• A comparison between different formulations of the “Sure-thing principle” in Bayesian decision theory.
• An analysis of the notion of conditional preferences in Savage-style system.
• A demonstration that Savage’s “sure-thing principal” (STP) is structurally different from his second postulate (P2).
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.