Baccelli, Jean (2023) The Sure-Thing Principle. Journal of Mathematical Economics.

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Abstract

The Sure-Thing~Principle famously appears in Savage's axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing~Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing~Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage's and the Anscombe-Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage's axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Baccelli, Jean jean.baccelli@gmail.com 0000-0003-0275-0377
Keywords:	Decision theory; Subjective Expected Utility; Sure-Thing Principle; State-Wise Dominance; Obvious Dominance; Savage; Anscombe-Aumann
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Probability/Statistics
Depositing User:	Jean Baccelli
Date Deposited:	02 Nov 2023 22:20
Last Modified:	02 Nov 2023 22:20
Item ID:	22728
Journal or Publication Title:	Journal of Mathematical Economics
DOI or Unique Handle:	10.1016/j.jmateco.2023.102915
Subjects:	General Issues > Decision Theory Specific Sciences > Economics General Issues > Game Theory Specific Sciences > Probability/Statistics
Date:	28 September 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/22728

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