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THE SURE-THING PRINCIPLE AND P2 YANG LIU Abstract. This paper offers a fine analysis of different versions of the well known sure-thing principle. We show that Savage’s formal formulation of the principle, i.e., his second postulate (P2), is strictly stronger than what is intended originally.
1. Introduction 1.1. Savage’s theory of subjective expected utility (1972) is widely celebrated as the paradigmatic system of Bayesian decision theory. The cornerstone of Savage’s theory is a rationality postulate known as the “sure-thing principle.” The principle is formally stated in Savage’s system as the second postulate (P2). In this short note, we point out that there is certain discrepancy between P2 and the sure-thing principle in its original form. We show that Savage’s P2 is, in fact, a strictly stronger principle. 1.2. Recall that a Savage decision model is a structure of the form (S, B , X, A,