Do Dynamic-Choice "Exploitation" Arguments Justify the Standard Rationality Axioms of Decision Theory?
Dissertation, Cornell University (
2000)
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Abstract
In a static decision problem the decision-maker faces just one up-front choice, while in a dynamic one there are some choices to be made after other choices or after the resolution of some uncertain events. The standard axioms for static decision-making require that choices under certainty or uncertainty be based on a weak order preference relation, and conform to the variously formulated independence condition for uncertainty; these axioms permit a derivation of the principle of maximizing expected utility. ;In a dynamic-choice "exploitation" argument, a decision-maker who violates at least one of the standard axioms is placed in a dynamic choice situation, one in which she is vulnerable to exploitation by another agent seeking to profit from the violation. E. McClennen's Rationality and Dynamic Choice provides an evaluation of this approach to justifying the standard axioms. He identifies and questions two premises implicit in these arguments, the principles of Plan Reduction and Separability. ;However, it remains an open question in the literature whether the project would really be successful, even if these assumptions were justifiable. The dynamic exploitation arguments that have been considered address particular violations of the standard axioms, but do not show that every violation of the axioms makes one exploitable. McClennen conjectures, on the basis of a partial argument, that the generalization is true. ;This dissertation shows that, even granting the assumptions identified by McClennen, the standard axioms cannot be justified by means of the dynamic exploitation arguments, since there are violations of the axioms to which they are not applicable. I first identify two different kinds of dynamic exploitability and their necessary conditions, and then show that some decision-making procedures violating the standard axioms fail to conform to these necessary conditions, and thus are not dynamically exploitable.