R2.1. Rational framing effects in the canonical experiments

One of the key claims in the target article is a sharp divide between the “easy” experimental framing effects and the “hard” cases where, I claim, rational framing effects can be found. Several commentators argue that framing effects can be rational even in the canonical experiments.

• • Levy argues that frames can provide genuine evidence, so that framing effects are the result of subjects responding rationally to evidence. Certain frames might be understood, for example, as conveying a recommendation – describing someone's publication record in terms of her acceptance rate rather than her rejection rate is more likely to generate a positive impression. Being sensitive to such forms of implicit recommendation can be ecologically rational, according to Levy. If a subject has no initial preference between two options A and B and option A is implicitly recommended by somebody who might reasonably be taken to be an authority, the subject thereby acquires a reason to choose A over B. (See also Flusberg et al., who emphasize more broadly the role of communicative effect, and pragmatic language processing more generally in creating framing effects.)

• • Kühberger points to a number of ways in which “risky choice framing effects can result from various cognitive processes, all being entirely intelligible and rational. Central is the idea that, rather than passively taking in information, people actively select and process information, taking also background knowledge into consideration.” There are multiple semantic and pragmatic factors that can be appealed to show that the different options in, for example, the Asian disease paradigm are not really informationally equivalent (see also Sher & McKenzie, Mandel, and Schwartz & Cheek).

• • Dorison reports experiments showing that third-party observers systematically penalize decision-makers who are not sensitive to gain/loss framing effects. It follows, then, that there can be reputational rewards for being susceptible to such framing effects. When those reputational rewards outweigh the non-reputational costs, then being susceptible to gain/loss framing effects can be rational.

All these observations are good ones. They add to the roster of plausible explanations of what is actually going on in the canonical framing effects. However, I don't really think that either succeeds in breaking down the contrast between rational framing effects and irrational ones. As formulated in the target article, the contrast is between (a) cases where frames prime responses, as in many of the classic framing experiments, and (b) more complicated situations where frames function reflectively by making salient particular reason-giving aspects of a thing or outcome.

The Levy analysis seems to be a form of priming (the implicit recommendation primes a positive response). There is a sense in which the subject has a reason, but nothing at all comparable to the complex reflection involved in the (b)-type cases. Similarly for Dorison's example – he shows that it can make sense reputationally to be susceptible to gain–loss framing effects, but that is not the same as showing them to be rational, in the sense of correct and normatively appropriate. For one thing, the subject does not make the preference-reversing choices because of the reputational consequences.

Flusberg et al. argue that the pragmatic phenomena they point to are not instances of priming. They cite studies showing that when crime is framed as a beast (rather than a virus) ravaging a city, subjects are more likely to propose law-enforcement solutions – an effect that disappears if subjects are simply primed with the concept beast. This is not convincing, however. A priming effect that only works in a particular context is still a priming effect. Metaphors and pragmatic processing are important tools for framing, but rational quasi-cyclical preferences require more reflective decision-making.

Żuradzki appreciates this and explicitly tries to show how even in the Asian disease case the different frames actually bring different moral considerations into play. The preference for a certain outcome in the positive frame (200 will be saved, as opposed to a 1/3 probability that all will be saved) reflects a preference for doing rather than allowing – the outcome is actively brought about, rather than being the luck of the draw. In contrast, he suggests, the negative frame focuses the attention on fairness. People choose the lottery because it is more egalitarian – either all will live or all will die, and the probability is the same for each. This is much closer to quasi-cyclical preferences, rather than just priming.

R2.2. New domains for rational framing effects?

The commentaries by Chater, Vasil, and Zentall offer suggestive proposals for extending the scope of rational framing effects to formal domains such as chess and mathematics (Chater), developmental psychology (Vasil), and animal learning (Zentall). Chater is broadly supportive, while the other two authors claim that the rational framing effects they identify are potentially problematic for my position.

According to H2 above, framing effects will occur in decision problems that are too complicated and multi-faceted to be subsumed under a single evaluative dimension. In my target article, I focused primarily on emotional and evaluative complexity, with different frames bringing different and incompatible responses into play. Chater points out convincingly that the same structure can emerge in the (relatively) emotion-free realms of mathematics and chess. Computational complexity makes framing a necessity. No individual move in chess can be evaluated on its own terms – it must be framed as part of a strategy, and quasi-cyclical preferences quickly emerge when the same move is (knowingly) considered under multiple frames/strategies.

This is surely correct, and offers another way of thinking about the rational power of frames – as heuristic tools for managing computational complexity, with rational framing effects an inevitable consequence.

Zentall's references to the animal learning literature are also very much to the point, since the preference reversal from long-term rewards (LL) to short-term ones (SS) typically used to frame discussions of human self-control has been well studied in the animal case, as have some of the models used to explain it (e.g., hyperbolic delay discounting). Zentall points to numerous relevant phenomena. For example, when pigeons are offered a choice between (i) an offer of one pellet of food resulting in a reward of one pellet, and (ii) an offer of two pellets of food resulting in a reward of one pellet, they will reliably choose (i), displaying some analog of loss aversion, because they disprefer the outcome where what they receive is less than what they chose (Sturgill et al., Reference Sturgill, Bergeron, Ransdell, Colvin, Joshi and Zentall2021). This is plausibly a framing effect. The same outcome (delivery of one pellet of food) is framed in two different ways – as involving a loss and as not involving a loss.

Also very interesting is the finding (Sturgill et al., Reference Sturgill, Bergeron, Ransdell, Colvin, Joshi and Zentall2021) that pigeons find it significantly easier to deal with reverse contingencies (when the animal has to choose a smaller amount in order to receive a larger amount) if they are presented with symbols rather than with the actual quantities. As Zentall points out, this is in some respects analogous to the reframing strategy I explore for self-control – either (as in this case) a “cool” reframing of the impulsive choice, or (as in the target article) a “hot” reframing of the long-term goal. Certainly, this shows that animals can be sensitive to the mechanisms that can be deployed in the rational framing effects that I discuss. However, it seems a stretch to describe these as rational framing effects. They are primed responses, rather than thought-strategies the animal engages in.

Vasil's discussion of developmental psychology is somewhat closer to the topics of the target article. Reporting joint work with Michael Tomasello, he finds interesting framing effects in young children. Framing tasks as social endeavors (e.g., by telling them that another child was working on the same puzzle in an adjacent room) seems to increase 5–6 year olds' motivation to persist in the tasks (Butler & Walton, Reference Butler and Walton2013). Higher degrees of commitment to their partners were observed in 3–4 year old's during activities that were framed collaboratively (as an activity that we engage in together), rather than as individualistically (Vasil & Tomasello, Reference Vasil and Tomasello2022). Vasil suggests that these are rational framing effects, because, as he puts it, “we” succeed only if “we” work together.

These are interesting results (relevant also to the “I”-frame vs. “we”-frame contrast in game theory – see further below). Vasil is correct that children of this age lack the sophisticated cognitive skills discussed in the last section of my target article (reflexive decentering, perspectival flexibility, etc.). I am not sure that this is a problem for me, however. I did not say, and nor do I believe, that those cognitive abilities are necessarily implicated in rational framing effects. I was arguing in the opposite direction – namely, that those skills and abilities are going to be needed in any successful attempts to resolve frame-based interpersonal conflict (what I called discursive deadlock) and that exercising those skills and abilities will bring with it rational framing effects.

Still, Vasil's commentary raises an important question. As discussed in section R2.1, I rely heavily on the distinction between framing effects produced by “mere” priming, and the rational framing effects that derive from competing reasons and require a degree of reflective understanding. I certainly need to spell out in more detail what exactly reflective understanding consists of. Looking at the ontogeny of framing effects will be an important tool here in the attempt to disentangle the different components – so too will aspects of the animal learning literature, which might point to a bottom-line set of frame-sensitive capacities without which rational framing effects could not possibly occur.

R2.3. Rational framing effects and moral reasoning

Roberts and Sirgiovanni both focus on the arguments of the target article in the area of moral philosophy. This brings refreshing new perspectives, as does Beal's exploration of what Bakhtin has called the polyphony principle in the context of Dostoyevsky's Crime and Punishment.

Sirgiovanni observes that there is an approach to the much-discussed trolley problem that seems to involve quasi-cyclical preferences. So, for example, I might prefer switching the lever as the trolley comes thundering down the track, which will save the five people on the tracks at the cost of sacrificing one person. At the same time, though, I might prefer letting the trolley kill the five people on the tracks to pushing one person off a bridge to stop the trolley. These preferences (which I and many others find quite appealing) would count as quasi-cyclical if we equate both choices as between the loss of one life and the loss of five lives.

This is not a very plausible way of looking at the matter, however. It would be hard to defend a view of outcomes on which the death of one person counts as the same outcome as the death of a completely different person. The number of lives lost is the same in the two cases, but surely the objects of choice are different. Choosing an action that leads to someone being pushed off a bridge is not the same as choosing an action that leads to a different person being run over by a trolley – so there is no way in which we can be dealing with different ways of framing the same outcome, as would be required for quasi-cyclical preferences. As we will see at greater length in section R4, there are important questions about how exactly to understand outcomes and what it is to prefer one outcome to another. At a minimum, though, for A to be the same outcome as B there must be at least a core of common consequences.

This brings us back to the aim of the target article, namely, the principle of extensionality, considered as a binding principle of rationality. Within the social and behavioral sciences, the validity of extensionality is almost unquestioned. Roberts observes, though, that extensionality is only held to be binding within moral philosophy by consequentialists (and decision theory, of course, typically reflects a strong form of consequentialism). From the perspective of deontology and virtue ethics, the idea that outcomes or actions can only be assessed and chosen when framed is not news.

As Roberts points out, Christine Korsgaard, the well-known contemporary Kantian, has claimed that agents must choose between actions, not between acts, where an action incorporates aspects of the reasons for which the act is performed. In my terminology, an action is an act under a particular reason-giving frame. Virtue ethicists, who value character dispositions, also typically think of actions in a way that incorporates the dispositions and character traits that they reflect. The same reasoning can be extended to outcomes. There are no bare outcomes – an outcome reflects the action that gave rise to it.

While this is an important insight, it is important not to exaggerate the parallels. Kantians such as Korsgaard and virtue ethicists are not known for their liberality when it comes to the admissibility of multiple frames. This means that neither is likely to accept the admissibility of quasi-cyclical preferences, for which being able to view a single action or outcome under multiple frames is a prerequisite. It is true that a Kantian can and should accept that an action can reflect multiple maxims or principles. But only one can be correct. I think that Kant would find deeply alien the view that it would be rationally permissible to prefer A to B and B to C where A and C are the same act or outcome framed according to different maxims or principles. The task of moral reasoning is to identify the current maxim or principle for the given situation, and once that has been found there is no room for further framing. In contrast, frame-sensitive reasoners cannot be tied to a single frame. Frame-bound moral reasoners are, in fact, one of the causes of the discursive deadlock discussed in the last part of the target article. It is no accident that the paradigm cases of discursive deadlock are all in the so-called values issues.

As Beal points out, the type of reasoning characteristic of frame-sensitive reasoners is much closer to the concept of polyphony, developed by the literary critic and philosopher Mikhail Bakhtin in connection with Dostoyevsky's Crime and Punishment. This is the idea that “an objectively single action may, with logical consistency, sustain diverse positive and negative judgments.” Raskolnikov offers a series of incompatible but internally coherent explanations of why he killed the pawnbroker and her sister. Each explanation is supported by a unique narrative that selects relevant details from a host of competing characterizations, motives, contextual factors, counterfactuals, and so on. Reality, according to Bakhtin and Beal, is too complex to be distilled into a single narrative. It is, one might say, frames all the way down. (For another artistic development of this basic idea, consider Kurosawa's well-known film Rashomon, which presents multiple tellings of a rape and a murder.)

R3.1. Extending the critique of classical theories

Sher and McKenzie have long argued against the traditional view that choice and decision should be frame-invariant (e.g., Sher & McKenzie, Reference Sher and McKenzie2006, Reference Sher, McKenzie and Keren2011, both of which maintained that the frames implicated in some of the classical framing effects are not informationally equivalent – on which also see Schwartz & Cheek). Here they turn their attention to how the case against rational framing effects rests upon the assumption that preferences are complete, in the following sense: That, given any two available options A and B, the agent either prefers A to B, B to A, or is indifferent between them. Failures of completeness can derive both from imprecision and from conflict.

Sher and McKenzie suggest that lifting the completeness requirement opens the door to rational framing effects: “In a finite choice menu, there may be distinct alternatives, A, B, unranked relative to one another, neither of which is outranked by any other option in the menu. If A is chosen under one descriptive frame and B under another, choices are frame-dependent but never suboptimal.” This point is important, but I should stress that the pattern of choices they describe are not rational framing effects in the sense I describe them. In my cases of quasi-cyclical preferences, there is only one outcome and the agent knows that there is only one outcome. In other words, the agent knows that A = F₁(D) and B = F₂(D), for a single outcome D and two distinct frames F₁ and F₂. So, Sher & McKenzie's description does not apply. Either what they characterize as A and B are framed outcomes, in which case it is falsie that they are unranked relative to each other. Or they are unframed outcomes, in which case A = B and so they cannot possibly be unranked relative to each other. (Nonetheless, completeness is very important in this area, and is discussed also by Pettigrew and Weirich.)

Schwartz and Cheek offer a very distinct perspective on the idea that distinct frames fail to be informationally equivalent. Various authors, including Sher & McKenzie, have suggested that frames are informationally “leaky” – that is, they “leak” choice-relevant information (see also Mandel and Kühberger). Schwartz & Cheek take this a step further, arguing that frames leak into experience. In other words, it is not just that what people choose between are framed outcomes and framed actions, they also experience framed outcomes, particularly following a frame-sensitive choice.

This, they suggest, has direct implications for rationality, even in the simplest framing effects. Even if we take a genuine framing effect, where there is complete informational equivalence between the two options, there can be experiential non-equivalence further downstream, when subjects experience the result of their decision. In other words, difference-making reasons can emerge downstream of actual decision-making. Schwartz and Cheek suggest, surely correctly, that a substantive theory of rationality must take into account not just the anticipated consequences of actions but also their actual consequences, where those actual consequences can experientially reflect the frame-driven choices that gave rise to them.

R3.2. New analyses of rational framing effects

Ainslie, Koi, and De Dreu offer helpful suggestions for deepening the analyses I offer of specific rational framing effects, tackling self-control (Ainslie and Koi) and game theory (De Dreu).

Ainslie suggests that I present framing as an unmotivated process in the context of self-control. The specific effect I discuss is when an agent comes to prefer LL (the long-term reward) to SS (the short-term reward) relative to the having successfully resisted temptation frame, although she prefers SS to LL framed more neutrally (e.g., as an abstract benefit in the future). He objects: “The notion that someone can make self-control hot – in effect, an occasion for aroused emotion – by assigning it utility would seem to violate the laws of motivational gravity. if you could assign utility just anywhere, why not assign it to the LL alternative in the first place.”

This criticism is a little unfair, however. My point is that different frames engage in different ways with values and emotions. The resisting temptation frame brings into play a new set of reasons for the agent. It is that process that results in different assignments of utilities (in accordance with what Ainslie engagingly describes as the laws of motivational gravity).

Having said that, I appreciate the suggestions that Ainslie makes for additional motivational mechanisms. He points out, surely correctly, that a choice looks very differently when it is framed as one of a series of choices, rather than as a one-off choice. Framed thus, the choice of LL can provide behavioral evidence (be a sign) of how the agent will act in the future. If the value of the summed LLs outweighs the value of the summed SSs, with both suitably discounted, then that will provide a powerful motivation that overrides the immediate attractiveness of SS.

Also on the topic of self-control, Koi sees framing as one tool among many. Framing works by modulating information salience (as in H1). But there are other ways of modulating information salience that can be deployed to help with self-control. Framing is an internal strategy, but there are also external ones, such as situation selection and situational modification. I can choose not to expose myself to SS cues, for example – or set up reminders and other mechanisms to increase the salience of LL.

Extending still further, self-control, Koi observes is just one area where informational salience can be modulated and manipulated. The overarching phenomenon is attention (although in a more high-level sense than standardly discussed in cognitive science and cognitive psychology). The role of attentional processes in modulating perception has been much more studied than its role in modulating action. But, as Koi observes, attention may be the most fundamental psychological mechanism. I argue in the target article that framing may be a better way of thinking about self-control than postulating mechanisms of willpower or ego depletion. The interesting possibility Koi raises is that what we are really talking about with dual process (e.g., hot/cold) theories are the results of attentional modulation of information salience.

Turning to game theory, De Dreu broadens my discussion of the “I” and “we” frames in social interactions to consider how those two frames interact with “gain” and “loss” frames. In the target article, I focused on the four-dimensional problem of two players, each of whom has two possible frames. As he observes, though, the dialectic between “I”-frame and “We”-frame becomes more complex and more interesting if we take more possible framings into account. Players can be influenced by the frames of others. I considered only how one player's movement between “I”-frame and “We”-frame is a function of the other player's movement between “I”-frame and “We”-frame, but “gain” and “loss” frames can also be relevant.

For example, De Dreu cites multiple studies showing that (in my terms) the move to the “We”-frame is primed when a player realizes that the other player is operating under a loss frame (e.g., De Dreu & Gross, Reference De Dreu and Gross2019). Empathy is a powerful force, and one that can be manipulated, as rational players in the “I”-frame adopt a loss framing to elicit cooperation from others, which they can then exploit. These are valuable insights. I am unconvinced, however, by his more general statement that the kind of rational reframing I discuss in the target article is unlikely to work, on the grounds that “human psychology gravitates towards minimizing my loss.” That may be so, but the very formulation presupposes an “I”–frame. De Dreu is too quick to equate the “I”-frame with the Defect strategy in, for example, the prisoner's dilemma (PD), and the “we”-frame with Cooperate. The way I distinguish them is through which columns in the pay-off table are taken into account. The “We”-framer takes the pay-offs to all players into account, which is why, despite what De Dreu says, it permits a solution in Stag Hunt. (See Chs. 8 and 9 of Bermúdez [Reference Bermúdez2020] for more details.)

R4.1. Is the project misconceived?

Fisher offers a thought-provoking argument that my basic project is misconceived. The problem comes, she claims, with my initial characterization of quasi-cyclical preferences. Recall that quasi-cyclical preferences occur when the agent prefers A to B and B to C despite knowing that A and C are the same outcome framed in different ways (e.g., as A = Following Artemis's Will and B = Murdering His Daughter). Fisher's objection is, in effect, that I can't eat my cake and have it. An agent can only have quasi-cyclical preferences if he or she knows that A and C are different ways of framing the same outcome. At the same time, Fisher argues, agents can only know that A and C are different ways of framing the same outcome if they have frame-neutral ways of thinking about that outcome. But if agents can think about outcomes in a frame-neutral manner then the framed outcomes that I claim to be the objects of preference and value simply fall out of the picture – a rational agent can ignore the framings and simply focus on the frame-neutral outcome.

This argument is ingenious, but unfortunately not compelling. Consider a time-honored analogy. I am aware that there is one person whom I can think about in one of two ways – as Clark Kent or as Superman. But it certainly does not follow from my knowing the identity of Clark Kent and Superman that I have some independent way of thinking about that person that does not involve either thinking of him as Clark Kent or thinking of him as Superman. By analogy, knowing that two different framed outcomes correspond to a single frame-neutral outcome does not require that I be able to think about that outcome in a frame-neutral way.

And in fact, there are good reasons for thinking that there could not be such a frame-neutral way of thinking about that outcome. That is the whole point of H2. Quasi-cyclical preferences arise in situations that are sufficiently complex and multi-faceted that they need to be viewed and considered from multiple perspectives, none of which is dominant and none of which subsumes the others. For this sort of situation, unlike the highly simplified and stylized examples standardly considered in formal theories of decision and choice, the notion of thinking about them in a frame-neutral manner makes neither descriptive nor normative sense.

This aspect of my overall approach is well understood by Mandel, who writes that my 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.” He does not deny that there are such things as quasi-cyclical preferences. However, he takes exception to my claim that quasi-cyclical preferences can be rational. His reason for saying so is that “the contrast to the small world case is never pinned down tightly.”

With respect simply to the structure of my argument, this objection seems misplaced. Nothing that I say about the complex cases rests upon the (alleged) irrationality of the small-world cases. It is a (sociological) fact, I believe, that most people in the area take the laboratory experiments to manifest irrationality, which is why I framed my own position in contrast to what I take to be the standard view. I am perfectly happy, though, to accept that the standard view may be mistaken, which is why I do not take the arguments of, for example, Dorison, Żuradzki, Flusberg et al., and Levy (all discussed above as challenging the alleged irrationality of the classic experimental behavior) to be objections to my view – and nor were they put forward as objections.

Still, stepping back a little, there is a good point to be extracted from Mandel's paper. His critiques of the classic experiments are all variations on the (important) theme that the different scenarios are not semantically equivalent, because of the type of “leakage” discussed by Schwartz and Cheek, Kühberger, and Sher and McKenzie (not to mention presented in his own work – e.g., Mandel, Reference Mandel2014). I think that his real concern, although it is not explicitly presented as such, is that it is simply impossible for rational framing effects to occur, because of the following lines of reasoning:

1. (1) In order to qualify as a framing effect, the different options must be semantically/informationally equivalent.

2. (2) In order to qualify as rational, a choice or preference must be made for (good) reasons.

3. (3) There cannot be (good) reasons for choosing between two different options that are semantically/informationally equivalent.

These lines of reasoning may be applicable to the Asian disease paradigm, and similar experiments, because subjects are typically asked to choose between descriptions. Crucially, however, it does not apply to the cases I consider.

It is absurd to ask whether the two options of Following Artemis's Will and Murdering My Daughter are semantically or informationally equivalent. Of course, they are not! The point is that they are, and are known by Agamemnon to be, different ways of framing the same outcome. It is the known identity of the outcome (the death of Iphigenia) that does the work done in the classic experiments by the semantic/informational equivalence of the described scenarios. In fact, this is precisely the contrast that Mandel is looking for between the small-world cases and the real-world cases.

R4.2. The nature of preference

The notion of preference is key to my argument. Guala, Lau, Weisel and Zultan, and Pettigrew propose (somewhat overlapping) ways of thinking about preference that, they claim, will undercut my claims about the rationality of quasi-cyclical preferences. Weirich is more conciliatory. He analyzes preference with a view to building a bridge between my account and standard decision theoretic models of rationality.

Guala suggests that I am confusing preferences with other psychological states, such as reasons, desires, emotions, and so on, when I state that the rationality of framing effects is a function of the rationality of a complex and multi-faced response to a complex and multi-faceted situation. Rational preferences have to be “all-things-considered.” The complex and multi-faceted responses that I discuss are not themselves preferences, but rather the inputs to a process of reflection that yields an “all-things-considered” preference. He writes: “Agamemnon may want to follow Artemis's will (under the grip of Frame A), and may want to fail his ships and people (under the grip of B), but he cannot prefer both. Macbeth may have a desire or a reason to fulfil his double duty to Duncan, and another desire or reason to take the throne, but he cannot prefer both, in the sense of rational preference.”

There is no doubt that Guala is correctly characterizing an orthodox account of rational preference (we concur in rejecting the theory of revealed preference). However, it does seem a little question-begging simply to quote back at me the theory I am criticizing. My claim is that preferences cannot be frame-neutral in the way that the Guala and the orthodox view hold. We both accept that there are frame-relative emotional responses, reasons, desires, and so forth. I argue, though, that it will not always be possible to turn those frame-relative reasons into frame-neutral all-things-considered preferences. This will happen when the force and appeal of the reasons are tied to the frame in which they emerge, so that stepping back from the frame weakens their hold.

An idea worth exploring, although not developed in the target article, or in Bermúdez (Reference Bermúdez2020), is that the requirement that rational preferences be all-things-considered can in fact be applied within my own context – that is, by requiring that rational, frame-relative preferences be all-things-considered (relative to that frame). In fact, my position is compatible with an even stronger claim: Which is that rational preferences must be maximally all-things-considered. That is to say, a rational preference ordering must be complete over all comparable outcomes and reasons (i.e., over all the things that can be considered together). I am not motivated to revise my fundamental claim, though, that a rational agent can have more than one maximally all-things-considered preference ordering, in cases where there are reasons, emotional responses, desires, and so on, that cannot be considered together. (On this see the discussion of Pettigrew below.)

I would emphasize similar points in response to Lau and Weisel and Zultan, both of whom propose that my quasi-cyclical preferences are best viewed as ceteris paribus preferences (i.e., preferences, all other things being equal). Lau suggests that ceteris paribus preferences are defeasible and general, whereas rational preferences are absolute and general. As he points out, it can be perfectly rational to have conflicting ceteris paribus preferences: “If I say I prefer coffee over tea, we normally take this to involve an implicit qualification – all else being equal, I prefer coffee to tea. This preference is defeasible and not absolute. I am not being inconsistent if I happen to choose tea over an overpriced, watery coffee.” Weisel and Zultan offer a similar set of considerations: “While a statement such as ‘Macbeth would like to bravely take the throne’ reasonably carries an implicit ceteris paribus (‘all other things being equal’), Bermúdez treats it as a coarse partition of the outcome space, in which Macbeth prefers any outcome that involves being the king to any outcome that does not. Quasi-cyclical preferences arise when considering a choice between actions for which different such partitions contrast. In the action space that Macbeth faces, the outcome that involves becoming the king necessarily involves breaching his double duty to Duncan. The cycle disappears when viewing Macbeth's preferences as ceteris-paribus rather than categorical preferences.”

The distinction both commentaries make is perfectly valid, but it is not really applicable here. With respect to Lau, I actually take quasi-cyclical preferences to be highly specific. Agamemnon does not, generally speaking, think that following the will of Artemis is to be preferred to failing one's ships and allies. Rather, in this highly specific context (being becalmed at Aulis), he prefers the outcome that he frames as following Artemis's will in this highly specific way (by sacrificing Iphigenia). The specific versus general contrast is somewhat of a red herring, therefore, and the real weight of his argument is taken by the defeasible versus absolute contrast – which takes us back to the discussion of Guala above, because Lau's absolute preferences are very similar to Guala's all-things-considered preferences. Likewise for Weisel & Zultan. My claim about Macbeth is highly specific. I don't think it's true that he prefers any outcome in which he is king to any outcome that does not. My whole point is that it all depends upon how the outcome is framed – there are frames (e.g., the loyalty frame) where what he prefers is not to be king, where that is framed as doing his double duty to Duncan.

Pettigrew offers an alternative account of Agamemnon's preferences, on which they do not come out as quasi-cyclical. As he notes, a natural response to my description of the case would be to say that Agamemnon fails to have complete preferences, because he is unable to weigh two competing reasons against each other. This would really be another variation on the theme pursued by Guala, Lau, and Weisel and Zultan, because of the close connections between being ceteris paribus, being defeasible, being incomplete, and failing to be all-things-considered. As Pettigrew notes, though, rationality seems to prescribe indifference between options that cannot be compared and this does not really seem to capture what is going on with Agamemnon, who does end up killing his daughter, but not because he tossed a coin. So, Pettigrew proposes an alternative. Perhaps, he suggests, Agamemnon has different complete preference orderings at different times – at any given moment his preferences are complete, but he jumps from one ordering to another depending on which set of reasons and corresponding affective responses are most salient at that time.

I am not sure that this is really a drastic alternative to my own description of the situation (particularly given the suggestion earlier that each frame-relative ordering is maximally all-things-considered complete). The difference between simultaneously having different frame-relative preference orderings and cycling through them in quick succession may not really amount to much. I do, however, want to take issue with the objection that he makes, which is, in effect, that having multiple preference orderings makes Agamemnon susceptible to a money pump/Dutch book (i.e., a series of bets that is guaranteed to lose him money). Quite apart from the fact that losing money is probably the least of Agamemnon's worries, there is a fundamental problem with money pump arguments. A money pump argument would only show that a particular preference structure was irrational if rationality mandates accepting the problematic series of bets. But of course it does not, because a rational agent can (and should) simply refuse to play the game.

Weirich also pursues the theme of all-things-considered preferences, but he does so to try to show that a version of the principle of extensionality is compatible with my arguments. The basic point he makes is that the principle of extensionality, considered as a basic principle of rationality, is really only applicable in the ideal case where an agent has an all-things-considered preference ordering (i.e., a unique one). As he puts it, “The principle assumes an ideal agent in ideal circumstances facing a standard decision problem and possessing rational all-things-considered preferences among options.” He continues: “Without these assumptions, an agent's choice may be rational despite failing to comply with the principle, or it may be irrational despite complying with the principle.”

To explore the first option, Weirich suggests the standard theory ought to be happy to entertain decision rules for agents without a unique all-things-considered preference ordering. He proposes the following rule. It is rational to choose an option if it is at the top of some completion of an incomplete preference-ordering. Imagine an agent with an incomplete preference-ordering. He might, for example, prefer beetroot to cauliflower to daikon radish, but not be entirely sure how to decide between eggplant and avocado, although he knows that he prefers each of them to the first three. One completion might have avocado at the top, followed by eggplant. Another might have eggplant at the top, followed by avocado. Both, by Weirich's lights could be rational, and, as he points out, frames can serve as a tool for suggesting one completion rather than another. In this way, then, it could be rational to have preferences that are frame-dependent.

It is churlish to look a gift horse in the mouth, and I am happy to accept Weirich's proposal. However, I am not sure that orthodox decision theorists would be happy with his maneuver, because applying it to the cases I discuss entails that a rational agent can simultaneously have multiple different (and incompatible) completions of an incomplete preference ordering. This is rather different from the claim, which an orthodox decision theorist would surely accept, that there can be multiple rational completions of an incomplete preference ordering.

R4.3. The nature of rationality

The commentaries discussed in section R4.2 challenge my claim that quasi-cyclical preferences can be rational by criticizing how I understand preference. Crockett and Paul, Przybyszewski et al., and Teoh et al. take issue in different ways with how I understand rationality.

Crockett and Paul accept that framing effects can give rise to rational quasi-cyclical preferences, but they argue that my account glosses over an important distinction. There are, they claim, examples of quasi-cyclical preferences that seem to meet all my requirements for rationality (e.g., by satisfying H1 through H3) but nonetheless seem to be irrational. They reach this conclusion by distinguishing between two types of quasi-cyclical preference, emerging from two different types of choice:

To illustrate, someone considering whether to have a child might end up with quasi-cyclical preferences, because the considerations may look very different relative to a first-personal framing (relative to her current, rewarding, child-free life) as opposed to a third-person framing (which would incorporate externalities, the testimony and advice of others, etc.). This would be self-involving, in the sense that it is a choice about the type of self one wants to be. But within that general category, some self-involving choices are also self-serving.

For example, “Macbeth might be able to convince himself he is ‘bravely taking the throne’ while observers see straight through his murderous power grab; Agamemnon assures himself he's ‘following Artemis's will” while the audience looks on in horror as he kills his child. These examples occupy the pantheon of high drama because the audience can clearly see that the protagonist is fooling himself (meaning his decision is third-personally irrational) but can also empathize with the dilemma of the protagonist (because his decisions are first-personally rational). In other words, my central examples of quasi-cyclical preferences fail to be rational, not because there is anything wrong with quasi-cyclicality, but because of self-deception and ethical blind spots.

Stepping back from the details of Macbeth and Agamemnon (to whom I suspect I am much more sympathetic than Crockett and Paul), this raises interesting questions about the scope of a theory of rationality. In Bermúdez (Reference Bermúdez2020) (but not, admittedly, in the target article) I discuss substantive constraints upon an account of rationality, in particular a version of the “no false belief” requirement: A model, frame-sensitive reasoner should not believe any false factual propositions, where a factual proposition is one for which there is a standardly accepted method for determining its truth value. It is a factual proposition, for example, that a 7-day-old fetus has a heart (false), but the proposition that a 7-day-old fetus is a person is non-factual. It would be an interesting result if it turned out that self-deception (and the other ethical/moral failings that Crockett & Paul discuss) could be shown to involve some breach of the “no false belief” requirement.

Przybyszewski et al. are also interested in the process by which rational preferences are reached and feel that I leave important evaluative questions unconsidered. They suggest, with some justice, that I am committed to a procedural notion of rationality – for example, that the outcome of a process of reasoning and reflection inherits the rationality of the process that yields it. The objection they raise is that I do not push the requirements of procedural rationality back far enough. In particular, I do not offer tools for evaluating the rationality of frames. They make the point through the lens of prospect theory and associated experimental work, which formalizes the construction of frames in terms of an editing process by which, for example, a reference point is set relative to which losses and gains are calculated. As they observe, the editing process is susceptible to multiple biases, such as the anchoring effect, the disposition effect, the endowment effect, and the certainty effect. All of these have the potential to introduce irrationality into the process.

This line of objection runs parallel to Crockett and Paul, because Przybyszewski et al. are in effect identifying a parallel set of ways in which frames can be generated irrationally, in a way that can contaminate the putative rationality of frame-sensitive reasoning. I think that this is a very valid point. I would be inclined, as above, to raise the possibility that constraints such as the “no false belief” requirement might screen out some or all of these biases. I would also be inclined to add that some of these biases are themselves the result of framing. Different frames will generate different anchors, for example. Similarly for loss aversion, which is a close relative of the endowment effect. What counts as a loss depends upon the horizon of evaluation. Do I calculate investment success relative to the last 12 months (yielding a modest loss) or relative to the 12 years since I made the investment (yielding a significant gain)? That depends upon how I frame my overall investment strategy. (For more on this, see Ch. 3 of Bermúdez, Reference Bermúdez2020).

Teoh et al. also emphasize how framing can be a non-rational process, but from a very different perspective. They emphasize computational complexity and the importance of attention (on which compare Koi). Real-world decision-making involves complex trade-offs with respect to the benefits of information versus the costs of gathering it. As they point out, the quantity of information available in the environment can only be managed through selective attention, and attention is often modulated in exogenous and stimulus-driven ways. They give numerous examples. The external environment is very influential, because attention is typically drawn to salient information in the environment. Appetites influence what is taken to be salient. And the way in which information is initially framed/attended to constrains and places limits on subsequent framings. They give an interesting illustration from the game theory discussion. In order to construct the “we”-frame a player needs not just to acquire information about their own pay-offs and the pay-offs of players (which would be required for best response reasoning in the “I”-frame), but also to combine them, using Pareto-optimality or some other criteria. This act of combination poses information costs that may prevent an agent from ever arriving at the “we”-frame.

These are important points. As indicated above and in the target article, however, I by no means want to say that all framing effects are rational, or even goal-driven. There is a spectrum of sophisticated and complexity, with primed responses at one end and the most complicated and reflective forms of what Crockett and Paul call self-involving choices at the other. Much of what Teoh et al. point to is most applicable at the primed response end of the spectrum. But the point is well taken that framing is not an abstract activity undertaken by computationally unbounded agents. It is a real-world activity subject to a multitude of constraints, both endogenous and exogenous.

Moldoveanu extends this line of reasoning, approaching the matter from the perspective of game theory. He agrees with me that frames can be useful tools for selecting equilibria in competitive games. For example, from the perspective of “I”-frame best-response reasoning, there is no way of choosing between the two equilibrium solutions in Stag Hunt – both players hunting hare and both players hunting stag, whereas the latter is clearly preferable from the “we”-frame. But, as Moldoveanu points out, this is the starting-point for investigations that I do not discuss in the target article. In particular (and complementing the points raised by Teoh et al.), we can and should raise questions of informational gain and computational cost with respect to frames themselves. The key question is: How much thinking is required to generate a reason R for acting from a frame F that structures the representation of the facts relevant to a situation? The computational complexity of the process of frame selection brings into play different notions of rationality (ecological/adaptive) that intersect with the computational benefits of using frames as efficient tools to shorten deliberation.