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Transformative Decision Rules - Foundations and Applications

by Peterson, Martin

Abstract (Summary)
A transformative decision rule alters the representation ofa decision problem, either by changing the sets of acts andstates taken into consideration, or by modifying theprobability or value assignments. Examples of decision rulesbelonging to this class are the principle of insfficientreason, Isaac Levi?s condition of E-admissibility, Luceand Raiffa?s merger of states-rule, and the de minimisprinciple. In this doctoral thesis transformative decisionrules are analyzed from a foundational point of view, andapplied to two decision theoretical problems: (i) How should arational decision maker model a decision problem in a formalrepresentation (?problem specification?,?formaldescription?)? (ii) What role can transformative decisionrules play in the justification of the principle of maximizingexpected utility?The thesis consists of a summary and seven papers. In PapersI and II certain foundational issues concerning transformativedecision rules are investigated, and a number of formalproperties of this class of rules are proved: convergence,iterativity, and permutability. In Paper III it is argued thatthere is in general no unique representation of a decisionproblem that is strictly better than all alternativerepresentations. In Paper IV it is shown that the principle ofmaximizing expected utility can be decomposed into a sequenceof transformative decision rules. A set of axioms is proposedthat together justify the principle of maximizing expectedutility. It is shown that the suggested axiomatization providesa resolution of Allais?paradox that cannot be obtained bySavage-style, nor by von Neumann and Morgenstern-styleaxiomatizations. In Paper V the axiomatization from Paper IV isfurther elaborated, and compared to the axiomatizationsproposed by von Neumann and Morgenstern, and Savage. The mainresults in Paper VI are two impossibility theorems forcatastrophe averse decision rules, demonstrating that given afew reasonable desiderata for such rules, there is no rule thatcan fulfill the proposed desiderata. In Paper VIItransformative decision rules are applied to extreme risks,i.e. to a potential outcome of an act for which the probabilityis low, but whose (negative) value is high.Key words:transformative decision rule, problemspecification, framing, expected utility, decision theory
Bibliographical Information:

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:transformative decision rule; problem specification; framing; expected utility; decision theory

ISBN:91-7283-460-9

Date of Publication:01/01/2003

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