In recent years a growing number of philosophers have started working on normative questions related to what may be called ‘pure’ attitudes risk. Pure attitudes to risk are attitudes to risk that cannot be reduced to attitudes to certain states of affairs, but rather are directed to the risk itself. Although such attitudes have gained much attention by economists, psychologists and philosophers in the past, most (but certainly not all) of this attention was directed at descriptive questions. The current trend in the literature deals explicitly with normative questions.

Paul Weirich’s new book constitutes a deep and comprehensive major contribution to this new line of literature. It also constitutes a very unique such contribution. I will point to two different – but related – senses in which this is the case, but before doing so it will be instructive to first cover some necessary background.

Although this goes against the spirit of his book (as will soon become clear), in order to understand the differences between Weirich’s account and other contemporary accounts, it will be useful to adopt, at the outset, a characterization of attitudes to risk in terms of preferences over risky options. Consider an agent who faces a decision between two gambles whose possible outcomes are different quantities of some divisible good, G. The two gambles have the same expectation in terms of G, but different variances.Footnote ¹ We can say that the agent is risk-averse with respect to G if she prefers the gamble with the lower variance, risk-seeking if she prefers the gamble with the higher variance and risk-neutral if she is indifferent between the gambles.

For example, consider an agent who faces a choice between a certain 100 units of G (gamble A) and a gamble that gives 200 units of G with probability 0.5 and nothing with probability 0.5 (gamble B). A risk-averse agent (with respect to G) prefers A to B, a risk-seeking agent prefers B to A and a risk-neutral agent is indifferent between the two gambles.

We can distinguish between three types of explanations for risk-aversion and risk-seeking with respect to G (for convenience let us concentrate on risk-aversion, though).^{Footnote 2} First, the agent might be risk-averse with respect to G (in the sense explicated above) because she values every additional unit of G in a marginally decreasing (increasing in the case of risk-seeking) way. If the agent values every additional unit of G less than she values the previous unit then she will prefer a certain 100 units of G to 0.5 probability of getting 200 units of G. This is the traditional explanation of neo-classical economics and Weirich accepts that it is a very powerful explanation that captures much of the observed phenomenon. He also accepts (like, I think, everybody else) that having such attitudes is completely rational. However, this is not what Weirich’s book is about. Weirich’s book is about attitudes to risk that are irreducible to attitudes to certain outcomes (i.e. outcomes that are characterized in a way that does not involve any reference to risk). The next two (families of) explanations belong to this latter category.

Some scholars (notably Buchak Reference Buchak2013) argue that a rational agent might have risk-averse preferences because, when evaluating some gambles, the agent (rationally) assigns weights to the possible outcomes of the gambles which are different from the outcomes’ probabilities, according to the gambles. For example, if the value of a gamble is a weighted sum of the utilities of its possible outcomes and if, when evaluating gamble B, the agent assigns to the outcome “get nothing” a decision weight which is higher than 0.5 and to the outcome “win 200 units of G” a weight which is lower than 0.5, the value she assigns to the gamble as a whole will be lower than the value she assigns to gamble A even if her marginal utility from units of G is constant.

Assigning decision-weights this way may express a risk-averse policy for handling risks. Rational agents that use the same probability and utility functions may differ, so argue proponents of this approach, in their policies for handling risks and thus may have different preferences. Still, relaxing the assumption that the decision-weight assigned to an outcome must be equal to the outcome’s probability, does not mean that no alternative restrictions on the assignment of decision-weights should be adopted. Different decision-theories in this family present different alternative sets of restrictions on the assignment of weights to outcomes. We can call such accounts non-expected utility accounts (because, according to them, the value of a gamble might be different from the gamble’s expected utility).

Finally, some scholars argue that rational agents might be risk-averse because they disvalue the risk as such. For example, the agent might prefer gamble B because, for her, getting a unit of G when there was a 0.5 chance that she will get nothing is less valuable than getting a certain unit of G. We can call such explanations re-individuation explanations (because they are based on an individuation of the outcomes which is more fine-grained than the individuation most people intuitively adopt).

In his book, Weirich argues against the non-expected utility approach (understood as a normative approach) and presents a specific re-individuation account. According to Weirich’s account, a rational agent prefers one gamble to another iff it has a higher utility. the utility of a gamble always equals its expected utility. However, the utility of each possible outcome of the gamble might be influenced by the risk associated with the gamble that brings the outcome about. Specifically, the utility of each outcome is the sum of the utility of the outcome ignoring the utility from the risk associated with the gamble, and the utility of the risk associated with the gamble. The latter component is equal for all outcomes, according to Weirich.

Although Weirich’s account is more permissive than orthodox decision-theory in terms of the range of preferences it counts as rational, it explicitly rules out two possibilities that other contemporary accounts allow for. First, and as mentioned above, unlike non-expected utility accounts, Weirich’s account does not allow rational agents to assign to a gamble’s possible outcomes weights which are different from their probabilities. Once the probabilities and utilities of the possible outcomes (including the utility of the risk associated with the gamble which manifests itself in each one of the outcomes) are set, the utility of the gamble is fixed. There is no further attitude that plays a role in the agent’s evaluation of the gamble. Thus, and unlike in the case in non-expected utility theories, two agents with identical beliefs and desires must have, according to Weirich’s account, identical preferences.

Second, Weirich does not allow rational agents to assign different utilities to the risk associated with a gamble given different possible outcomes of the gamble. For example, according to Weirich, valuing positively the risk associated with a given risky activity (say, free solo climbing) conditional on the activity bringing about a positive outcome (e.g. reaching the top of the mountain), but valuing it negatively conditional on the activity bringing about a negative outcome (e.g. falling down) is irrational. However, to me, this pattern of evaluations seems completely reasonable.

Moreover, other re-individuation accounts do allow for such patterns. Specifically, the existence of different risk components of outcomes-utilities for different outcomes of the same gamble is allowed by the account suggested by Stefansson and Bradley (Reference Stefánsson and Bradley2015, Reference Stefánsson and Bradley2017; see also Goldschmidt and Nissan-Rozen Reference Goldschmidt and Nissan-Rozen2021) that Weirich cites. In that account, the desirability of a proposition that represents a gamble equals, just like Weirich’s utility, a sum of two expectations, the expected desirability of the proposition only in virtue of the sure outcomes the gamble that the proposition represents might lead to, and the expected conditional desirability of the gamble given each one of the possible outcomes. The latter component represents the desirability for the risk itself. However, in their account the conditional desirability for the gamble given different outcomes might be different.

Without rehearsing Weirich’s complex arguments for these two central demands (i.e. the demand that decision-weights will always be equal to the outcomes’ probabilities and the demand that the risk-component of an outcome-utility will be equal for all the outcomes of a given gamble) I will note that both arguments are based on the assumption that gambles, like outcomes, have utilities. While in orthodox decision-theory utility is attached only to outcomes and the demand that a rational agent’s preferences will rank gambles according to their expected utility needs an independent justification, in Weirich’s account (as in Jeffrey’s (Reference Jeffrey1965) account) a gamble’s utility is equal to the gamble’s expected utility and thus the demand that preferences will rank gambles according to their expected utilities reduces to the demand that an agent prefers options (sure outcomes or gambles) with higher utility. The latter demand seems trivial and in no need for a justification. The challenge for such accounts is to justify the demand that a gamble’s utility is always equal to its expected utility.

The uniqueness of Weirich’s account, I have mentioned above, is rooted in the methodology he employs when justifying this assumption. This methodology is non-standard in two (related) senses. First, while most of the relevant discussions in the literature understand attitudes to risk as a phenomenon that operates at the level of preferences, Weirich understands it as a phenomenon that operates at the level of desires. The standard approach characterizes attitudes to risk in terms of patterns of preferences over risky options and then uses representation theorems to represent those preferences as resulting from the agent maximizing some function that takes as input utilities, probabilities and some formal representation of attitudes to risk. Weirich’s, on the other hand, goes the other way round. He takes utility to be a measure of degrees of desires, probability to be a measure of degrees of evidential support and treats attitudes to risk as types of desires. Then, using some assumptions about how these measures behave and some normative assumptions about the rationality of beliefs and desires, he explains why a gamble’s utility must always be equal to the gamble’s expected utility.

Second (and relatedly), while other accounts of the rationality of attitudes to risk are mostly based on normative assumptions about the permissibility or impermissibility of different types of preferences patterns, most of Weirich’s arguments in the book are based on a careful and rigorous conceptual analysis of the concepts of risk and desire. Weirich makes fine-grained distinctions between types of desires and types of relations between desires and then, using these distinctions and only very few minimal (in some cases, implicit) normative assumptions, reaches conclusions regarding the rationality of preferences over risky options. These parts of the book are an excellent example of the way philosophy can offer to interdisciplinary discussions a contribution that other disciplines cannot, by exposing confusions that arise as a result of using conceptual frameworks that are not rich enough to express the full range of relevant categories.

It is important to note, however, that Weirich’s arguments (both for the claim that a gamble’s utility equals its expected utility and for the claim that the risk-component of an outcomes’ utility is equal for all outcomes of the same gamble) support their conclusions only under the assumption that the possible outcomes of a gamble are individuated in a maximally specific way. Weirich does not deny (or, at least, he does not have to), for example, that a rational agent might positively value the thrill associated with free solo climbing only under the assumption that she will not fall down to her death while climbing, but negatively value it under the assumption that she will.

However, a maximally specific individuation of the outcomes in this case includes an explicit reference to this thrill and so, when evaluating the possible outcomes of the decision whether to climb the mountain free solo, it is possible to separate between the agent’s attitude to the risk itself and her attitude to the thrill associated with the risk. Weirich argues that while a rational agent might have different attitudes to the latter given different possible outcomes, she must have the same attitude to the former given any one of the outcomes.

Thus (and somewhat ironically), although Weirich’s arguments do not employ (like most other accounts) representation theorems, his claims should be understood as claims about the possibility of representation. His arguments (if successful) establish that it is possible to represent a decision problem in such a way that it is a demand of rationality that the utility of an option equals its expected utility and that the utility of the riskiness of the option is equal for all of the option’s possible outcomes. However, this will not be the case under every possible (accurate) representation of the decision problem.

I do not take this feature of Weirich’s arguments to be a drawback. Conclusions regarding the possibility of representing a decision problem in a specific way are, in some cases, very useful when it comes to both practical and theoretical applications of decision-theoretic accounts. Indeed, Weirich convincingly demonstrates the usefulness of his account in several such contexts (e.g. choosing for others or advising others how to choose, sequential choices, compound choices and more).

I do, however, want to critically examine one assumption that Weirich uses and that plays a significant role in several of the main arguments in the book (including the arguments for the two central restrictions mentioned above). It is the assumption that a rational agent must have a basic intrinsic aversion to risk.Footnote ³

On the face of it, this feature of Weirich’s account stands in sharp contrast to the permissiveness of most competing accounts that allow rational agents to be risk averse as well as risk inclined. However, the qualification of the demand only to “intrinsic” and “basic” attitudes is important here. An “intrinsic attitude” to an event is, in Weirich terminology, an attitude which is directed only to the a priori implications of the event. An extrinsic attitude is directed also to the a posteriori implications of the event. An intrinsic attitude to an event is basic if no other intrinsic attitude to the event is a reason for it. The demand that a rational agent be risk averse applies only when the aversion is understood as intrinsic and basic. As mentioned, Weirich does not deny that rational agents sometimes value the thrill associated with risky activities. However, such inclination to risk is extrinsic because it is directed to an a posteriori implication of the decision.

While the qualification of the risk-aversion demand only to intrinsic attitudes makes it much more plausible, its qualification not only to intrinsic attitudes but also to basic ones makes it hard to assess.^{Footnote 4} In order to argue for the claim that in a given case (or family of cases) risk inclination is rational one should, presumably, point to a reason to desire the risk and so to the extent that such an explanation is successful it does not concern an inclination which is basic. An intrinsic and basic risk inclination is a desire that one has no reason to have (other than the desire itself) and so, unless one has it, convincing one that one should have it seems hopeless.

However, exactly the same consideration arises when considering risk-aversion: a successful argument for risk-aversion would probably point to a reason for the aversion which, in turn, will make it an argument that applies only to non-basic risk-aversion. Indeed, when Weirich tries (on page 70) to justify his assumption that intrinsic and basic risk-aversion is a demand of rationality, he (as, of course, he must) does not point to a reason for the aversions but instead just states the demand in a way that (presumably) makes it more intuitive:

While this description does somewhat move me to accept the claim that in some cases intrinsic and basic risk aversion is rational, it does not undermine my intuition that the basic and intrinsic risk inclination that I (think I) sometimes have is rational too. Now, for me this desire mainly comes in a conditional form, i.e. I positively desire the risk associated with some risky acts only conditional on some of their outcomes obtaining (specifically when the risk is assessed conditional on the decision bringing about good outcomes). As we saw, Weirich thinks that this pattern of desires (i.e. having different attitudes to the risk associated with a gamble, conditional on different outcomes of the gamble obtaining) is irrational when the risk-inclination in question is understood to be both basic and intrinsic. However, his argument for that assumes that, when it comes to basic attitudes, intrinsic risk aversion is a demand of rationality, which is exactly the assumption I question.

Thus, I think an unqualified version of Weirich’s account might ultimately be too restrictive. However, the account can still be understood as applying only to cases in which people do, as a matter of fact, have a basic and intrinsic risk-aversion. In such a form the account seems much more plausible to me and surely this family of cases is a very important one.

In this review I have focused on the main structure of Weirich’s account. Space limitations do not allow me to engage with the many fascinating discussions one can find in Weirich’s book that deal with, among other things, the way in which his account can be extended to cover less than ideally rational agents, the account’s implications for public policy and more. These discussions are insightful as much as they are rigorous. I highly recommend this book to anyone who is interested in normative decision-theory.