Essays in Decision Theory: Induced and Revealed Preference

Abstract

This collection of essays investigates dynamic choices and the revealed preference of indirect choices.In Chapter 1, I study dynamic choices when new information is ambiguous. I introduce a new updating rule, the conditional maximum likelihood rule (CML) for updating ambiguous information. CML satisfies a new axiom, increased sensitivity after updating, while existing updating rules do not. With CML, a decision maker's posterior is unaffected by the order in which independent signals arrive. CML accommodates recent experimental findings on updating ambiguous information and has applications on learning and information design. In Chapter 2, (co-authored with Mu Zhang), we propose a new model of menu preference that captures the optimism of decision makers. We model a decision maker who anticipates her preference to change in the future and optimistically evaluates each menu according to the best choice that could possibly be made by her future self. We characterize this menu preference, discuss its uniqueness and propose a comparative measure of optimism. The model connects optimism with the naive quasi-hyperbolic discounting model and has novel predictions on decision makers' choices over menus. In Chapter 3, (co-authored with Gaoji Hu, Jiangtao Li and John K.-H. Quah), we develop a theory for testing the rationality of decision makers when their indirect preferences over menus are observed. A preference over menus is said to be an indirect preference if it is induced by a preference over the objects that make up those menus. We consider partial information of a decision maker's ranking over certain menus and provide necessary and sufficient conditions on those rankings that guarantee the existence of a preference over objects that induces the observed menu rankings. We then apply this basic result to a wide variety of applications.