Consequentialism and dynamic consistency in updating ambiguous beliefs
- 118 Downloads
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.
KeywordsDynamic consistency Consequentialism Choquet expected utility Conditional comonotonicity Conditional preferences Dempster–Shafer updating rule Naive Bayes’ updating rule Fagin–Halpern updating rule
JEL ClassificationC71 D81 D90
We acknowledge an anonymous reviewer and the co-editor, Mark Machina, whose comments improve this paper substantially. We are grateful to Youichiro Higashi, Hidetoshi Komiya, Hiroyuki Ozaki, Shin’ichi Suda, Masayuki Yao, and participants at Nagoya University, Keio University, and China Meeting of Econometric Society 2016 (Chengdu, China). This research is financially supported by the JSPS KAKENHI Grant Numbers 17K03806, 16K03558, 26380240, 25380239, and 23000001, and the Joint Research Program of KIER.
- Dempster, A.P.: A generalization of Bayesian inference. J. R. Stat. Soc. Ser. B 30, 205–232 (1968)Google Scholar
- Fagin, R., Halpern, J.Y.: A new approach to updating beliefs. In: Bonissone, P.P., Henrion, M., Kanal, L.N., Lemmer, J.F. (eds.) Uncertainty in Artificial Intelligence, vol. 6, pp. 347–374. Springer, Berlin (1991)Google Scholar
- Hanany, E., Klibanoff, P.: Updating preferences with multiple priors. Theor. Econ. 2, 261–298 (2007)Google Scholar
- Hanany, E., Klibanoff, P.: Updating ambiguity averse preferences. B.E. J. Theor. Econ. 9(1 (Advances)), Article 37 (2009)Google Scholar
- Kreps, D.: Notes on the Theory of Choice. Westview Press, Boulder (1988)Google Scholar
- Machina, M.: Dynamic consistency and non-expected utility models of choice under uncertainty. J. Econ. Lit. 27, 1622–1668 (1989)Google Scholar
- Savage, L.J.: The Foundation of Statistics. New York, Wiley (1954) (Second edition in 1972, Dover)Google Scholar
- Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)Google Scholar