 The axiom in Savage’s theory that has received most attention is the Sure Thing Principle. It is not hard to see that this principle conflicts with Allais’ preferences for the same reason these preferences conflict with Independence (recall  Section 2.3).  Allais’ challenge will be discussed again later. For now, our concern is rather the Sure Thing Principle vis-à-vis the internal logic of Savage’s theory. To begin with, the Sure Thing Principle, like State Neutrality, exacerbates concerns about the Rectangular Field Assumption. This is because the Sure Thing Principle is only plausible if outcomes are specific enough to account for any sort of dependencies between outcomes in different states of the world. For instance, if the fact that one could have chosen a risk-free alternative—and thereby guaranteed an acceptable outcome—makes a difference to the desirability of receiving nothing after having taken a risk (as in Allais’ problem), then that has to be accounted for in the description of the outcomes. But again, if we account for such dependencies in the description of the outcomes, we run into the problem that there will be acts in the preference ordering that are nonsensical (see, e.g., Broome 1991a: ch. 5).