Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization

The completeness axiom of choice has been questioned for long and theoretical models of decision making allowing for incomplete preferences have been developed. So far the theoretical accomplishments have not been paired with empirical evidence on the actual existence of incomplete preferences under uncertainty. We provide empirical evidence in support of the existence of incomplete preferences due to multiple priors over an ambiguous event, i.e. Bewley preferences. We design experimental decision tasks where specific choice patterns are consistent with Bewley preferences but inconsistent with models assuming completeness. We find that approximately half of the subjects behave consistent with variational Bewley preferences and that the observed behavioral pattern cannot be attributed to probability weighting, choice mistakes, or intransitive indifference. In a robustness test we show that the observed behavior is robust to a prize variation in the ambiguous prospect and consistent with comparative statics predictions based on variational Bewley preferences.

[1]  José Heleno Faro.  Variational Bewley preferences , 2011, J. Econ. Theory.

[2]  Seymour Epstein,et al.  Individual Differences in Intuitive-Exp eriential and Analytical-Rational Thinking Styles , 1996 .

[3]  S. Frederick.  Journal of Economic Perspectives—Volume 19, Number 4—Fall 2005—Pages 25–42 Cognitive Reflection and Decision Making , 2022 .

[4]  J. Jaffray,et al.  Experimental comparison of individual behavior under risk and under uncertainty for gains and for losses , 1987 .

[5]  Fabio Maccheroni,et al.  Expected utility theory without the completeness axiom , 2004, J. Econ. Theory.

[6]  R. Aumann.  UTILITY THEORY WITHOUT THE COMPLETENESS AXIOM , 1962 .

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

[8]  Jacob S. Sagi,et al.  Inter-temporal Preference for Flexibility and Risky Choice , 2006 .

[9]  Robin P. Cubitt,et al.  Experimental Economics: Rethinking the Rules , 2009 .

[10]  M. Degroot,et al.  Measuring utility by a single-response sequential method. , 1964, Behavioral science.

[11]  Efe A. Ok,et al.  Incomplete preferences under uncertainty: Indecisiveness in beliefs versus tastes , 2012 .

[12]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[13]  Pietro Ortoleva,et al.  Stochastic Choice and Preferences for Randomization , 2015, Journal of Political Economy.

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

[15]  Santiago I. Sautua.  Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness , 2016 .

[16]  T. Bewley.  Knightian decision theory. Part I , 2002 .

[17]  Efe A. Ok.  Utility Representation of an Incomplete Preference Relation , 2002, J. Econ. Theory.

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

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

[20]  Robin P. Cubitt,et al.  On preference imprecision , 2015, Journal of Risk and Uncertainty.

[21]  Pietro Ortoleva,et al.  Status quo bias, multiple priors and uncertainty aversion , 2010, Games Econ. Behav..

[22]  Timothy N. Cason,et al.  Misconceptions and Game Form Recognition: Challenges to Theories of Revealed Preference and Framing , 2014, Journal of Political Economy.

[23]  Sophie Bade,et al.  Randomization devices and the elicitation of ambiguity-averse preferences , 2015, J. Econ. Theory.

[24]  Massimo Marinacci,et al.  Uncertainty averse preferences , 2011, J. Econ. Theory.

[25]  Michael Mandler.  Status Quo Maintenance Reconsidered: Changing or Incomplete Preferences? , 2004 .

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

[27]  Graham Loomes,et al.  Imprecision as an Account of the Preference Reversal Phenomenon , 2007 .

[28]  A. Baillon,et al.  Experimental elicitation of ambiguity attitude using the random incentive system , 2015, Experimental Economics.

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

[30]  Michael Mandler,et al.  Incomplete preferences and rational intransitivity of choice , 2005, Games Econ. Behav..

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

[32]  Jörg Oechssler,et al.  Unintended hedging in ambiguity experiments , 2014 .

[33]  Eric Danan,et al.  Are preferences complete? An experimental measurement of indecisiveness under risk , 2006 .

[34]  D. Kahneman.  Maps of Bounded Rationality: Psychology for Behavioral Economics , 2003 .

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

[36]  Paolo Ghirardato,et al.  Ambiguity in the Small and in the Large , 2012 .

[37]  Yoram Halevy,et al.  Eliciting risk preferences using choice lists , 2019, Quantitative Economics.

[38]  P. Wakker.  Explaining the characteristics of the power (CRRA) utility family. , 2008, Health economics.

[39]  Christopher P. Chambers,et al.  Incentives in Experiments: A Theoretical Analysis , 2018, Journal of Political Economy.

[40]  J. Sonnemans,et al.  Does the elicitation method impact the WTA/WTP disparity? , 2018 .

[41]  Lise Vesterlund,et al.  Error-Prone Inference from Response Time: The Case of Intuitive Generosity in Public-Good Games , 2018 .

[42]  Adrian Bruhin,et al.  Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting , 2010 .

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

[44]  Massimo Marinacci,et al.  Differentiating ambiguity and ambiguity attitude , 2004, J. Econ. Theory.

[45]  P. Wakker.  Prospect Theory: For Risk and Ambiguity , 2010 .

[46]  Yusufcan Masatlioglu,et al.  Rational choice with status quo bias , 2005, J. Econ. Theory.

[47]  Adam Dominiak,et al.  Attitudes toward uncertainty and randomization: an experimental study , 2011 .

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

[49]  Kfir Eliaz,et al.  Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences , 2006, Games Econ. Behav..

[50]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[51]  Adrian Bruhin,et al.  Risk and Rationality: Uncovering Heterogeneity in Probability Distortion , 2009 .

[52]  I. Gilboa,et al.  Objective and Subjective Rationality in a Multiple Prior Model , 2010 .

[53]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[54]  Ambiguity Attitudes in a Large Representative Sample , 2015 .