Probabilistic Sophistication and Stochastic Monotonicity in the Savage Framework

Machina & 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.

JEL Classification: D81

Keywords: Subjective probability; Probabilistic sophistication, Stochastic monotonicity, Sure-thing principle, Cumulative dominance