Consequentialism and dynamic consistency in updating ambiguous beliefs

By proposing the notions of upper-constrained dynamic consistency and lower-constrained dynamic consistency that are weaker axioms than dynamic consistency, this paper axiomatizes the Dempster–Shafer updating rule and naive Bayes’ updating rule within the framework of Choquet expected utility. Based on the notion of conditional comonotonicity, this paper also provides an axiomatization of consequentialism under Choquet expected utility. Furthermore, based on the idea of the mean-preserving rule, this paper provides a unified approach for distinguishing capacity updating rules (the Dempster–Shafer updating rule, naive Bayes’ updating rule, and Fagin–Halpern updating rule) according to the degree of dynamic consistency.

[1]  Tan Wang,et al.  Conditional preferences and updating , 2003, J. Econ. Theory.

[2]  Takao Asano,et al.  An axiomatization of Choquet expected utility with cominimum independence , 2015 .

[3]  P. Wakker,et al.  Dynamic Choice and NonExpected Utility , 1998 .

[4]  Itzhak Gilboa,et al.  Updating Ambiguous Beliefs , 1992, TARK.

[5]  Massimo Marinacci,et al.  Revealed Ambiguity and Its Consequences: Updating , 2008 .

[6]  Marciano M. Siniscalchi,et al.  Dynamic Choice Under Ambiguity , 2006 .

[7]  Peter Klibanoff,et al.  Updating Ambiguity Averse Preferences , 2009 .

[8]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[9]  Arthur P. Dempster,et al.  A Generalization of Bayesian Inference , 1968, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[10]  D. Schmeidler.  Integral representation without additivity , 1986 .

[11]  Peter Duersch,et al.  A dynamic Ellsberg urn experiment , 2012, Games Econ. Behav..

[12]  David M. Kreps.  Notes On The Theory Of Choice , 1988 .

[13]  Mayumi Horie.  Reexamination on updating Choquet beliefs , 2013 .

[14]  L. J. Savage,et al.  The Foundation of Statistics , 1956 .

[15]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[16]  M. Machina.  Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty , 1989 .

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

[18]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

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

[20]  Marciano M. Siniscalchi,et al.  Dynamic choice under ambiguity: Dynamic choice under ambiguity , 2011 .

[21]  Eran Hanany,et al.  Updating Preferences with Multiple Priors , 2006 .

[22]  Martin Schneider,et al.  Recursive multiple-priors , 2003, J. Econ. Theory.

[23]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[24]  C. Pires.  A Rule For Updating Ambiguous Beliefs , 2002 .

[25]  Peter J. Hammond,et al.  Consistent Plans, Consequentialism, and Expected Utility , 1989 .

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

[27]  Paolo Ghirardato,et al.  Revisiting Savage in a conditional world , 2002 .

[28]  Atsushi Kajii,et al.  Cominimum Additive Operators , 2007 .

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

[30]  Adam Dominiak,et al.  Unambiguous events and dynamic Choquet preferences , 2011 .

[31]  Larry G. Epstein,et al.  Dynamically Consistent Beliefs Must Be Bayesian , 1993 .

[32]  Ronald Fagin,et al.  A new approach to updating beliefs , 1990, UAI.

[33]  J. Eichberger,et al.  Updating Choquet Beliefs , 2007 .

[34]  P. Hammond.  Consequentialist foundations for expected utility , 1988 .