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Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory?

Baccelli, Jean and Mongin, Philippe (2021) Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory? Philosophical Studies. ISSN 0031-8116

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Abstract

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility (EU) formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity (i.e., being cut off from the methods and results of decision theory). To give the strategy more structure, philosophers have developed "principles of individuation"; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion (i.e., it is duly developed using the available tools of decision theory). We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Baccelli, Jeanjean.baccelli@gmail.com0000-0003-0275-0377
Mongin, Philippemongin@greg-hec.com
Keywords: decision theory; binariness property; expected utility; Sen; von Neumann and Morgenstern; Savage; Allais paradox; Ellsberg paradox; redescription of outcomes; principles of individuation
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
General Issues > Game Theory
Specific Sciences > Probability/Statistics
Depositing User: Jean Baccelli
Date Deposited: 16 Sep 2021 18:41
Last Modified: 16 Sep 2021 18:41
Item ID: 19569
Journal or Publication Title: Philosophical Studies
Publisher: Springer (Springer Science+Business Media B.V.)
DOI or Unique Handle: 10.1007/s11098-021-01723-z
Subjects: General Issues > Decision Theory
Specific Sciences > Economics
General Issues > Game Theory
Specific Sciences > Probability/Statistics
Date: 2021
ISSN: 0031-8116
URI: http://philsci-archive.pitt.edu/id/eprint/19569

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