Frames, Reasons, and Rationality

In his recent book, Frame It Again: New Tools for Rational Decision-Making, J. L. Bermúdez argues that it can be rational to evaluate the same thing differently when it is described using alternative ‘frames’. His central example, taken from the eponymous play, sees Agamemnon leading the Greek fleet against Troy, to avenge the abduction of Helen by Paris. Agamemnon is faced with the following dilemma:

The key question is whether Agamemnon's preferences can be rational here. Bermúdez makes the bold claim that they can.
In what follows, I will present a critique of Bermúdez's argument, before pointing towards a potentially more promising route to the same conclusion. The structure of the paper is as follows: §2 recaps the key notions of 'framing', 'frame', and 'framing effect'. §3 explains why framing effects are standardly held to violate rational decision-making. §4 summarises Bermúdez's argument against that standard view. §5 presents objections to his argument. §6 introduces an alternative -pragmatic -approach. §7 sketches how this might be applied to Agamemnon's dilemma. I conclude that, while the jury is still out on whether Agamemnon's preferences are ultimately rationalisable, a pragmatic approach looks more promising than the one Bermúdez pursues.

Framing, Frames, and Framing Effects
Framing involves describing the same thing in different ways. I focus here on linguistic framing, which involves describing the same thing in different words. Linguistic frames (henceforth simply 'frames') are sets of linguistic expressions that are used to describe the same thing, thus being 'co-extensive'. For example, a glass containing water to the halfway mark can be described as 'half full' or 'half empty'. Agamemnon's frames describe possible acts. In Agamemnon's context, two different frames -'following Artemis's will' and 'murdering his daughter'describe the same act and are thus co-extensive. (Of course, there are plenty of contexts in which these verb phrases would not describe the same act. In other words, they do not share an intension. As will be discussed later, that distinguishes the Agamemnon case from many cases used in the psychological literature, where frames are supposed to share both an intension and an extension.) I will restrict my focus here to cases in which the agent knows that two frames are co-extensive. As we saw, Bermúdez stipulates that Agamemnon knows full well that 'following Artemis's will' and 'murdering his daughter' are two ways of describing the same act. (Again, it is less clear whether decision-makers are always assumed to have such knowledge in the mainstream psychological literature on framing but we can set this point aside for now.) Turning finally to the notion of a 'framing effect', this refers to a shift in agents' judgements, preferences, or choices, induced by the use of alternative frames. Thus, Agamemnon evaluates the act of killing Iphigenia differently, depending on whether it is framed as 'following Artemis's will' or as 'murdering his daughter'. In particular, he rates the act more highly under the first frame (preferring it to the alternative of failing his ships and people) than under the second frame (now preferring to fail his ships and people after all).
Let us next examine why framing effects are usually seen as paradigm examples of irrational behaviour.

Description Invariance
Rational choice theory makes some basic assumptions about the coherence of agents' preferences. One such assumption is reflected in the principle of description invariance. Roughly speaking, this principle requires rational agents' choices to be unaffected by mere redescriptions of the options. While it does not appear as an explicit axiom of rational choice theory, the principle is built into the theory's mechanics. Thus, the pioneers of psychological framing research, Amos Tversky and Daniel Kahneman, describe it as 'so basic that it is tacitly assumed in the characterization of options' (Tversky and Kahneman, 1986, p. S253).
The underlying idea is that rational agents take consistent attitudes to objects. Consider first attitudes towards a single object. If an agent values an object at $5, that agent should not simultaneously value it at $10 (at least not while knowing it to be exactly the same object).
The same idea can be extended to the distribution of attitudes across multiple objects. If one prefers object A to object B, and object B to object C, one should not then prefer object C to object A. That would leave one with 'intransitive ', or 'cyclical', preferences. As Bermúdez (2020, chapter 4) points out, cyclical preferences are not only intuitively difficult to make sense of but have practical consequences that are clearly bad. They render agents ripe for exploitation and potential bankruptcy, as shown by 'moneypump' arguments. Imagine, for example, someone who prefers apples to bananas, bananas to clementines, and clementines to apples. Imagine this person starts out with an apple. Preferring clementines to apples, the person agrees to trade the apple for the clementine at an extra cost of, say, 10 cents. Next, preferring bananas to clementines, the person agrees to trade the clementine for a banana at a further cost of, say, another 10 cents. Then, preferring apples to bananas, the person agrees to trade the banana for the original apple at a cost of a further 10 cents. As a result, this person ends up spending 30 cents to buy back an apple she or he started out with; and this process can go on indefinitely. Such behaviourexpending resources for zero gain -is imprudent as well as intuitively incoherent. That has been enough for theorists (including Bermúdez) to deem it irrational.
It has standardly been assumed that rational agents must also maintain consistent attitudes to objects, regardless of how the objects are described (at least when the descriptions are known to be co-extensive). This is because valuations and preferences are supposed to track the objects themselves, not mere descriptions of them. Therefore, most theorists have treated the principle of description invariance as equally inviolable by rational agents. For example, Tversky and Kahneman (1986, p. S272) describe it as 'normatively indispensable', in the sense that 'no adequate prescriptive theory should permit its violation' (ibid).
Despite its widespread acceptance, the principle of description invariance turns out to be difficult to specify precisely (for further discussion, see Bermúdez 2009Bermúdez , 2018. However, keeping in mind Agamemnon's dilemma as our central case, we can begin with the following characterisation 1 : Description Invariance (1). When a rational agent knows a set of descriptions to be co-extensive, the use of one description rather than another has no effect on the agent's judgements, preferences, or choices.
As we will see in the next section, Bermúdez wants to deny that this principle has normative force in all circumstances.

Bermúdez's Argument
Bermúdez argues that there are 'ultraintensional' contexts in which the principle of description invariance does not bind rational agents. In these contexts, agents' judgements, preferences, and choices may shift under co-extensive descriptions. Unlike in standard 'intensional' contexts, this is not because the relevant equivalences are unknown to the agent. Instead, in Bermúdez's ultraintensional contexts it is assumed that the agent does know the descriptions to be co-extensive. So what is going on here?
Importantly, the decision problem facing the agent must be sufficiently complex for frame-sensitive preferences to be rational. Agamemnon's dilemma is a case in point. One dimension of the problem concerns whether the goddess Artemis is placated or angered. Another involves whether the Greek ships and people win or lose at Troy. Yet another involves Agamemnon killing or sparing his daughter. The choice problem is multidimensional, bringing in various different considerations. It thus contrasts with unidimensional decision problems of the kind standardly operationalised in psychological studies of framing effects. As an example of a unidimensional problem, the choice between accepting a 'half full' or 'half empty' glass concerns only the single dimension of its contents. Unidimensional framing effects are thus explicitly excluded from the scope of Bermúdez's account. 2 On Bermúdez's analysis, while the principle of description invariance has normative force over preferences in unidimensional choice problems, it does not apply in multidimensional problems like Agamemnon's. Why not? The first step in the argument is that the alternative frames bring into play distinct reasons in such cases. As we saw above, Agamemnon's frames evoke various different considerations affecting his decision to act in one way or another. The frame 'following Artemis's will' evokes reasons to kill Iphigenia (so as to placate the goddess) and not to spare her (which would anger Artemis). In contrast, the frame 'murdering his daughter' brings into play reasons for 1. A refinement will be suggested in §6 below, when we see how probabilistic contextual informationand not just strict extensional information -can be rationally relevant. 2. The distinction between unidimensional and multidimensional decision problems seems to track the distinction, mentioned in §2, between frames that only share an extension, and those which share both an extension and an intension. Accordingly, a different way to gloss Bermúdez's claim may be that framing effects can be rational when the alternative frames are co-extensive but have different intensions.
Agamemnon to spare Iphigenia (since this would accord with his paternal inclinations and responsibilities) and not to kill her (which would not -to put it mildly!).
In the next step, Bermúdez points out that there is nothing irrational about the alternative frames initially bringing into play such distinct considerations (presumably because the frames' divergent intensions simply make different reasons salient). And of course, there is also nothing irrational about Agamemnon entertaining both frames, since they are both accurate and mutually consistent descriptions of the act in question. 3 Far more controversially, Bermúdez denies that there is anything irrational about Agamemnon subsequently failing to integrate the distinct reasons, despite recognising the frames to be co-extensive. In other words, the considerations brought into play by a frame remain in play just under that frame. Thus, Bermúdez does not think Agamemnon is obliged to reach a consistent valuation of the act itself, independently of how it is framed. I will return to critique this point in §5.
Alongside his reasons-based argument, Bermúdez notes that alternative frames also bring into play distinct emotions. Again, he denies that there is anything intrinsically irrational about this, even once alternative frames are recognised to be co-extensive. 4 Bermúdez then shows how emotions, as a matter of fact, mediate people's valuations and preferences.
The overall result is that Agamemnon ends up, apparently through no fault of his own, with what Bermúdez dubs 'quasi-cyclical' preferences, preferring to kill Iphigenia when that act is framed as 'following Artemis's will' but not when it is framed as 'murdering his daughter'. Stated generally: [A] decision-maker might rationally prefer A to B and B to C, even though they know perfectly well that A and C are the same outcome framed in two different ways. (Bermúdez 2020, 112) Note how quasi-cyclical preferences are supposed to differ from straightforward cyclical preferences of the kind discussed in §3. The cyclical preferences we saw there concerned three distinct entities, A, B, and C, where A was preferred to B, B to C, and C to A (with nothing being said about how A, B, and C are described). In the case of quasi-cyclical preferences, in contrast, there are only two entities. The order of preferences between these two entities simply reverses under alternative ways of describing one of them. Thus, B is preferred when the alternative is described as 'C' but not when the alternative is described as 'A'.
3. Indeed, by entertaining both frames, Agamemnon meets Bermúdez's 'due diligence' requirement, characterised as follows: In setting up a decision problem, rational decision-makers need to be appropriately sensitive to as many potential consequences of the different courses of action available to them as possible. (Bermúdez 2020, 121) Bermúdez's inclusion of due diligence as a rational requirement clearly expands the notion of rationality beyond a purely coherence-based concept. Whether or not this is appropriate has no effect on my argument here, so I will remain entirely neutral on the issue. 4. One might well wish to challenge the argument on this point but I will not attempt to do so here. While Bermúdez considers cyclical preferences to be straightforwardly irrational, he argues that quasi-cyclical preferences can be rational. As the case of Agamemnon is supposed to illustrate, someone can end up with these preferences even when each step in their reasoning process is faultless. Let us now consider whether the argument withstands scrutiny.

Critique
I begin by looking more closely at Bermúdez's characterisations of cyclical and quasi-cyclical preferences. As we saw, in discussing cyclical preferences, he follows the standard convention of using the letters 'A', 'B', and 'C' to represented three distinct things (like apples, bananas, and clementines, in the example in §2). In contrast, in Bermúdez's characterisation of quasi-cyclical preferences, the same three letters are used to represent only two distinct things, since 'A' and 'C' are co-extensive. I believe this difference in convention obscures the fact that quasi-cyclical preferences ultimately are a subset of cyclical preferences (and therefore, by Bermúdez's own lights, irrational). To see why, consider again Agamemnon's dilemma, in which there are two possibilities: killing or sparing Iphigenia. Following the convention of using a unique letter to represent a unique entity (as in the discussion of cyclical preferences) let's use 'A' to represent the act of killing Iphigenia and 'B' to represent the act of sparing Iphigenia. Agamemnon prefers A to B (when A is framed in terms of 'following Artemis's will'); and he simultaneously prefers B to A (when A is framed in terms of 'murdering his daughter'). His preferences are thus straightforwardly cyclical.
The point becomes still clearer with a different example. Imagine I have a homegrown apple that is exceptionally tasty but slightly maggot damaged. Imagine that when the apple is described as 'exceptionally tasty' I prefer it to the banana; but when the apple is described as 'slightly maggot damaged' I prefer the banana. What this implies is that I will be willing to pay someone to trade their banana for my 'slightly maggot damaged' apple. I will then be willing to pay them again to take back the same banana in return for my original 'exceptionally tasty' apple. This cycle can continue indefinitely and the expenditure of resources is entirely fruitless (excuse the pun!). The fact that the apple is framed in two different ways, plausibly bringing into play distinct considerations and emotional responses, does not in any way prevent this from being a straightforward case of cyclical preferences. Of course, we could also characterise it as a case of quasi-cyclical preferences. We could assign the letter 'A' to the apple when it is framed as 'exceptionally tasty' and 'C' to the apple when it is framed as 'slightly maggot damaged'. However, this doesn't affect the basic logic: quasi-cyclical preferences are a subset of cyclical preferences, and cyclical preferences are irrational, so quasi-cyclical preferences are also irrational.
Suppose, then, that one concedes that quasi-cyclical preferences are indeed cyclical preferences, and Agamemnon's preferences are therefore cyclical. One might still argue that cyclical preferences can sometimes be rational; specifically, when the same entity is being described in different ways. I think this approach is unlikely to succeed, however, so long as it does not generate relevantly different assumptions about the entity or the wider context in which it is situated. The apple example above demonstrates the clearly bad practical results of framesensitive preferences, giving us little prima facie motivation to think of them as rational. Moreover, insofar as these preferences result from a basic failure to integrate information, they seem clearly irrational. After all, Agamemnon knows that he is framing a single act in two different ways. Why, then, should he only consider each of the distinct reasons for or against it when entertaining one or other frame? Wouldn't a rational agent recognise that the reasons apply equally under each frame?
In response, perhaps the failure to integrate information across frames could be thought of as the result of limited cognitive resources. Perhaps it is simply too cognitively demanding for human agents to infer that the reasons brought into play by one frame also apply under another. If true, that could justify Agamemnon's cyclical preferences, making them 'boundedly rational' rather than irrational.
I find this proposal implausible, though, at least with respect to the case of Agamemnon. He is quite clearly painfully aware of the extent of his predicament. He recognises that there are strong reasons both for and against killing Iphigenia and the problem is rather which he should accord more weight to. It would seem, then, that he has already successfully integrated the reasons brought into play by each frame. (Indeed, given the stakes involved, it would be rather surprising if he hadn't made the effort to do so.) Accordingly, even when Agamemnon frames the act in one way, he does not thereby lose sight of his conflicting reasons. Rather, he remains aware that he faces a genuine dilemma. Therefore, we should not think that his reasons remain stubbornly isolated under each frame.
A different line of attack for Bermúdez here could be to pursue a more radical metaphysical thesis. Up to now, I have assumed that when he talks about reasons, he is talking about reasons for or against killing Iphigenia, where this is understood as an act. However, Bermúdez does not always clearly distinguish between acts and descriptions. For example, towards the end of the book he writes: [Quasi-cyclical preferences] occur when an agent or decision-maker prefers A to B and B to C, in the full knowledge that A and C are different ways of formulating the same outcome or action. (Bermúdez 2020, 217) Note how this differs from his earlier formulation of quasi-cyclical preferences, in which the letters stand for the things, not descriptions or formulations. On a charitable reading, Bermúdez's equivocation here may be intended as a feature of his account, not a bug. Elsewhere, Bermúdez discusses a kind of object intermediate between acts and descriptions and suggests that it is over these intermediate objects that preferences range: We can only represent Agamemnon as having cyclical preferences if he both prefers Murdering Iphigenia to Failing his Ships and People and Failing his Ships and People to Murdering Iphigenia. There is no cycle or intransitivity if we instead represent Agamemnon's preferences in a more fine-grained way, so that instead of talking about a single outcome that is framed in two different ways we think of him as having preferences over two distinct objects. The first object is Following Artemis's Will. The second object is Murdering his Daughter. (Bermúdez 2020, 81) The idea suggested here is that preferences (and reasons) can apply not to acts themselves but to different sorts of objects that are defined in a more fine-grained way. While this is intriguing, it remains unclear in the book precisely what these intermediate objects are and why they might have rational significance.
One possible interpretation is that it may sometimes be impossible to think about acts themselves rather than, say, acts-under-descriptions. Thus, in a couple of places, Bermúdez talks about 'the illusion of frame-neutrality', noting that 'when issues get sufficiently complicated, there are no neutrally characterizable outcomes' (Bermúdez 2020, 11-12). That could, in turn, help explain why reasons might turn out to be persistently frame-sensitive.
However, even if we were to accept this claim about the lack of neutrally characterisable outcomes, I do not believe it could rationalise the kinds of framing effects Bermúdez is concerned with. Specifically, the idea that Agamemnon cannot think about the act of killing Iphigenia itself seems incompatible with the original gloss of the case, in which Agamemnon is stipulated as knowing that 'following Artemis's will' and 'murdering his daughter' are two ways of describing one and the same act. How could Agamemnon know this if he can only think about the act-under-a-description? That would seem to preclude his recognising that a single act is being described.
Following on from this, as soon as it is acknowledged that Agamemnon can think about the act itself, independently of how it is described, it becomes immediately unclear why reasons and preferences should attach to anything more fine-grained than the act itself. It seems that Agamemnon should -and does -recognise that the full suite of reasons brought into play by the alternative frames apply to the act, regardless of how it is described. I doubt, then, whether even a more radical metaphysical picture can save Bermúdez's account.
Concluding my argument in this section, I do not think Bermúdez gives us a convincing argument for suspending the principle of description invariance in multidimensional choice problems like Agamemnon's dilemma. What this means for Agamemnon as a rational agent is that his preferences should be based on the reasons for and against the act of killing Iphigenia; and he may reach a rational decision only by treating one set of reasons as outweighing the other. In the next section, I sketch an alternative approach, which could explain why Agamemnon might reasonably weigh reasons differently under the alternative frames (although it too might ultimately fail, rendering Agamemnon's preferences unjustifiable in the end).

A Pragmatic Approach
In recent years, psychologists have begun to question whether the alternative frames used in experimental paradigms are truly informationally equivalent, arguing instead that they may have importantly different pragmatic effects (Leong et al. 2017;McKenzie 2004;McKenzie and Nelson 2003;Sher and McKenzie 2006, 2008, 2011. This, in turn, has led them to attack the received view that framing effects are irrational. While Bermúdez acknowledges that such approaches 'raise important criticisms of the framing experiments', he sees them as tinkering around the edges and 'unlikely to upset the entire paradigm' (Bermúdez 2020, 94). I will argue, on the contrary, that such approaches are relatively promising.
The basic insight is that language users systematically choose different frames in different contexts. This, in turn, allows their audiences to infer information about the context from their use of one or other frame. For example, McKenzie and Nelson (2003) find that speakers are more likely to describe a glass as 'half full' when it was previously emptier than when it was previously fuller; and they are more likely to describe it as 'half empty' when it was previously fuller than when it was previously emptier. Recipients of these frames are, in turn, more likely to think that a glass was previously emptier when it is described as 'half full' than when it is described as 'half empty'; and they are more likely to think that it was previously fuller when it is described as 'half empty' rather than 'half full'.
In a different scenario, describing a basketball player as having 'made 40%' of his shots rather than as having 'missed 60%' is associated with his having made a relatively large proportion. Conversely, describing a player as having 'missed 60%' is associated with his having missed a relatively large proportion (Leong et al. 2017). It seems reasonable for this additional contextual information to affect subsequent judgements and decisions in relevant ways. For example, the basketball player may rationally be evaluated more favourably under the 'made' frame than under the 'missed' frame. After all, unless one knows what counts as good or bad performance in absolute terms, a player who makes relatively many shots is better than one who makes relatively few.
This insight highlights the need for a refinement of the description invariance principle along the following lines, to include the italicised text: Description Invariance (2). When a rational agent knows a set of descriptions to be co-extensive and equally likely to be used in relevantly different contexts, the use of one description rather than another has no effect on the agent's judgements, preferences, or choices.
Note that this reformulation does not in any way undermine the argument mounted in §5 against Bermúdez's account. That account trades not on the context-dependent use patterns of alternative frames, but on the idea that frames are inextricably linked to distinct reasons for action. It is that latter idea which I rejected, together with the associated attempt to weaken the description invariance principle. I suggest instead that something like the revised principle (2) has normative force across both unidimensional and multidimensional choice problems.

Return to Aulis
Inspired by the pragmatic approach to framing effects, I will now sketch a hypothesis about Agamemnon's preferences, which I believe to be potentially more powerful, parsimonious, and plausible than the one put forward by Bermúdez. Nevertheless, I want to be quite clear upfront that this hypothesis may ultimately run aground during empirical testing. In that case, we may need to accept that Agamemnon's frame-sensitive preferences are irrational after all.
My suggestion is that Agamemnon's frames could turn out to convey information about the relative weight of the conflicting reasons for and against killing Iphigenia. Framing the act as 'following Artemis's will' may implicitly signal that Artemis's will is the more important consideration (and therefore that Agamemnon should kill Iphigenia). In contrast, framing the act as 'murdering his daughter' may signal that filicide is the more important issue (and therefore Agamemnon should spare Iphigenia). Accordingly, Agamemnon might prefer the act under the first frame than the second. This, at least, is the basic idea. Let's now explore it in a little more depth.
First, one might wonder why Agamemnon's frames should convey any information at all about the relative weight of reasons. In response, while I readily acknowledge that the proposal is a speculative one, I think it is not implausible that speakers tend to make explicit in their linguistic formulations those features of a situation which are particularly salient to them; indeed, Sher and McKenzie (2006) make a similar suggestion. A speaker's choice to frame the killing of Iphigenia as 'following Artemis's will' might reflect the relative salience of Artemis's will in the speaker's decision-making context, while framing it as 'murdering his daughter' might reflect the relative salience of filicide. A given consideration could, in turn, be made more salient by its presumed importance. Thus, the connection between the choice of frame and the relative importance of a reason could sensibly be hypothesised.
A different wrinkle concerns the application of an approach grounded in interpersonal interactions to the intrapersonal case of deliberation. After all, Agamemnon is framing to himself the act of killing Iphigenia. Is it still legitimate, then, to appeal to a broadly pragmatic approach, even though that approach paradigmatically concerns information conveyed from one language user to others? This is an interesting question which deserves fuller consideration than I can give it here. For now, though, I suggest that we should perhaps not be surprised if Agamemnon's deliberation exploits features of interpersonal linguistic communication. We know, after all, that he is thinking in language, as otherwise it would make no sense to talk about him framing things to himself in one way or another. In turn, it does not seem unreasonable to suppose that information commonly associated with alternative frames carries over from external use to internal use. In a similar way, we can appreciate outward features like rhyme when we think in language, even though thoughts do not sound any particular way. Of course, though, we would not want to say that Agamemnon intends to convey additional contextual information to himself but rather that he ends up doing so implicitly, by entertaining different frames that are typically used in different contexts. 5 Clearly, there is much more to say here, and the hypothesis I have begun to sketch -that frames like Agamemnon's convey information about the weight of reasons -needs further theoretical development and empirical testing to be 5. On a terminological point, then, insofar as pragmatic effects are understood narrowly, as being necessarily speaker-intended, we should ultimately avoid this label for the transfer of contextual information by frames, and appeal to something more brutely associative. made convincing. Therefore, I do not wish to claim at this stage that it is the right gloss of Agamemnon's decision-making process. On one hand, there might be better ways to implement a broadly pragmatic approach, such that Agamemnon's alternative frames convey information of an entirely different kind. On the other hand, it may be that Agamemnon's preferences are simply not amenable to rational explanation. Nevertheless, the key point I want to make is this: pursuing a broadly pragmatic approach is both more promising than Bermúdez acknowledges (since it could potentially explain the kinds of framing effects he is concerned with, which arise from multidimensional decision problems) and preferable to the account he offers. In particular, I believe it has the benefit of greater power, parsimony and -most importantly -plausibility. I conclude by briefly discussing each of these three aspects in turn.
The first point is that the pragmatic approach has greater explanatory power than Bermúdez's account. This is because it covers a wider range of framing effects. It has the potential to rationally explain framing effects that arise both from multidimensional choice problems and unidimensional choice problems. Bermúdez's account, in contrast, only extends to the multidimensional case.
Second, insofar as the pragmatic approach offers a unified account of framing effects, it seems more parsimonious than Bermúdez's account. Compounding its greater parsimony is the fact that we are not required to posit the existence of additional intermediate objects like 'acts-under-descriptions' as part of our ontology.
Finally, the pragmatic approach renders framing effects more plausibly rational. If alternative frames reliably convey distinct choice-relevant information, agents canand should -respond differently to each. In contrast, as I argued in §5, Bermúdez's account ultimately fails to give a convincing justification for frame-sensitivity.
By way of conclusion, what all this suggests is that the pragmatic approach that psychologists have begun to develop is likely to be preferable to the one Bermúdez's pursues. That said, whether or not it can ultimately make sense of preferences like Agamemnon's remains to be seen.