p19

Thus the theorist will interpret the agent as being as close to ideally rational as possible: we 19 might say, as maximizing expected utility in general, but as occasionally failing to do so. Furthermore, this allows us to interpret the agent as failing to maximize the expectation of her utility function on occasion – that is, as having desires on this occasion but failing to prefer in accordance with them – precisely because her obeying the axioms in a large set of her preferences or having a closest ideal counterpart points to a utility function that is genuinely hers. I note that “closest” here might be cashed out either as differing least from the agent’s actual preferences, or as preserving the values that the agent would endorse in a clear-headed frame of mind, or as best according with other facts about her psychology, such as her utterances. I also note that in some cases there will be no close counterpart, and it will be precisely these cases in which the interpretive theorist will count the agent as unintelligible, as not intentionally acting. There is one problem with this method, however. It does not allow us to interpret an agent as having genuinely inconsistent beliefs or desires, only as failing to have preferences that accord with them on occasion. While I don’t have space to fully explore the possibilities here, there seem to me to be several options. First, and perhaps less plausibly, an interpretive theorist might postulate that an individual “really” has a coherent set of beliefs and desires, though these aren’t always correctly translated into preferences. Second, one might postulate that an agent’s degree of belief in a proposition is derived from (the closest ideal set to) some privileged set of preferences; for example, as many propose, that p(E) is derived from the bets in small amounts of money one is willing to make on E. And similarly, perhaps, for desire, although it is harder to say what the privileged set might be. Finally, if some of one’s preferences cluster towards one ideal counterpart and some towards another, along a natural division, and we could postulate that the agent is of two minds in a very particular way. Decision theory appears in philosophy in two different strands. The normative theorist is interested in what your preferences ought to be given your beliefs and desires or given other of your preferences. Adopting EU maximization or conformity to the axioms as the correct norm, she says that you ought to prefer that which maximizes expected utility, and she is interested in which acts would do so; or she says that you ought to have consistent preferences, and is interested in which sets of preferences are consistent. The interpretive theorist is interested in discovering what your beliefs and desires are from your preferences. Adopting EU maximization or conformity to the axioms as the correct principle of interpretation, she says that 20 you do (approximately) maximize expected utility or have consistent preferences, and she is interested in what beliefs and desires make it the case that you do so. When thus described, we can see that rationality plays a different role in each use of the theory: the interpretive theorist takes it as an assumption that individuals are rational in the decision-theoretic sense, and the normative theorist takes decision theory as a way to answer the question of whether individuals are rational. Although on the face of it this makes it seem that the two uses are in tension, I have proposed that on the best way to make sense of the interpretive project, the concept of rationality that is meant to be analyzed by EU theory is importantly different in the two projects. Specifically, the rationality norm of the normative project is “strong” in that normative theorists are interested in whether all of the individual’s preferences adhere to it, and the rationality assumption in the interpretive project is “weak” in that interpretive theorists make the assumption that an agent more-or-less follows it but not the stronger assumption that she follows it exactly and always. 5. Outcome Descriptions A lot has been made so far of the fact that by connecting preferences to subjective utility and probability functions, we can discover how much an agent values outcomes and how likely she takes various states to be. But one issue that has not yet been remarked upon is that just as how the agent values the outcomes and views the world are not intrinsic features of any situation she faces, neither is how the agent conceptualizes the outcomes. An illustrative example is due to John Broome (1991: 100-101). Maurice is offered choices between various activities. If the choice is between going sightseeing in Rome and going mountaineering, Maurice prefers to go sightseeing, because mountaineering frightens him. If the choice is between staying home and going sightseeing, he prefers to stay home, because Rome bores him. However, if the choice is between mountaineering and staying home, he prefers to go mountaineering, because he doesn’t want to be cowardly. If we consider Maurice’s preferences among Rome, home, and mountaineering, they appear to be intransitive: he prefers Rome to mountaineering, home to Rome, and mountaineering to home. Given that transitivity is necessary for EU maximization, the interpretive theorist is unable to make sense of him given the preferences as stated; but his motivation is perfectly comprehensible (we’ve just described it). In addition, the normative 21 theorist must automatically count Maurice’s preferences as irrational, without considering whether his reasons for them make sense; but it is not clear – at least not without further argument – that there really is anything wrong with his preferences. Here is what each theorist ought to be able to say: for Maurice, choosing mountaineering when the alternative is going to Rome is different from choosing mountaineering when the alternative is staying home. Therefore, there are really (at least) four options involved in this decision problem: Rome, home-when-the-alternative-is-Rome, home-when-the-alternative-ismountaineering, and mountaineering. And Maurice’s preferences among these options are not, so far as we know, intransitive. The lesson is that insofar as we are concerned with capturing the agent’s actual beliefs and desires, we cannot assume that there is a privileged description of outcomes independent of the agent himself. Furthermore, insofar as we are interested in determining whether an agent is genuinely consistent or genuinely prefers the means to his ends, we cannot rule out his caring about certain features of outcomes out of hand. What the agent believes and desires is what we are trying to determine, and that includes what the agent believes about the choices he faces. Thus, there is an additional “moving piece” in the interpretation of an agent or in a judgment about whether his preferences are rational: how he sees the outcomes. This poses two related challenges. The first is about how to settle on the correct interpretation of the agent’s preferences. The second has to do with the extent to which individuating outcomes more finely commits the agent to having preferences in choice situations that could never even in principle be realized, and how we ought to treat these preferences. I will discuss these issues in reverse order. To illustrate the second problem, notice that it is assumed in decision theory that preferences are complete: for any two options, a decision maker must prefer one to the other or be indifferent. This means that if “home-when-the-alternative-is-Rome” and “home-when-thealternative-is-mountaineering” are to count as options in some of the choice problems described above, the decision-maker must prefer one to the other or be indifferent. But one could never actually face a choice between these two options, by definition. Broome (1991) refers to preferences like these as “non-practical preferences.” I will not discuss the metaphysics of these preferences: although there are interesting questions here, they do not obviously bear on the issues this article has been focusing on. But the epistemology of these preferences is important, 22 because it will make a difference to how we resolve the interpretive problem more generally. There will be a divide among those who think that which of these options an agent prefers is up to the agent, and those who think that which of these options an agent prefers is up to the decision theorist to fill in; and where one falls on this divide will determine how much freedom a decision theorist has to interpret an agent’s preferences. The other problem, then, is how to settle on an interpretation of the agent’s preferences. As we’ve just seen, we cannot allow that the theorist’s initial presentation of the outcomes is how the agent sees them. However, if we allow that the agent makes maximally fine distinctions between outcomes, then none of the outcomes will be the subject of more than one practical preference. For example, choosing each outcome in a pair-wise choice always involves rejecting the other alternative. If the agent’s non-practical preferences are up to the theorist to fill in, then this will mean that the agent can never fail to maximize expected utility or fail to satisfy the axioms, since no practical preferences will be inconsistent with each other. If the norm of EU theory were impossible to violate, the normative theory would lose its bite, since it will be trivially true that every agent adheres to the norm. But would this also be a problem for the interpretive EU theorist? Some might say that it wouldn’t be; indeed, that EU maximization is trivially satisfied would lend support to the idea that it is a good interpretive assumption that agents actually maximize EU. But there are at least two problems with this approach for the interpretive theorist. The first is that we will be unable to tell the difference between when an individual is trying to maximize EU (or follow the axioms) but making a mistake and when she is aiming at something else,23 although perhaps this is okay if it is argued that to act at all is to maximize EU. The second problem is that allowing outcomes to be individuated maximally finely means that ‘deriving’ an agent’s beliefs and desires from her preferences won’t be very informative. Her practical preferences in combination with each possible filling out of her non-practical preferences will give rise to a unique (up to positive affine transformation) utility and probability function, by the representation theorems. But there may be many possible fillings out. Therefore, there will be multiple and incompatible ways to interpret her beliefs and desires. And on the level of preferences, knowing what she prefers in one particular context won’t tell us anything about what she prefers in an only slightly different 23 See Hurley (1989: 55-83) 23 context, so we won’t get a very robust explanation of her psychology. In either case, the theory is rendered uninformative: we cannot make much sense of what the agent is doing. Most philosophers accept that either the theorist’s ability to individuate outcomes or the theorist’s ability to set non-practical preferences must be constrained. To constrain them, one can either introduce a rule about when two outcomes are allowed to count as different, or allow that outcomes can be individuated as finely as possible but introduce a rule about what nonpractical preferences the theorist can interpret the agent as having. For most purposes, these come to the same thing, since refusing to allow that x and y are different outcomes and requiring that the correct interpretation of the agent makes her indifferent between x and y permit the same sets of practical preferences. But there are two very different types of constraining rules that the theorist could introduce (this distinction crosscuts the distinction just mentioned). To see this, consider the following suggested rules: R1: Outcomes should be distinguished as different if and only if they differ in a way that makes it rational to have a preference between them. (Broome 1991: 103). R2: Outcomes should be distinguished as different if and only if the agent actually has a preference between them. (Dreier 1996: 260). R3: Outcomes should be distinguished as different if and only if they differ in regard to properties that are desired or undesired by the agent. (Pettit 2002: 212) Maurice’s preferences can be accommodated by EU theory according to rule R1 only if it is rational for Maurice to care about what option he turns down when he decides to stay at home, according to rule R2 only if he in fact does care about what option he turns down when he decides to stay at home, and according to rule R3 only if turning down an option instantiates a property he in fact cares about. Rules R2 and R3 make the possibility of distinguishing outcomes dependent on the agent’s internal state, whereas R1 makes this possibility dependent on some objective feature of the agent’s situation. Rules like R1 that introduce an external constraint on interpretation might be seen as principles of charity for interpretation: we should interpret an agent as making a distinction only if it is rational to make that distinction. Since these “externalist” rules restrict preferences beyond what the agent herself values, Broome has rightly pointed out that they are against the spirit of Humeanism (Broome 1993). Of course, rules like R2 and R3 can only be applied if the theorist has access to the agent’s non-practical preferences or other relevant 24 properties of her internal state. Therefore, using these “internalist” rules relies on the theorist knowing more about an agent’s psychology than the externalist rules do. The same strategy can be applied to ensuring that the norm of normative decision theory is not trivial. As long as there is a restriction on when two outcomes can count as different, there will be sets of preferences that violate the norm of EU theory. Which type of rule to adopt will depend on the use to which normative decision theory is being put: if the theorist is using it to assess an agent, whether the theorist can rely on an internalist rule will depend on how much she can know about the agent’s internal state, and if the agent is using normative decision theory to guide her own actions, whether she can rely on an internalist rule will depend on how much introspective access she has to her own internal state. 6. Descriptive Decision Theory Although a third type of decision theory, descriptive decision theory (which sometimes goes by the name “behavioral economics”), is largely the provenance of psychology and economics rather than philosophy, it is important to say something about it both for completeness and to make clear the contrast with interpretive decision theory. Like interpretive decision theory, descriptive decision theory is interested in describing the behavior of individuals rather than in what they ought to do. However, there is an important difference between the two approaches, which can be seen in how they have responded to findings that actual agents fail in reliable ways to maximize expected utility. Whereas interpretive decision theory has retained EU maximization as the guiding principle of interpretation, and in many cases pushed for a more complex interpretation of outcomes (as described in the previous section), descriptive decision theory has by and large abandoned expected utility maximization as an unrealistic assumption of agents and proposed alternatives. I do not have space to go into the alternatives to EU theory that descriptive theorists have proposed (see Sugden (2004) and Schmidt (2004) for helpful surveys), but it is worth saying two ways in which these alternatives tend to differ from EU theory. First, while they generally include a function that plays the role of utility and a function that plays the role of probability, they either subject these to different constraints (e.g. the ‘probability’ function needn’t be additive) or else combine them in a non-expectational way. Second, at least one notable alternative, Kahneman and Tversky’s (1979) prospect theory, posits an “editing phase” during 25 which the decision-maker simplifies the alternatives using various heuristics before subjecting them to the maximization schema. The differing responses of the two types of theorists to purported violation reveals two important differences between the aims of descriptive decision theory and the aims of interpretive decision theory. First, descriptive theorists are generally interested in building parsimonious models of preferences, and they are less concerned than interpretive theorists with interpreting the utility and probability functions as desires and beliefs. Interpretive theorists, by contrast, are primarily interested in extracting desires and beliefs with few or no initial assumptions, including assumptions about how an agent views the outcomes; and in doing so need be only as parsimonious about outcomes as an agent’s actual psychology is. Therefore, descriptive decision theorists are more inclined to treat the outcomes (for them, generally, monetary values) as theoretical bedrock, and interpretive decision theorists are more inclined to treat the rationalization principle as theoretical bedrock. It is worth noting that for the same reasons that economists concerned merely with modeling behavior will be uninterested in the interpretive project, formalists will also not be interested in the interpretive project, since for them, there aren’t any interesting entities worth discovering. The other difference, which I will discuss further in the next section, concerns predictable deviation from rationality. Roughly, if agents predictably have preferences against the dictates of rationality, the descriptive theorist will want to include this as part of her model, since it is an accurate characterization of what the agent does, but the interpretive theorist will not, since, recalling the discussion in section four, those preferences do not accurately reflect her beliefs and desires (though predictable deviations may be included somewhere in the theory of action). Interpretive theorists are interested in characterizing the preferences of an idealized version of the agent, and descriptive theorists in those of the actual, non-ideally-rational agent. We might put these two points succinctly, although this is certainly too coarse: descriptive theorists are concerned with prediction, and interpretive theorists are concerned with explanation in terms of beliefs and desires and with discovering something about an agent’s mental states.24 24 I should note that while I separate explanation from prediction, Bermúdez (2009) thinks they ought to be considered a single dimension of decision theory, and thus that the same formal theory must play both roles. 26 How does the descriptive project bear on the interpretive project? If the analogues of u and p in the descriptive project should be taken in a formalist vein, then the descriptive project does not have a clear bearing on the interpretive project. But insofar as the entities involved in the descriptive project can be thought of as beliefs and desires, rather than convenient ways to represent preferences, I think there is a way in which the descriptive project aids the interpretive project, and in another way it cuts against it. On the one hand, the descriptive project can help illuminate the relationship between an agent’s actual choices and desires and those of her ideal counterpart. For example, one of the findings of prospect theory (Kahneman and Tversky 1979: 273) is that when a new frame of reference is experimentally induced, e.g., the agent believes she will receive $2000, her preferences over total amounts of money are altered in the sense that receiving less than (e.g.) $2000 will be treated as a “loss.” If what this shows is that inducing a reference point causes people to underestimate their actual (subjective) utility below the reference point, then we can expect that the ideal counterpart will assign higher utility below the reference point than the actual agent in the grip of framing effects. On the other hand, if what the descriptive project reveals is that an agent cannot be interpreted as having stable beliefs and desires – beliefs and desires that are independent of the ways in which choices are presented – then the descriptive project undermines the interpretive project. 7. The Mutual Dependence of the Normative and Interpretive Project In this section, I will explain how the normative and interpretive project depend on each other. Recall that the rationality assumption in interpretive decision theory is that agents are approximately expected utility maximizers; and an agent’s beliefs and desires are the p and u extracted from the preferences of her ideal counterpart. But why should we think that the beliefs and desires of an agent’s ideal counterpart are her beliefs and desires? After all, the preferences of her ideal counterpart aren’t her actual preferences. The crucial idea is that acting consists not in actually taking the means to your ends, but in aiming at doing so. Therefore, the preferences of an agent’s ideal counterpart are the preferences that she ought to be thought of as aiming at satisfying when she acts. This doesn’t mean that she consciously aims at satisfying these preferences, or even that she consciously takes herself to be maximizing expected utility; rather, she participates in an activity (acting) which is constituted by aiming at being an EU maximizer. In the means-ends idiom, to act is to aim to take the means to your ends (or more precisely the 27 means that will on average and by your own lights lead to your ends), even though you might sometimes fail to do so. That aiming is not the same as succeeding explains the fact that the rationality assumption in interpretive theory is not that agents are perfectly rational but rather that they are approximately rational.25 Now that it is clear what the rationality assumption in interpretive decision theory amounts to, it should also be clear how the interpretive project depends on the normative project. Interpretive EU theory rests on two claims. First, on the claim that action aims at conforming to the norm that analyzes what it is to take the means to ones ends or to be consistent. Second, on the claim that this norm is captured by EU theory, either in the maximization formulation or the axiom formulation. If we were to conclude that a different norm holds of rational preferences, then interpretive decision theory would have to follow suit in adopting that norm as the one action aims at. The interpretive project depends on the correctness of the normative theory’s norm, i.e., on the normative theorist being correct about which sets of preferences are candidates for those of an agent’s ideal counterpart. (Note that this is another difference between interpretive and descriptive decision theory: the latter is not at all governed by what the correct norm is.) The normative project, if it is able to say anything interesting about agents who fall short of the norm, also depends on the interpretive project. This is because identifying how an agent is falling short of the norm depends on correctly interpreting what her beliefs and desires are. Clearly, a simple yes or no answer to the question of whether the agent is doing what she ought doesn’t rely on discovering the agent’s beliefs and desires: if her preferences don’t conform to the axioms, then she fails to do what she ought. The formalist will say that normative decision theory ends here. However, there are two additional questions the psychological realist might be interested in. First, what is the source of the agent’s irrationality? And second, where should the agent go from here? 25 We should untangle the question of whether postulating that agents aim at EU maximization allows the preferences of an agent’s ideal counterpart to reveal her beliefs and desires from the more general question of whether postulating that agents aim at whatever the correct norm of rationality is allows this. Meacham and Weisberg (2011) argue against the former claim on empirical grounds, but we might still uphold the latter claim by arguing that rationality is best analyzed by a different norm which people in fact come closer to adhering to. 28 Recall that preference inconsistency could come from one (or more) of three sources: inconsistency in beliefs, inconsistency in desires, or inconsistency in the norm connecting beliefs and desires. But we need to be able understand the agent as having beliefs and desires even when she is inconsistent if we want to claim that her beliefs or her desires are inconsistent. And so if we adopt the interpretive idea that an agent’s beliefs and desires can be discovered even when she is not fully in accord with the axioms by working backwards from the preferences of her ideal counterpart(s), we can say in what respect she is falling short of the normative ideal. Unless one can introspect one’s beliefs and desires to a precise degree, diagnosing where the irrationality comes from depends on the possibility of interpreting agents as having beliefs and desires even when they are not obeying the axioms. Furthermore, since the interpretive use of the theory allows us to discover an agent’s beliefs and desires, it allows us to say what sort of underlying change moving from the agent’s actual preference to a set of preferences that conform to the theory involves. For example, consider an individual who is willing to add $200 to the purchase price of a car he is buying if it has a radio but would not pay $200 to have a radio installed if the car came without one at the cheaper price.26 Let us assume the closest ideal agent prefers $200 to the radio, so that the actual agent desires $200 more than she desires the radio. The narrow-scope norm says she ought to alter the preference concerning the initial purchase. The wide-scope norm of decision theory is more permissive. It says that she can resolve the irrationality by adopting any consistent set of preferences: so she can alter the preference concerning the initial purchase and retain the rest of her preferences, or she can keep that preference and alter the rest of her preferences. But even if we adopt the wide-scope norm, interpreting the agent is crucial because it allows us to say what each resolution involves: the former resolution involves conforming her preferences over acts to her underlying desires; the latter involves bringing her underlying desires in line with the preference about purchasing a new car. This doesn’t by itself show how she ought to resolve the decision, since in principle it may be that the one preference is more important than her desires, but it does tie different ways of resolving the decision to preserving specific different features of his situation. 26 Example adapted from Savage (1954: 103). 29 In sum, if the normative theorist wants to say more than that the agent is not doing what she ought, or that she ought to bring her preferences in line with the axioms somehow or other but with no guidance on what considerations are involved in potential resolutions, she will have to interpret the agent. The assumption of rationality in interpretive decision theory is that the agent aims at maximizing EU, and so approximates an EU maximizer. And the goal of rationality in normative decision theory is that the agent maximizes EU in every instance. This, then, is how the two projects are mutually dependent: that agents are approximately EU maximizers depends on EU maximization being the aim of rational action, and that agents bring their preferences into line with EU maximization in a way that is governed by reasons depends on locating the source of their current deviation, which depends on understanding what their beliefs and desires are. Descriptive decision theory also bears on these projects. As I alluded to in section six, one thing that descriptive decision theory could reveal is that it would be seriously misguided to think of action as aiming at maximizing expected utility. This would undermine interpretive EU theory. But what would it say about rational action more generally? As mentioned, interpretive decision theory makes two assumptions, one that action aims at adhering to the norm of rationality and one about what the norm is. If action doesn’t aim at the maximization of EU, then we must drop either the assumption that action aims at the norm or the assumption that EU is the correct norm. If we keep the latter assumption, then it may be possible to use a descriptive theory to extract beliefs and desires and a normative theory that takes these as the real beliefs and desires and enjoins you to maximize expected utility.27 On the other hand, we might keep the former assumption and propose a different norm, one that coheres closely enough with actual behavior that interpretive decision theory can use the norm to backwards engineer beliefs and desires despite some deviations that the correct descriptive theory predicts. Which of these positions to take will not be determined by empirical findings but by arguments about what the correct norm is, although the knowledge that humans diverge wildly from EU theory might give 27 Bermúdez (2009: 165-167) considers but rejects a possibility like this in his discussion of whether decision theory could play multiple roles at once. 30 us reason to examine more closely whether EU is the correct norm, given how successful human behavior is in general.28 8. Challenges and Extensions In fact, philosophers have challenged the idea that EU theory is the correct theory of rationality. Recall that in the expected utility equation, the utility value of each outcome is weighted by the probability the decision-maker assigns to the state in which she receives that outcome, and this probability is supposed to reflect her belief about that state. This assumes two things: first, that the norm relating beliefs and desires to preferences is indeed that of EU maximization, in which the average value of a gamble suffices to determine its position in the agent’s preference ranking (whether this is derived from the axioms or not); second, that rational beliefs are “sharp” in that they can be measured by point-probabilities. Challenges to each of these points have been around for at least 50 years, but they have resurfaced recently. One might similarly challenge that the structure of desire is that posited by EU theory, though I don’t have space to discuss such a challenge here. Each of these challenges can be posed directly about the functions p, u, or the maximization norm, but each can also take the form of criticizing one or more of the axioms, so the challenges do not rest on a particular interpretation of the utility function. The first challenge is to the idea that we ought to care only about the expectation of utility, and not other “global” features of a gamble, such as its minimum utility value, its maximum utility value, or the spread or variance of utility. Again, since utility is derived or discovered via a representation theorem, this point must take the form of or be accompanied by a challenge to one or more axioms of EU theory. Maurice Allais (1953), taking what appears to be a non-constructivist realist view of the utility function, argued that agents might care not just about the mean utility value of a gamble, but also about its variance and skewness. But his famous counterexample to EU theory (which has since become known as the Allais Paradox) poses a challenge even for constructivists, since it shows that most decision-makers violate one of the axioms of EU theory.29 I have recently defended axioms that give rise to other 28 For argument that humans did not evolve to be EU maximizers, see Okasha (2007). 29 At least under the assumption that outcomes cannot be individuated more finely. 31 maximization norms than that of EU theory (Buchak, forthcoming): my view is that EU maximization is one of a more general class of norms any of which an agent may adopt. In the same spirit as the idea that agents have subjective u and p function, I propose that the norm that connects these to preferences is also up to the agent. Just as u and p are subject to structural constraints, so too is the norm; and, furthermore, the question mentioned in section three about whether a particular norm (such as EU maximization) is reasonable in addition to rational can be posed. The second challenge is to the idea that we ought to be “probabilistically sophisticated” in the sense of assigning to every event a point probability (or acting as if we do). Daniel Ellsberg (1961) proposed a pair of choice problems that have become known as the Ellsberg Paradox, purporting to show that when individuals lack precise information about objective probabilities, they don’t act as if they make choices based on a single probability function. In recent years, the challenge has come from the side of epistemology rather than observed decision-making behavior, the idea being that our evidence is often imprecise or incomplete, so requiring precise degrees of belief would mean requiring degrees of belief that outrun the evidence.30 Denying that we have sharp degrees of belief and that we need them in order to make rational decisions requires stating both what non-sharp (or “imprecise”) degrees of belief are and how to make decisions with them.31 9. Conclusion: Decision Theories Given both the historical progression and the issues that are currently under discussion, we ought not think of decision theory as a single theory, but rather as a collection of theories that each contains both a structural and interpretive element. The structural element describes both the internal structure of several functions and the formal relationship between these functions on the one hand and preferences on the other; a formal relationship which holds just in case a particular set of axioms is satisfied. This internal structure and relationship are argued to be those that hold for rational agents. In EU theory, the posited functions are a numerically valued utility function and a point-probability function that obeys the probability calculus; and the 30 See the discussion found in White (2009), Elga (2010), Joyce (2010). 31 For some examples, see Levi (1974), Sahlin and Gärdenfors (1982), and Joyce (2010). 32 posited relationship is that of EU maximization. The interpretive element concerns how these functions are to be interpreted: as psychologically real and in principle separate from preferences; as psychologically real and tightly connected to preferences; or merely as a representation of preferences. Whichever combination of structural element and interpretation we adopt, the underlying issues discussed in the previous few sections – the relationship between decision theory and rationality, how to individuate outcomes, and the relationship between normative decision theory and interpretive decision theory – remain the same.