Essays in Decision Theory

Open Access
Borhani, Fateme
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
May 31, 2016
Committee Members:
  • Edward James Green, Dissertation Advisor
  • Edward James Green, Committee Chair
  • Kalyan Chatterjee, Committee Member
  • Andres Aradillas-Lopez, Committee Member
  • Lisa Lipowski Posey, Outside Member
  • Decision theory
  • Ambiguiy
  • Probabilistic Sophistication
  • Evidence Based Decision Making
The present dissertation consists of three essays in decision theory. The first essay is on ambiguity. Second and Third essays are concerned with Bayesian decision making. The first essay investigates beliefs of a decision maker who cannot assign precise odds to every event and considers a set of distributions over the state space to be relevant. Main theorem of this essay provides necessary and sufficient conditions, in a version of Anscombe and Aumann's framework, for a preference relation to be consistent with beliefs in the form of multiple priors. A controversial axiom, state monotonicity, is not imposed on the preference relation. It is shown in theorem \ref{subset} that, when beliefs are modeled using multiple priors, the set of acts over which probabilistic sophistication has a force (clear acts) typically is strictly larger than the set of unambiguous acts. A behavioral definition of such acts is provided. The second essay explores evidential structures. Primitive entities of the theory to be presented are a body of evidence available to an agent (called an evidential state) and an alternative in a set, from which the agent might choose. Assumptions are stated regarding the space of possible evidential states. Under those assumptions, while the space of evidential states is not necessarily a Boolean algebra, it can be embedded in a structure-preserving way into a canonical sigma-field of events. A plan is a mapping from evidential states to choice alternatives. A consistency condition for plans, reminiscent of Savage's sure-thing principle, is formulated. The condition is neither necessary nor sufficient for a plan to be rationalized by subjective-utility maximization with respect to a probability measure on the canonical sigma-field. A structure of evidential states may contain, or coincide with, a substructure that models a process of experimental learning. A plan specified on such a substructure satisfies the consistency condition if, and only if, it can be rationalized by maximization of subjective conditional expected utility. The third essay is built upon the second essay. It provides the necessary and sufficient condition for rationalizability of a general plan.