Machina and Schmeidler (1992) show that probabilistic sophistication can be obtained in a Savage setting without imposing expected utility by dropping Savage’s axiom P2 (sure-thing principle) and strengthening his axiom P4 (weak comparative probability). Their stronger axiom, however, embodies a degree of separability analogous to P2. In this note, we obtain probabilistic sophistication using Savage’s original axiom P4 and a weaker analog of Savage’s P2.
Grant, Simon; Ozsoy, Hatice; and Polak, Ben, "Probabilistic Sophistication and Stochastic Monotonicity in the Savage Framework" (2007). Cowles Foundation Discussion Papers. 1918.