Probabilistic sophistication and stochastic monotonicity in the Savage framework

Abstract

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.

What Are Asset Demand Tests of Expected Utility Really Testing?*

“…Remark Axiom 7 will be recognised to be similar to the probabilistic sophistication property introduced by Machina and Schmeidler () in an SEU setting (Grant et al ., ). Because this property is based on subjective probabilities, it is necessary to introduce axiomatic structure to ensure that the endogenous probabilities satisfy probabilistic sophistication. However in the case of Axiom 7, the probabilities are given exogenously and the axiom can be directly assumed .…”

Expected Utility Preferences for Contingent Claims and Lotteries

“…Remark 2 Axiom 5 will be recognized to be similar to the probabilistic sophistication property introduced by Machina and Schmeidler (1992) in an SEU setting (also see Grant, Özsoy and Polak 2008). Because this property is based on subjective probabilities, it is necessary to introduce axiomatic structure to ensure that the endogenous probabilities satisfy probabilistic sophistication.…”

Rational risk‐aversion: Good things come to those who weight

“…He assumes a smooth preference constraint-in the Appendix, we provide sufficient conditions that do not rely on smooth preferences. 37 We could either (i) directly restrict the set of admissible functions to those satisfying FOSD, or (ii) introduce an additional preference axiom that captures first-order stochastic dominance such as Stochastic Monotonicity (see Grant et al (2008)). misrepresent probabilities.…”