition.

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

[38]  Thomas Langer,et al.  Measuring the time stability of Prospect Theory preferences , 2010 .

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

[40]  C. Steele,et al.  Stereotype Threat Affects Financial Decision Making , 2010, Psychological science.

[41]  J. Dana,et al.  Transitivity of preferences. , 2011, Psychological review.

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

[43]  B. Newell,et al.  Using hierarchical Bayesian methods to examine the tools of decision-making , 2011, Judgment and Decision Making.

[44]  Michel Regenwetter,et al.  Random relations, random utilities, and random functions , 2001 .

[45]  Christopher K. Hsee,et al.  Cross-National Differences in Risk Preference and Lay Predictions , 1999 .

[46]  E. Wagenmakers,et al.  Hierarchical Bayesian parameter estimation for cumulative prospect theory , 2011, Journal of Mathematical Psychology.

[47]  Jeffrey N. Rouder,et al.  Modeling Response Times for Two-Choice Decisions , 1998 .

[48]  L. Jones Measurement of Values , 1959, Nature.

[49]  Diederich,et al.  Dynamic Stochastic Models for Decision Making under Time Constraints , 1997, Journal of mathematical psychology.

[50]  R. Ratcliff,et al.  Multialternative decision field theory: a dynamic connectionist model of decision making. , 2001, Psychological review.

[51]  Jacob Marschak,et al.  Stochastic models of choice behavior , 2007 .

[52]  Mauricio R. Delgado,et al.  Acute Stress Modulates Risk Taking in Financial Decision Making , 2009, Psychological science.

[53]  N. Chater,et al.  Exaggerated risk: prospect theory and probability weighting in risky choice. , 2009, Journal of experimental psychology. Learning, memory, and cognition.

[54]  P. Samuelson A Note on Measurement of Utility , 1937 .

[55]  F. Restle Psychology of judgment and choice , 1961 .

[56]  Camelia M. Kuhnen,et al.  The Neural Basis of Financial Risk Taking , 2005, Neuron.

[57]  R. Hertwig,et al.  Decisions from Experience and the Effect of Rare Events in Risky Choice , 2004, Psychological science.

[58]  N. Wilcox Stochastic models for binary discrete choice under risk: a critical primer and econometric comparison , 2008 .

[59]  Robert Sugden,et al.  A Microeconometric Test of Alternative Stochastic Theories of Risky Choice , 2002 .

[60]  H. D. Block,et al.  Random Orderings and Stochastic Theories of Responses (1960) , 1959 .

[61]  J. Townsend,et al.  Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment. , 1993, Psychological review.

[62]  Thorsten Pachur,et al.  Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice , 2015, Psychonomic bulletin & review.

[63]  Sudeep Bhatia Sequential sampling and paradoxes of risky choice , 2014, Psychonomic Bulletin & Review.

[64]  H. Stott Cumulative prospect theory's functional menagerie , 2006 .

[65]  Colin Camerer,et al.  Neural Response to Reward Anticipation under Risk Is Nonlinear in Probabilities , 2009, The Journal of Neuroscience.

[66]  H. Zur,et al.  The effect of time pressure on risky choice behavior , 1981 .

[67]  Kimberly J. Vannest,et al.  Measuring Time , 2010 .

[68]  Stephen B. Broomell,et al.  Parameter recovery for decision modeling using choice data. , 2014 .

[69]  E. Wagenmakers,et al.  Bayesian parameter estimation in the Expectancy Valence model of the Iowa gambling task , 2010 .

[70]  D. McFadden Conditional logit analysis of qualitative choice behavior , 1972 .

[71]  James L. McClelland,et al.  Loss aversion and inhibition in dynamical models of multialternative choice. , 2004, Psychological review.

[72]  M. Birnbaum True-and-error models violate independence and yet they are testable , 2013, Judgment and Decision Making.