Boundedly rational expected utility theory

We build a satisficing model of choice under risk which embeds Expected Utility Theory (EUT) into a boundedly rational deliberation process. The decision maker accumulates evidence for and against alternative options by repeatedly sampling from her underlying set of EU preferences until the evidence favouring one option satisfies her desired level of confidence. Despite its EUT core, the model produces patterns of behaviour that violate standard EUT axioms, while at the same time capturing systematic relationships between choice probabilities, response times and confidence judgments, which are beyond the scope of theories that do not take deliberation into account.

[1]  Graham Loomes,et al.  On the Measurement of Strength of Preference in Units of Money , 2014 .

[2]  M. Rabin Risk Aversion and Expected Utility Theory: A Calibration Theorem , 2000 .

[3]  N. Wilcox Lottery choice: incentives, complexity and decision time , 1993 .

[4]  Alan D. J. Cooke,et al.  Is choice the correct primitive? On using certainty equivalents and reference levels to predict choices among gambles , 1993 .

[5]  Albert N. Shiryaev,et al.  Optimal Stopping Rules , 2011, International Encyclopedia of Statistical Science.

[6]  T. Tyebjee Response Time, Conflict, and Involvement in Brand Choice , 1979 .

[7]  John W. Payne,et al.  The adaptive decision maker: Name index , 1993 .

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

[9]  Donald G. Jamieson,et al.  Relation between probability of preferential choice and time to choose changes with practice. , 1978 .

[10]  J. Marschak Rational Behavior, Uncertain Prospects, and Measurable Utility (1950) , 1950 .

[11]  Stefan T. Trautmann,et al.  Tempus Fugit: Time Pressure in Risky Decisions , 2011, Manag. Sci..

[12]  Joseph G. Johnson,et al.  A dynamic, stochastic, computational model of preference reversal phenomena. , 2005, Psychological review.

[13]  M. Allais Le comportement de l'homme rationnel devant le risque : critique des postulats et axiomes de l'ecole americaine , 1953 .

[14]  A. Rubinstein Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?) , 1988 .

[15]  Neil Stewart,et al.  On the Origin of Utility, Weighting, and Discounting Functions: How They Get Their Shapes and How to Change Their Shapes , 2015, Manag. Sci..

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

[17]  Philip L. Smith,et al.  A comparison of sequential sampling models for two-choice reaction time. , 2004, Psychological review.

[18]  Pietro Ortoleva,et al.  Cautious Expected Utility and the Certainty Effect , 2013 .

[19]  Robert B. Barsky,et al.  Information, Animal Spirits, and the Meaning of Innovations in Consumer Confidence , 2009 .

[20]  Timothy J. Pleskac,et al.  Two-stage dynamic signal detection: a theory of choice, decision time, and confidence. , 2010, Psychological review.

[21]  A. Tversky,et al.  Substitutability and similarity in binary choices , 1969 .

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

[23]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

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

[25]  Gordon M. Becker,et al.  An experimental study of some stochastic models for wagers , 2007 .

[26]  A. Rubinstein Instinctive and Cognitive Reasoning: A Study of Response Times , 2006 .

[27]  Denis Bouyssou,et al.  Bounded Rationality Modeling , 1999 .

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

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

[30]  Michele Bernasconi Nonlinear Preferences and Two-Stage Lotteries: Theories and Evidence , 1994 .

[31]  Ariel Rubinstein,et al.  Lecture Notes in Microeconomic Theory , 2006 .

[32]  Winston R. Sieck,et al.  Exposition Effects on Decision Making: Choice and Confidence in Choice , 1997 .

[33]  Manfred Kochen,et al.  On the economics of information , 1972, J. Am. Soc. Inf. Sci..

[34]  M. Elliott,et al.  Financial Networks and Contagion , 2014 .

[35]  P. Moffatt Stochastic Choice and the Allocation of Cognitive Effort , 2005 .

[36]  Daniel Hausmann,et al.  Sequential evidence accumulation in decision making: The individual desired level of confidence can explain the extent of information acquisition , 2008, Judgment and Decision Making.

[37]  J. Elster The Multiple Self , 1987 .

[38]  Graham Loomes,et al.  Decision difficulty and imprecise preferences , 1988 .

[39]  Pavlo R. Blavatskyy,et al.  Stochastic expected utility theory , 2005 .

[40]  Alʹbert Nikolaevich Shiri︠a︡ev,et al.  Optimal stopping rules , 1977 .

[41]  A. Tversky,et al.  The weighing of evidence and the determinants of confidence , 1992, Cognitive Psychology.

[42]  Pavlo R. Blavatskyy,et al.  A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance , 2011, Manag. Sci..

[43]  Eric J. Johnson,et al.  The adaptive decision maker , 1993 .

[44]  R. Hertwig,et al.  The priority heuristic: making choices without trade-offs. , 2006, Psychological review.

[45]  R. Selten,et al.  Bounded rationality: The adaptive toolbox , 2000 .

[46]  W. Bossert,et al.  Interpersonal Comparisons of Well‐Being , 2004 .

[47]  D. Acemoglu,et al.  Consumer Confidence and Rational Expectations: Are Agents' Beliefs Consistent with the Theory? , 1994 .

[48]  I. Gilboa,et al.  Case-Based Decision Theory , 1995 .

[49]  H. Simon,et al.  Rationality as Process and as Product of Thought , 1978 .

[50]  Steven J. Humphrey Regret aversion or event-splitting effects? more evidence under risk and uncertainty , 1995 .

[51]  P. Blavatskyy Violations of betweenness or random errors , 2006 .

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

[53]  Manel Baucells,et al.  Stability of risk preferences and the reflection effect of prospect theory , 2010 .

[54]  Clyde H. Coombs,et al.  Tests of the betweenness property of expected utility , 1976 .

[55]  Charles F. Manski,et al.  How Should We Measure Consumer Confidence , 2004 .

[56]  James T. Townsend,et al.  Sequential sampling models of choice: Some recent advances , 2008 .

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

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

[59]  Kfir Eliaz,et al.  Comments on the Risk and Time Preferences in Economics , 2002 .

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

[61]  Sydney C. Ludvigson,et al.  Consumer Confidence and Consumer Spending , 2004 .

[62]  Robert Sugden,et al.  Testing for juxtaposition and event-splitting effects , 1993 .

[63]  M. Jackson,et al.  The Effects of Social Networks on Employment and Inequality , 2004 .

[64]  Carlos Alós-Ferrer,et al.  Fast or Rational? A Response-Times Study of Bayesian Updating , 2014, Manag. Sci..

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

[66]  Simon Peters,et al.  Testing for the Presence of a Tremble in Economic Experiments , 2001 .

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

[68]  M. Birnbaum,et al.  A theory of comparative response times and “difference” judgments , 1990, Cognitive Psychology.

[69]  F. Strack,et al.  From dual processes to multiple selves: Implications for economic behavior , 2014 .

[70]  Ronald M. Harstad,et al.  Bounded-Rationality Models: Tasks to Become Intellectually Competitive , 2013 .

[71]  N. Wilcox Random expected utility and certainty equivalents: mimicry of probability weighting functions , 2017 .

[72]  K. Binmore Interpersonal Comparison of Utility , 2009 .

[73]  M. Birnbaum Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting , 2004 .

[74]  Gordon D. A. Brown,et al.  Decision by sampling , 2006, Cognitive Psychology.

[75]  Peter J. Hammond,et al.  Interpersonal Comparisons of Well-being: Interpersonal comparisons of utility: Why and how they are and should be made , 1990 .

[76]  R. Luce A Theory of Certainty Equivalents for Uncertain Alternatives , 1992 .

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

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

[79]  Preference and the time to choose , 1977 .

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

[81]  J. Gold,et al.  The neural basis of decision making. , 2007, Annual review of neuroscience.

[82]  A. Rubinstein Response time and decision making: An experimental study , 2013, Judgment and Decision Making.

[83]  A. Tversky Elimination by aspects: A theory of choice. , 1972 .

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

[85]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[86]  B. Fischhoff,et al.  Reasons for confidence. , 1980 .

[87]  J. L. Myers,et al.  Contingent gains and losses in a risk-taking situation , 1965 .

[88]  Frederick Mosteller,et al.  An Experimental Measurement of Utility , 1951, Journal of Political Economy.

[89]  Andrea Isoni,et al.  Beyond choice: investigating the sensitivity and validity of measures of strength of preference , 2014 .

[90]  Derek J. Koehler,et al.  Explanation, imagination, and confidence in judgment. , 1991, Psychological bulletin.

[91]  Eric J. Johnson,et al.  Aspects of Endowment: A Query Theory of Value Construction , 2007, Journal of experimental psychology. Learning, memory, and cognition.

[92]  A. Ortmann,et al.  The BCD of response time analysis in experimental economics , 2016, Experimental Economics.