2 CPT debiasing

As descriptive theories, the aim of decision theories is to represent agents’ preferences and/or choices with a convenient formalism that facilitates the prediction of yet unobserved choices. Insofar as the formalism plausibly captures aspects of an agent’s underlying psychology, such as her beliefs and desires, we might take the theory to be explanatory as well. As normative theories, decision theories claim that agents rationally ought to have preferences and choose in such a way that they are well described by the decision theory.

In EUT under risk, agents’ preferences over outcomes and lotteries (that is, probability distributions over outcomes) can be captured just in terms of the probabilities and a function assigning utilities to outcomes. Preferences then track the probability-weighted sum of the utilities of the possible outcomes of an agent’s choices. Various representation theorems, most famously that due to von Neumann and Morgenstern (Reference von Neumann and Morgenstern1944), henceforth vNM, show that preferences are representable as such if and only if they abide by a number of axioms, including transitivity and the independence axiom. Consequently, when EUT is accepted as a normative theory, the normative content of EUT is usually taken to be that agents ought to have preferences that abide by these axioms. Representability of a set of preferences within the EUT framework does not guarantee that utility captures, as a cardinal measure, some real psychological quantity the expectation of which is maximized, and indeed part of my argument below relies on scepticism regarding whether it does.

CPT, which incorporates elements both of original prospect theory (Kahneman and Tversky Reference Kahneman and Tversky1979) as well as RDU, includes significantly more structure than EUT. ^{Footnote 6} First, outcomes are represented in terms of deviations from a reference point, usually the agent’s status quo, which can potentially vary over a series of choices. Agents are then ascribed a basic utility function over these gain and loss outcomes. Next, we make room for one source of loss aversion—what Harrison and Ross (Reference Harrison and Ross2017) call “utility loss aversion”—by defining a composite or total utility function, which coincides with basic utility for gains, but weights the basic utility for losses by a loss aversion parameter λ. Lastly, preferences over lotteries are not determined as a probability-weighted sum of outcome utilities as in EUT, but rather as in RDU, allowing for the weighting of probabilities themselves: Probabilities are transformed by a weighting function, and outcomes ranked from best to worst. The total utility of the best outcome is multiplied by the weighted probability of getting at least that outcome. The total utility of receiving at least the second best outcome is multiplied by the weighted probability of receiving at least that outcome, minus the weighted probability of receiving at least the best outcome, and so on for the other outcomes. In the end we sum up, and preferences should track this sum. What the weighting of probabilities (henceforth “probability weighting”) allows for is that agents can give proportionately higher or lower weight to better or worse outcomes than their probabilities. As Harrison and Ross (Reference Harrison and Ross2017) note, apart from introducing other potential distortions from EUT, this introduces a second way of capturing loss aversion. Axiomatizations for CPT have since been developed, including under risk (see Chateauneuf and Wakker Reference Chateauneuf and Wakker1999), specifying strictly weaker conditions on preferences over lotteries than EUT for representability within CPT. CPT is therefore more permissive regarding what preferences over lotteries agents may have, at the same time as representing them with a more complex formalism.

We can now say more precisely what CPT debiasing involves. If CPT is descriptively adequate for some agent, then there will be some CPT model that has good fit with the agent’s preferences (which are in turn inferred from her choices). From her choice behavior, we can infer robust measures of the probability weights, λ, and, importantly, basic utility. We then take that basic utility function measured in our CPT model, and use it within an EUT model to calculate the expected utility of the various lotteries the agent is choosing between. This way, we have eliminated both loss aversion and probability weighting in the valuation of lotteries (although, interestingly, not other potential forms of reference dependence). We conclude that the correct, unbiased preferences for this agent track this expected utility. And we consider policies that serve those corrected preferences.

One curious feature of this procedure should be noted straight away: Proponents of CPT debiasing assume that it is in principle possible to take utilities measured in one theoretical framework (CPT), and then use them in another (EUT). This only makes sense if we think that utilities are meant to represent the same thing in both theoretical frameworks. In fact, this is a common presupposition in the literature out of which the CPT debiasing proposal emerged: Based on the observation that applying EUT to attempt to measure utility results in inconsistent utility measurements, various authors have tried to find alternative measurement procedures, based on different decision theories, that would result in a consistent measurement of utility. ^{Footnote 7} These authors clearly think of utility as a measure of some theory-independent quantity, and of different decision theories that feature utility functions as different potential tools for measuring it. Since utilities in both CPT and EUT are unique up to positive affine transformations, utility is a cardinal measure: Ratios of utility differences are meaningful. Whatever utilities in both frameworks are taken to represent by behavioral welfare economists must thus be something that comes in degrees.

What is this theory-independent quantity that utility is intended to be a cardinal measure of, according to the behavioral welfare economists in question? Bleichrodt et al. (Reference Bleichrodt, Pinto-Prades and Wakker2001) frame the task of utility measurement in the context of helping a client make better decisions as aiming to get an accurate measure of “clients’ values” (1500), and to “better represent the interests of the client” (1510). Similarly, Abdellaoui et al. (Reference Abdellaoui, Bleichrodt and l’Haridon2008) express the ambition behind finding an unbiased utility measure to be to enable us to make decisions in a client’s best interest. Writing in the context of health-related decision-making, Pinto-Prades and Abellan-Perpiñan (Reference Pinto-Prades and Abellan-Perpiñan2012) take utility to be “the value we associate to health-related quality of life” (573), and Oliver (Reference Oliver2003) speaks of different decision theories as frameworks for eliciting “cardinal health state values” (659). What they appear to have in mind is that utility is meant to be a cardinal measure of the degree to which an agent subjectively values the potential outcomes of the decisions to be made.

Policies designed to promote CPT debiased preferences, if agents have not explicitly consented to them, are intuitively paternalist. As we noted above, economists are usually opposed to paternalism. However, proponents of these measures might defend them as “merely means paternalist.” Such a defense would first assert that these measures are only paternalist regarding how an agent’s ends should be pursued. They do not impose ends on agents. And secondly, such a defense would try to show that means paternalist policies are in fact less objectionable than other forms of paternalism. The next section will present the best case for such a means paternalist defense of CPT debiasing.

3 The means paternalist defense of CPT debiasing

In the most general terms, paternalism is interference with a person’s actions or affairs, without her consent, motivated or justified by her own good. More precise definitions often work by specifying the nature of the interferences that may count as paternalist, and the nature of the motivation and justification of the interference. While, traditionally, paternalism has often been thought of as the restriction of an agent’s liberty for her own good (e.g., in the form of legal bans), in the context of welfare economics less invasive measures are often thought of as paternalistic. For instance, a welfare state that hands out in-kind benefits when it could have handed out money to those in need is often thought of as paternalistic insofar as the measure is motivated by the recipients’ own good, even though, when compared to a no-benefits world, the measure increases rather than decreases opportunities for choice.

This is as it should be if we think of the characteristic harm or wrong of paternalism as a lack of respect for an agent’s own choices and judgments in matters where we should defer to the individual. I thus agree with Haybron and Alexandrova (Reference Haybron, Alexandrova, Coons and Weber2013) and Hausman (Reference Hausman2018) that any effect on a person, even if it is liberty preserving or liberty enhancing, could potentially be paternalistic insofar as it concerns only the person’s own wellbeing, or matters that should be under the person’s control or should fall under the person’s judgment, while showing a non-deferential attitude to the agent’s own judgments and choices.

We can identify at least two dimensions along which different paternalist policies can be more or less severe: Paternalist policies can be more or less intrusive, with libertarian paternalist policies designed to be minimally intrusive; and they can exhibit a more or less non-deferential attitude to the agent’s choices and judgments. I will not discuss the first dimension any more in the following, as it is along the second dimension that means paternalism is usually thought of as being less problematic. It remains understood that the intrusiveness of the policy should also be taken into account when making judgments about particular cases.

Why might one think that policy-makers and the economists advising them should respect people’s choices or defer to people’s judgments regarding their own wellbeing? There are at least four common justifications for this anti-paternalist conviction. The first appeals to a subjectivist conception of what wellbeing is. If we think that wellbeing just consists in the satisfaction of individuals’ actual preferences, which is a common conception of wellbeing in economics, then deferring to people’s judgments and choices is just what one should do in order to promote wellbeing. A second justification does not rely on such subjectivism about wellbeing, but claims that people generally are in a much better position to make accurate judgments about what is good for them than a policy-maker or economist. ^{Footnote 8} A third justification is not welfarist, but appeals to a core principle of liberalism, namely liberal neutrality—the idea that the state or other authorities should not impose any particular conception of the good life on its citizens, but should rather remain neutral between competing conceptions in a pluralist society. And a fourth type of justification holds that there is a distinct and non-derivative harm or wrong involved in interfering for an agent’s good without deferring to her judgment, e.g., because it is insulting, as argued by Quong (Reference Quong2011), or an impermissible intrusion into what is rightfully for the individual to decide, as argued by Shiffrin (Reference Shiffrin2000), Groll (Reference Groll2012), and, more specifically in the context of welfare economics, Sugden (Reference Sugden2018).

Whichever is our favorite justification for anti-paternalism, means paternalism appears to turn out less problematic than other forms of paternalism. Means paternalists do show a deferential attitude at least to agents’ judgments about their ends or ultimate objectives, or what are variably called their direct value judgements (e.g., by Bernheim Reference Bernheim2016), or judgments about non-instrumental, intrinsic, or final value. Means paternalists show a non-deferential attitude only regarding agents’ judgments about or choices of means to their ends, or their indirect value judgments, or judgments about instrumental value. The means paternalist overrides people’s instrumental judgments about means to their ends, in order to help them pursue their ends.

As means paternalism still involves overriding an agent’s judgments that pertain to her own wellbeing (albeit indirect judgments), I think it still counts as a form of paternalism. But even those with generally anti-paternalist convictions might judge it to be justifiable when non-invasive, given it ultimately serves to help agents pursue their own values. Moreover, the four standard justifications for anti-paternalism just described don’t apply to the same extent to means paternalism. First, the only plausible subjectivist accounts of wellbeing take wellbeing to be constituted by an agent’s preferences regarding their ultimate ends only, and not by their preferences over means to the realization of those ends. For instance, where an agent’s preferences over means to her ends are tainted by false beliefs, we generally don’t think satisfying her preferences over means always makes her better off. ^{Footnote 9} Second, the claim that people are in a better position to make accurate judgments about what is good for them is likely to be true in a wider range of circumstances for judgments about ultimate ends rather than instrumental judgments. Again, judgments about means that are tainted by false beliefs are a case in point: A policy-maker might, for instance, have more accurate beliefs about the likely health outcomes of some activities, and know they have more accurate beliefs. And lastly, means paternalists do seem to respect liberal neutrality, and show respect where it counts most.

In addition to Thaler and Sunstein (Reference Thaler and Sunstein2008), means paternalism is advocated by many, if not most, behavioral welfare economists, insofar as they would like to keep a door open for correcting for irrational judgments about means, as they seem to be revealed in findings of behavioral anomalies. For further explicit defences, see, e.g., Camerer et al. (Reference Camerer, Samuel Issacharoff, O’Donoghue and Rabin2003), Bernheim (Reference Bernheim2016), and Le Grand and New (Reference Le Grand2015). Returning to our central topic, the question now is whether CPT debiasing can be given a means paternalist justification. I take it that at least two things need to be shown in order for some policy to be defensible as “merely means paternalist” towards an agent: First, the policy-maker needs to have some reliable way of determining what the agent’s relevant ends are. And second, the policy-maker needs to be confident that she can make a better judgment about the best means to the agent’s ends than the agent herself. If the first condition fails, then the means paternalist has no way of being deferential to the agent’s judgments where it counts, so that the general anti-paternalist considerations count against the measure. And if the second condition fails, the policy loses its positive appeal of helping agents serve their ends better, in which case it seems we should err on the side of deference to the agent’s judgments.

Importantly for my argument later on, the second condition also rules out paternalist interventions in some cases where the policy-maker can both determine the agent’s ends and an effective way for the agent to pursue them, namely in situations where the policy-maker imposes one effective way of pursuing her ends on an agent in a situation where the agent merely pursued a different, but equally effective and rationally permissible, way of achieving her ends. Take, for illustration, a situation where two roads (which have no intrinsic merits) lead an agent to her goal equally well. She would choose the left road if left to her own devices, but a policy-maker imposes the choice of the right road on her. The policy-maker does respect her goals, and is proposing one effective way of pursuing them—just not a better way than the one the agent would have chosen herself. In such situations, too, the policy seems to have no positive appeal of helping agents serve their ends better than they would themselves, leading to the conclusion that the policy-maker should err on the side of non-interference and deference. In fact, in situations where there is rational leeway in how to pursue one’s ends, it seems a special kind of liberal neutrality might apply, demanding that the policy-maker should not only refrain from imposing a particular view of the good life, but also from imposing any particular one of the rationally permissible ways of pursuing one’s idea of the good life.

As pointed out in the introduction, doubts are often raised about paternalist policies proposed by behavioral economists that point to the failure of one of the two conditions just spelled out. The mere observation of behavioral inconsistency points to no particular way of resolving that inconsistency that would honor the agent’s ends, and do so better than the agent’s own choices. CPT debiasing seems different as there is initial plausibility to both conditions holding. Regarding the first condition, we have just seen that in the literature where CPT debiasing is proposed, it is commonly held that the basic utility function identified within CPT provides us with a cardinal measure of an agent’s subjective valuations of outcomes, or in other words her ends. And regarding the second condition, accepting the normative adequacy of EUT, as we have seen proponents of CPT debiasing also do, might seem to imply that maximizing the expectation of such a cardinal measure of subjective outcome valuations is the only rational way of pursuing one’s ends.

In the rest of this paper I will raise doubts about both conditions in fact being met in the case of CPT debiasing. First, I will argue in the next section that there is no special reason to think that the basic utility function identified by CPT should provide us with a cardinal measure of an agent’s ends. And secondly, section 5 will argue that even if the CPT basic utility function provided us with a cardinal measure of the agent’s ends, EUT does not imply that an agent must maximize the expectation of that utility function in order to be instrumentally rational. Instrumental rationality and EUT are more permissive than that.

4 The first challenge: Isolating ends

CPT debiasing can only be means paternalist if the basic utility function identified in CPT models in fact provides us with a reliable and complete measure of all the agent’s relevant ends. I here want to raise three worries about its ability to do so. First, note that the basic utility function can only be a reliable measure of the agent’s ends if everything the agent subjectively values as an end can be reduced to a property of outcomes. In other words, agents cannot intrinsically care about irreducible features of lotteries. For instance, attitudes regarding the thrill of gambling, or the anxiety of uncertainty, or structural features of gambles such as their mean, mode, and variance (as discussed by Lopes Reference Lopes1981, Reference Lopes1996) are not naturally described as attitudes to outcomes. Nevertheless, we might think that these attitudes represent non-instrumental subjective valuations: Such agents may care about gambles not merely as means to getting good outcomes, but rather see some features of gambles as ends in themselves. And if they do, a utility function over outcomes, such as the basic utility function in CPT, cannot capture all an agent’s ends in the context of risk. ^{Footnote 10}

Arguing along these lines, in the philosophical decision theory literature, Stefansson and Bradley (Reference Orri and Bradley2015, Reference Orri and Bradley2019) have recently denied the idea that a clear distinction can be drawn between preferences over lotteries being merely instrumental (in the sense that lotteries are valued just as means to achieving good outcomes) and preferences over outcomes expressing the agent’s ends. In the decision theory they develop, both preferences over lotteries and preferences over outcomes can express an agent’s ends. If that is so, unless we know we are dealing with the special case of an agent who values lotteries only as means to good outcomes, we cannot dismiss an agent’s preference over lotteries merely as a bad choice of means to her ends. And we cannot use the basic utility function identified in CPT as a complete representation of the agent’s ends. If we were to use it as it is used in CPT debiasing, we would be disregarding some of the agent’s relevant ends in risky contexts.

Of course, this picture is consistent with saying that CPT preferences are ultimately irrational. But the kind of irrationality involved in CPT preferences cannot, or at least need not, be of the purely instrumental type, because preferences over lotteries should not be evaluated purely instrumentally. Instead, on this picture, rational restrictions on all types of preferences are better interpreted as restrictions on what combinations of ends an agent may have. If CPT preferences are irrational, it must then be because there is an incoherence in the agent’s ends. This would be unfortunate, but it is also the kind of irrationality that is not suitable for means paternalist intervention. Resolving incoherence in an agent’s ends in a non-deferential way amounts to ends paternalism, not means paternalism.

A common response to this in the philosophical literature is to insist that, insofar as attitudes that appear to be irreducibly about lotteries are not merely instrumental, we can in principle redescribe outcomes so that these attitudes can be captured by a utility function over outcomes after all. If needs be, we could even include in the description of outcomes the description of the gambles the outcome was part of. Buchak (Reference Buchak2013) calls this “global individuation,” and it is defended by Pettigrew (Reference Pettigrew2015). Even if it seems unnatural, we could simply treat it as a modeling norm that outcomes need to be described such that everything an agent values non-instrumentally is captured in the outcome description. ^{Footnote 11} There is some evidence that this is indeed treated as a modeling norm by economists, as calls for redescription of outcomes is a common response to at least some behavioral anomalies (e.g., cooperation in the Prisoner’s Dilemma, or gambling behavior by otherwise risk-averse agents).

At the same time, however, outcomes in most economic applications, including applications of CPT, are described in very simple terms, for instance as mere monetary gains and losses. Moreover, the redescription strategy is only a convincing response for the proponent of CPT debiasing if we have a reliable way, in practice, to determine how outcomes need to be described in order for the utilities measured within CPT to effectively capture all the agent’s ends. And this is the second worry I want to raise in this section. It is a harder problem than merely finding a model that has a good enough fit with the choices we observe. Imagine two agents who make exactly the same choices, and are representable with the same CPT model, say with a basic utility function defined over simple monetary outcomes. It is entirely possible that one of them genuinely only cares about outcomes described in monetary terms, and sees lotteries merely as means to good monetary outcomes, while the other one genuinely cares about features of lotteries as ends in themselves, such as the probability of not making any loss. For descriptive purposes, this difference might be irrelevant. But it is not irrelevant for the prescriptive purposes of the means paternalist. CPT debiasers, for the reasons we saw above, are committed to a particular psychological interpretation of what the utility function should capture: it must be a cardinal measure of an agent’s ends. The problem this example illustrates is that choice behavior alone may not allow us to distinguish between cases where it is such a measure and cases where it is not. The two agents make the same choices, are ascribed the same utility function in a CPT model, but that utility function does not capture all of the second agent’s ends, while it does for the first. CPT debiasing might thus point to a legitimate means paternalist intervention for the first agent. For the second agent, it does not, or at least not using this CPT model. To distinguish between the two cases, we need further information about the agents’ subjective values, beyond choice data. In practice, and especially for large-scale applications, this will be very hard to come by.

A related practical issue arises and is discussed in the CPT literature when distinguishing the basic from the final or composite utility, which includes the loss aversion parameter λ as a weight on the basic utilities of losses relative to the reference points. It is the basic utility function that is used for the purposes of CPT debiasing. But why should the basic, rather than the composite, utility be taken to measure the agent’s ends? The answer depends on whether whatever λ is capturing should be taken to be part of utility in the relevant sense. But this just seems to again depend on the agent’s values, in a way that will be hard to detect in choice data alone: Does she genuinely care more about losses than about gains, or is it rather that the loss frame biases her towards giving more weight to losses than her true values warrant? ^{Footnote 12} If it is the former, then what λ is capturing should be included in a true measure of the agent’s ends. Notably, given this would import reference point dependence, the resulting measure would be unsuitable for just plugging into an EUT model. What the practice of using the basic utility function for CPT debiasing presupposes, on the other hand, is that what λ is capturing is a bias distorting the agent’s true ends.

What emerges from this discussion is that even once we have found a CPT model with good empirical fit, the normative interpretation of its parameters, and in particular the question of whether the basic utility function effectively captures the agent’s ends, can remain controversial, or, to use McQuillin and Sugden’s (Reference McQuillin and Sugden2012) term, essentially contestable. ^{Footnote 13} Of course, there are ways of resolving this controversy in particular cases, but this would require information about agents’ values that is hard to infer from traditional economic data. We would need to know quite a bit about the agents’ psychology. And while we might be able to enquire into an agent’s subjective values in a laboratory setting, in the field, where ultimately we would like to implement means paternalist policies, the relevant information will be harder to come by. This problem is especially devastating given CPT debiasing was developed specifically for cases where preferences cannot be debiased directly in conversation with a client.

One tempting response here is to claim that, as in the case of descriptive models, we can make various approximations and idealizations as long as the models serve their purposes well enough, or can be expected to describe most people well enough. However, for the means paternalist normative project, this response is not good enough. Recall that one prominent justification for opposition to ordinary paternalism was that agents generally are in a better position to know what is good for them, and policy-makers are often in a poor position to do so, in which case it seems better to err on the side of deference to the agent herself. Means paternalism was supposed to do better. Now indeed we are in a situation where the policy-maker is in one sense in a superior position to the agent, in that she may be confident that the agent is in violation of what we accept as the normatively correct theory of rational choice. But there is no point in overriding irrational preferences when we are not confident we can help the agent pursue her own goals any better. The contestability of the normative interpretation of CPT models alone should undermine any such confidence in most applications. Agents may not be serving their ends well, but in contrast to the policy-maker, at least they can be sure what their ends are.

A third worry remains even if we think that the outcomes the basic utility function in our CPT model ranges over capture everything the agent non-instrumentally cares about, and that neither loss aversion nor probability weighting are to any extent explained by the agent valuing features of lotteries non-instrumentally. Even in such a case, we can’t be guaranteed that the basic utility function provides us with a cardinal measure of the agent’s subjective valuation of outcomes. To see that, I’d first like to point out that the same isn’t guaranteed within EUT either. The reason for this is that, as I am about to argue, representability of an agent’s preferences with an EUT model is compatible with the agent having what have been called “pure” attitudes to risk.

For some function to be a cardinal measure of an agent’s ends, not only must the function order outcomes according to how much the agent values them, but the shape of the function must also reflect the degree to which the agent subjectively values outcomes. For my argument, it will be useful to have a hypothetical example of which it is uncontroversial that an accurate cardinal measure of the agent’s subjective valuations would be linear in some good of interest. Take, for instance, the Cookie Monster. ^{Footnote 14} To be ecumenical between different accounts of what it might mean to subjectively value an outcome, imagine that the Cookie Monster has an equally strong desire for any cookie, judges each cookie to be equally useful or good for him, is equally committed to the consumption of any cookie, gets the same amount of pleasure out of any cookie (and so on for any other notion of value one might have). We should say then, on any account of value, that he values each cookie to the same degree, no matter how many cookies he has already had, and that thus a true cardinal measure of his subjective valuations would be linear in cookies.

Now suppose Cookie Monster abides by the axioms of vNM expected utility theory. Must the utility function in an EUT model representing his preferences be linear in cookies? Clearly not, because Cookie Monster may be risk averse or risk loving. Within EUT, agents who are risk averse or risk loving with regard to some good must be assigned a utility function that exhibits decreasing or increasing marginal utility respectively with regard to that good. For instance, if, for any lottery over different amounts of cookies, the Cookie Monster prefers some sure amount of cookies below the expected number of cookies in the lottery, we must assign decreasing marginal utility of cookies to him. And we must do so despite him valuing each cookie to the same degree. The EUT utility function thus need not be a cardinal measure of an agent’s subjective valuations, even if it ordinally tracks them.

For those interested in identifying a function that provides a true cardinal measure of subjective valuations, as the behavioral economists who are my target here are, the underlying issue is that capturing risk aversion with decreasing marginal utility in an EUT model blends together two kinds of psychological causes of risk aversion: One might be risk averse because the more one already has of a good, the less one values it. Or one might be risk averse because one simply prefers to err on the side of not taking chances, and of ensuring one ends up with decent outcomes rather than risking all for the chance of ending up with more. This second kind of risk aversion is often called “pure” risk aversion (and respectively we speak of pure risk seeking attitudes), and I will follow this terminology here, meaning it to refer to any risk aversion that is not explained by an agent valuing a good less the more she already has of it. ^{Footnote 15} Cookie Monster’s risk aversion is pure: he values all cookies the same; nevertheless, he is risk averse. This must simply be because he does not want to risk ending up with fewer cookies.

The important point from this for our discussion is that in the absence of pure attitudes to risk, the utility function in an EUT model may well be a cardinal measure of subjective value. But in the presence of pure attitudes to risk, such as in Cookie Monster’s case, it clearly is not. The shape of the EUT utility function may, in addition to degrees of subjective value, also capture pure attitudes to risk. Capturing risk aversion with regard to ordinary consumption goods with a concave utility function in an EUT model is very familiar. And there is no formal reason to rule out assigning a concave utility function even though the type of risk aversion involved is “pure,” as long as the preferences abide by the vNM axioms. ^{Footnote 16}

In the philosophical debate on the interpretation of EUT it is sometimes argued that utility within this theory should be understood as a measure of the degree to which an agent values outcomes. Insisting that utility must be such a cardinal measure when EUT is correctly applied amounts to ruling out pure attitudes to risk within EUT. Expected utility maximizers would by definition be agents who pursue subjective value in a risk-neutral way. But this would have a restrictive implication for the application of EUT models: It would mean that some agents who abide by all the axioms of the theory, and whose choices can be accurately captured with an EUT model, should nevertheless not be modeled as expected utility maximizers. In our example, a risk-averse Cookie Monster, despite abiding by all the vNM axioms, should not be described as an expected utility maximizer. I think this is not a helpful restriction in most applications. Moreover, I will argue in the next section that there are good normative grounds for accommodating pure attitudes to risk.

For the present purposes, however, the point I have been making stands either way: Just because we have an EUT model with good fit does not mean that the utility function featuring in it is a cardinal measure of subjective value. This is because agents who have pure attitudes to risk can abide by the vNM axioms, as Cookie Monster does. If we think that for a model to be a proper application of EUT the utility function must be a cardinal measure of subjective value, then the implication is that there are always doubts about the validity of EUT models unless we can check that the agents in question do not have pure attitudes to risk—which we can’t do with standard choice data alone. Otherwise, the implication is simply caution about how we should interpret the utility functions in our EUT models.

Returning to CPT, if the shape of the utility function in an EUT model can in part express pure attitudes to risk and need not be a cardinal measure of an agent’s subjective valuations, it is not clear why the same shouldn’t be true of the basic utility function in CPT. As in the case of EUT, merely abiding by the axioms that guarantee CPT representability does not imply that the utility function must be a cardinal measure of subjective value. For that to be the case, we would need to be sure that any pure attitudes to risk are fully captured by probability weighting and loss aversion. Confidence that this is so can ultimately only come from looking more closely at the psychology of choice. Here, there is in fact some cause for optimism for the proponent of CPT debiasing. Utility functions measured within EUT systematically diverge from utility functions determined in riskless contexts using strength-of-preference judgments, which we might argue are an adequate cardinal measure of subjective valuation of outcomes. But there are at least some studies, for example Abdellaoui et al. (Reference Abdellaoui, Barrios and Wakker2007) and Stalmeier and Bezembinder (Reference Stalmeier and Bezembinder1999), that suggest that CPT utilities and the riskless measures do coincide. Nevertheless, these studies are limited in the kinds of lotteries studied. For instance, Abdellaoui et al. (Reference Abdellaoui, Barrios and Wakker2007) consider only two-outcome monetary lotteries where both outcomes are gains (and thus do not distinguish between CPT and RDU). Given the relative sparsity of evidence, the claim that the utilities identified in a particular CPT model provide us with a cardinal measure of the agent’s subjective valuations also seems to remain essentially contestable. Consequently, the means paternalist usually can’t be confident enough she can identify a cardinal measure of the agent’s ends to base an intervention on it.

5 The second challenge: Permissiveness of instrumental rationality

Even though the last section raised a number of doubts about this, let us grant now that the basic utility function identified in CPT models provides us with a cardinal measure of an agent’s complete non-instrumental subjective valuations, that is, her ends. CPT debiasing now proceeds by plugging the utility function obtained in the CPT model into an EUT model. For prescriptive purposes, the CPT debiaser recommends lotteries to an agent (or chooses them on her behalf) maximizing the expectation of that basic utility obtained in the CPT model. This would be uncontroversially doing better than the agent herself does if maximizing the expectation of the CPT-obtained utility is the uniquely most effective way to serve the agent’s ends. But in this section, I will argue that instrumental rationality and EUT are more permissive than that. I will then explain why this undermines CPT debiasing, even if the CPT utility function is a valid cardinal measure of the agent’s ends.

I take it to be intuitively uncontroversial that instrumental rationality is permissive under risk in the following sense: Keeping fixed all an agent’s subjective valuations of outcomes, instrumental rationality does not prescribe a unique preference relation over lotteries the agent must adopt in pursuit of good outcomes. An example should help to support this intuition. Take again the case of the Cookie Monster, who values all cookies the same. Now he is given the choice between 47 cookies for certain and a 50/50 chance between 0 or 100 cookies. Which should he choose? I submit that both answers are rationally permissible for the Cookie Monster. There is some rational leeway in how he may rationally choose to pursue his cookie-eating goals.

Suppose the Cookie Monster prefers the 47 cookies for certain. And through inquiring more into his preferences, we find out he reaches a point of indifference between the lottery and a sure outcome when the sure outcome is 45 cookies. Below that, he prefers the lottery. Now imagine the Cookie Monster has a cousin, Cookie Aficionado, who is like the Cookie Monster in her evaluation of outcomes: she values all cookies the same. But, unlike the Cookie Monster, she prefers the lottery to the 47 cookies for certain. For her, we find out, the point of indifference is at 50 cookies. By presupposition, Cookie Monster and Cookie Aficionado have exactly the same ends (even though, within EUT, we will have to assign them different utility functions). They merely pursue them differently. And, intuitively, neither of them is instrumentally irrational. If we grant this, then we grant that instrumental rationality is (within bounds—we may rule out extreme attitudes) permissive under risk.

Note that in the terms of our earlier discussion, Cookie Monster, but not Cookie Aficionado, displays some pure risk aversion. So the claim that instrumental rationality is permissive under risk amounts to the claim that some non-neutral pure attitudes to risk are rationally permissible. As we noted in the previous section, EUT does not rule out non-neutral pure risk attitudes, as long as agents abide by the vNM axioms. For the same reason, EUT is not incompatible with permissiveness under risk. Cookie Monster and Cookie Aficionado could both be expected utility maximizers. They would need to be represented with different utility functions: concave for the Cookie Monster and linear for Cookie Aficionado. This is compatible with them nevertheless valuing cookie outcomes in the same way. We just need to accept that for at least one of them, Cookie Monster in this case, the utility function is not a cardinal measure of her ends.

Thus, I take it that, intuitively, instrumental rationality is permissive under risk, and accepting vNM EUT does not introduce restrictions strong enough to do away with this permissiveness. Unless stronger rational restrictions than those of the orthodox vNM EUT are accepted, we are thus left with permissiveness under risk, and the rational permissibility of some non-neutral pure attitudes to risk. Before returning to the topic of CPT debiasing, note that this permissiveness of instrumental rationality under risk now creates the possibility of one problematic type of means paternalism already characterized in more general terms above. Suppose that we impose on the Cookie Monster the choices that Cookie Aficionado would have made. Despite his preference for the 47 sure cookies, we choose the 50/50 lottery on his behalf instead. Given that this is a permissible way of pursuing his cookie-eating ends (after all, we permitted this for Aficionado, who has the same ends), we are taking seriously and deferring to his subjective valuation of outcomes in this act of means paternalism. However, we are not deferring to his instrumental preferences over how he would like to pursue his cookie eating goals. In this case, given his own way of pursuing his ends is perfectly fine, we have no claim to pursuing his goals any more effectively than he would have himself by overriding him. And then general anti-paternalist considerations speak against overriding his instrumental preferences. This is means paternalism, but a problematic kind of means paternalism.

Returning to CPT debiasing, my argument now is that CPT debiasing is generally problematic in the same way. CPT debiasing involves identifying, for each agent, what lotteries would be favored by an expected utility calculation using the utility function identified in a CPT model of her preferences. If this utility function is a cardinal measure of her subjective valuations of outcomes, as we are granting now, then what this procedure does is impose risk neutrality with regard to subjective value on the agent. It removes any pure risk aversion or pure risk seeking inclinations the agent might have had. Given the actual permissiveness of instrumental rationality, the procedure thus imposes not the uniquely rational way of pursuing her ends on the agent, but rather just one of the permissible ones, the risk-neutral one. And it imposes not the unique way of abiding by EUT in a way that respects the agent’s subjective valuations, but rather just one such way. For instance, we could equally implement EUT in a way that respects her ends by letting the utility in the EUT model be a concave transformation of the CPT utility function. Under the assumption that the CPT utility function is a cardinal measure of subjective value, this would implement pure risk aversion. Despite the presence, then, of various rationally permissible options for how to pursue the agent’s ends, CPT debiasing imposes just one, the one that is risk neutral with regard to subjective value. And it does so regardless of what the agent’s own preferences are regarding how she would prefer to pursue her ends, expressed in her actual preferences over lotteries.

Now, a defender of CPT debiasing might point to one crucial difference to the Cookie Monster case just discussed, which is that the Cookie Monster is, by hypothesis, an expected utility maximizer. The agents that CPT debiasing would be applied to are not and are thus, we have granted, in violation of the normatively correct theory of rational choice. Their CPT preferences might express their preferences regarding how to pursue their goals, but they express faulty instrumental judgments. The probability weighting and loss aversion captured by CPT are often taken as identifying the “mistakes” or “biases” of agents who violate EUT, and the thought is that they justify correction.

If we accept the normative correctness of EUT, then the need for probability weighting and loss aversion to feature in descriptively adequate models of an agent’s choice behavior is indeed indicative of a mistake—the violation of the standard axioms of EUT. But CPT debiasing seems to presuppose that they capture mistakes in a stronger sense, namely that the entire difference that probability weighting and loss aversion make in the CPT model captures a mistake by the agent. In effect, this presupposes that agents were trying but failing to pursue their ends in a risk-neutral manner. It is hard to see where this conviction should come from. As I have argued, EUT does not require such risk neutrality. And given the actual heterogeneity in risk preferences we find using CPT and RDU representations, ^{Footnote 17} it seems very unlikely that all agents would really be risk neutral in the pursuit of their subjective values were it not for some reasoning mistake. ^{Footnote 18} Rather, at least some of the risk attitudes captured by probability weighting ^{Footnote 19} and loss aversion in a CPT model would likely remain as a pure attitude to risk were agents themselves to correct their preferences in accordance with EUT. But, most importantly, we simply don’t know without asking agents what their preferred way of abiding by EUT would be, out of the various permissible options, and asking them arguably obviates the need for paternalist intervention. All the means paternalist has to work with in terms of what the agent’s preferred ways of pursuing her ends are, are her actual CPT preferences.

Now even if risk neutrality is only one of the permissible ways of pursuing one’s ends, given we grant that the CPT preferences are irrational, we might think it is unproblematic for the policy-maker to impose one, albeit an arbitrary one, of the rational ways for the agent to pursue her ends. But there is a way to honor the normative authority of EUT while being much more deferential to the CPT agent’s instrumental preferences over lotteries. And that is to identify the EUT model that has the closest fit with the agent’s preferences over lotteries, and thus to minimize deviations from her judgments and choices. ^{Footnote 20} The results of this procedure can be radically different from the results of CPT debiasing, as also noted by Harrison and Ross (Reference Harrison and Ross2017, footnote 12). Suppose an agent values money linearly, and, pace the worries of the last section, the basic utility function identified by CPT reflects this linearity. CPT debiasing would then impose an EUT model with linear utility in money, and thus risk neutrality with regard to money on such an agent. However, the agent’s original preferences over lotteries might have exhibited strong risk aversion with regard to money, which in the CPT model would be captured in terms of probability weighting and loss aversion. If so, then the closest-fitting EUT model would feature a concave utility function, not a linear one.

The two procedures can thus have different results, and imposing the closest-fitting EUT model on the agent strikes me as the clearly superior option on anti-paternalist grounds. Overriding an agent’s preferences over means to her ends may be justifiable for those with anti-paternalist sentiments if and insofar as the policy-maker is confident she can identify a better way for the agent to pursue her ends, but whenever CPT debiasing deviates from the closest-fitting EUT model, it recommends deviating further from the agent’s preferences than necessary in order to secure instrumentally rational pursuit of the agent’s ends. And that should be no longer acceptable for those with anti-paternalist sentiments.