Transformative Decision Rules : Foundations and Applications

Abstract: A transformative decision rule alters the representation of a decisionproblem, either by changing the sets of acts and states taken intoconsideration, or by modifying the probability or value assignments.Examples of decision rules belonging to this class are the principleof insufficient reason, Isaac Levi’s condition of E-admissibility, Luceand Raiffa’s merger of states-rule, and the de minimis principle. Inthis doctoral thesis transformative decision rules are analyzed froma foundational point of view, and applied to two decision theoreticalproblems: (i) How should a rational decision maker model a decisionproblem in a formal representation (‘problem specification’, ‘formaldescription’)? (ii) What role can transformative decision rules play inthe justification of the principle of maximizing expected utility?The thesis consists of a summary and seven papers. In Papers Iand II certain foundational issues concerning transformative decisionrules are investigated, and a number of formal properties of this classof rules are proved: convergence, iterativity, and permutability. InPaper III it is argued that there is in general no unique representationof a decision problem that is strictly better than all alternative representations.In Paper IV it is shown that the principle of maximizingexpected utility can be decomposed into a sequence of transformativedecision rules. A set of axioms is proposed that together justify theprinciple of maximizing expected utility. It is shown that the suggestedaxiomatization provides a resolution of Allais’ paradox that cannot beobtained by Savage-style, nor by von Neumann and Morgenstern-styleaxiomatizations. In Paper V the axiomatization from Paper IV is furtherelaborated, and compared to the axiomatizations proposed byvon Neumann and Morgenstern, and Savage. The main results in PaperVI are two impossibility theorems for catastrophe averse decisionrules, demonstrating that given a few reasonable desiderata for suchrules, there is no rule that can fulfill the proposed desiderata. In PaperVII transformative decision rules are applied to extreme risks, i.e.to a potential outcome of an act for which the probability is low, butwhose (negative) value is high.