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School of Economics and Finance Seminar The Sure-Thing Principle

Speaker: Dr Jean Baccelli, Oxford University

Abstract: The Sure-Thing Principle famously appears in Savage's axiomatisation 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 anymore. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. We show that each of P2 and P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance condition; 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 arguably the two most fundamental properties of rational choice under uncertainty. They imply, as corollaries, potential simplifications for Savage's and the Anscombe-Aumann axiomatisations of Subjective Expected Utility. Most surprisingly, perhaps, they reveal that in Savage's axiomatisation, P3 can be weakened to a natural strengthening of so-called Obvious Dominance.

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