What distinguishes alternative frames from mere re-descriptions of a referent is the requirement that frames represent elements of a set that are semantically, if not pragmatically, identical. Thus, when Tversky and Kahneman (Reference Tversky and Kahneman1981) introduced the “Asian disease” problem, they claimed, “it is easy to see that the two problems [i.e., alternative frames] are effectively identical” (p. 453). Some years later, they again stated that “it's easy to verify that options C and D in Problem 2 are undistinguishable in real terms from options A and B in Problem 1” (Kahneman & Tversky, Reference Kahneman and Tversky1984, p. 434).

This intuitive argument is an appeal to a watered-down extensional equivalence claim: To avoid contradictions, alternative frames constitute semantically equivalent inputs and should therefore yield identical behavioral outputs. Of course, extensional equivalence does not assume intensional equivalence, as is well known in computational theory (Bruni, Giacobazzi, Gori, Garcia-Contreras, & Pavlovic, Reference Bruni, Giacobazzi, Gori, Garcia-Contreras and Pavlovic2020). Prospect theory (Kahneman & Tversky, Reference Kahneman and Tversky1979) exploits examples such as the Asian disease problem to make the case that intensional non-equivalences (e.g., the psychophysics of valuation) from “extensionally equivalent” inputs causes extensionally nonequivalent outputs. The scare quotes are meant to call out the sleight-of-hand trick in which objectively different inputs are nevertheless said to be the same. In the application of extensional equivalence in the theory of computation, same inputs means identical inputs and not merely semantically synonymous: for example, IV is not the same input as 4, even if these symbols represent the same quantity.

In order to show a rationality-violating contradiction, it is, therefore, vital (a) that semantic equivalence be the only equivalence that matters and (b) that at least semantic equivalence is guaranteed. Neither of these conditions is generally met. McKenzie and colleagues (e.g., McKenzie & Nelson, Reference McKenzie and Nelson2003; Sher & McKenzie, Reference Sher and McKenzie2006) have been clear in articulating that alternative frames such as in the Asian disease problem are informationally non-equivalent, even if they happen to be semantically equivalent because, pragmatically, the alternatives are indisputably nonequivalent. For instance, a positive frame will convey more optimism than a negative frame even if the two share the same quantity semantics (i.e., 200 saved out of 600 implies 400 not saved out of the same number).

However, even if we put the informational nonequivalence of frames aside, it is, in fact, not “easy to verify” that the alternative frames are semantically equivalent. Tversky and Kahneman certainly did not offer any such verification, only the claim itself (which, sadly, seems to have been enough to have convinced most psychologists and behavioral economists for over four decades). It did not take long for some to question this claim. Notably, Macdonald (Reference Macdonald1986) hypothesized that people tend to interpret quantifiers as lower bounds, but remarkably, the idea remained untested for a quarter century. However, in experiment 3 of Mandel (Reference Mandel2014), I found that Macdonald's hypothesis had support. Participants responded to an Asian disease problem variant (substituting war for disease as a cause of deaths) and after making their choice, they indicated whether they thought the quantifier they had encountered meant at least, exactly, or at most that value. Most participants (64%) in the Asian disease problem variant indicated that they interpreted the quantifiers “200” or “400” in options A and C, respectively, as meaning at least that amount (30% said exactly and 6% said at most). Since saving at least 200 out of 600 (option A in the gain frame) is objectively better than letting die at least 400 out of 600 (option C in the loss frame), the preference for A over B (the gain-frame gamble) and D (the loss-frame gamble) over C is hardly a preference reversal. Indeed, it cannot be a preference reversal because lower-bounding of the quantifiers destroys semantic equivalence across “frames.”

By now, the reason for the scare quotes should be obvious: options A and C are not frames at all. The Asian disease problem is not a framing problem. Therefore, it can yield no framing effect, no matter how replicable the behavioral effect is (sorry, inductivists). The effect does not demonstrate a violation of description invariance in risky choice because the descriptions are not semantically invariant and cannot merely be assumed to be so through hand-waving exercises. The said effect, therefore, does not demonstrate a rationality-violating contradiction.

Now to Bermúdez's argument. Bermúdez does not question whether the behavioral evidence from the central base of framing research implies irrationality. Rather, his approach is to carve away the so-called small-world of toy problems entirely and focus on what he describes as the larger complex world in which multi-attribute decisions are the result of conflicting perspectives. Here, we are told, quasi-cyclical preferences induced by the consideration of alternative frames are rational. To be sure, such preferences exist (as his Agamemnon and Macbeth examples illustrate), but the case for why they should be viewed as rational is uncompelling because the contrast to the small-world case is never pinned down tightly. In the complex case, we are told that “preferences are not basic. They are made for reasons” (sect. 3.4, para. 3), and “reasons are frame relative” (sect. 3.4, para. 4). But, surely, the same applies in the small world. The individual who prefers to save 200 lives for sure rather than gamble on a 1/3 chance of saving all 600 (with a corresponding 2/3 chance that all will die) will have a reason for this preference (e.g., “people who could surely be saved should be saved”) even though the same individual will have a different reason for preferring the gamble had the outcomes been framed as losses (e.g., “you shouldn't accept any deaths that could be surely prevented”). This individual may have differing reasons even if the options were semantically equivalent (which they are not).

In short, Bermúdez's carve-out is unsustained and we are left with a contradiction: Bermúdez accepts the irrationality of framing effects in small-world cases but rejects it in complex-world cases for reasons that often apply equally well to the small world. Meanwhile, the conceptual quagmire sketched earlier (also see Fisher & Mandel, Reference Fisher and Mandel2021; Mandel, Reference Mandel2021) deserves full attention, but is largely neglected.