Conditional preferences and updating

This paper axiomatizes updating rules for preferences that are not necessarily in the expected utility class. Two sets of results are presented. The first is the axiomatization of conditional preferences. The second consists of the axiomatization of three updating rules: the traditional Bayes rule, the Dempster-Shafer rule, and the generalized Bayes rule. The last rule can be regarded as the updating rule for the multi-prior expected utility (Gilboa and Schmeidler (1989)). Operationally, it is equivalent to updating each prior by the traditional Bayes rule. ∗TanWang is with the Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2. [email protected]. The author is grateful to Lorenzo Garlappi, Jacob Sagi, Jiang Wang, Jiankang Zhang, and especially Larry Epstein for their comments and discussions, and to the Social Sciences and Humanities Research Council of Canada for financial support.