We have all experienced ‘moral uncertainty’, in the sense of being unsure of the correct morality. Despite such uncertainty, we must make morally loaded decisions. Here is one obvious response: first, identify the moral theory you find the most plausible; then, make decisions as prescribed by this theory. But the monograph under review represents a recent literature that explores a different approach, based on maximizing expected choiceworthiness.

For example, suppose I am invited to dinner, and I can order Meat or Tofu. If I order Tofu, it will hurt my host’s feelings. However, I am torn between two moral theories. I assign 95% credence to Theory X, which says it is okay to eat meat. But I assign 5% credence to Theory Y, which says meat is an atrocity. My moral decision problem can be described by the following table.

Tofu has a higher expected choiceworthiness, so this is what I should choose. This is not the carnivorous recommendation of the moral theory that I find the most likely (namely, Theory X). So maximizing expected choiceworthiness is not the same as following the most likely theory.

This example assumes every moral theory assigns a ‘choiceworthiness’ value to every alternative, and these values can be meaningfully averaged across theories. The authors are aware that these assumptions are problematic; much of this book is dedicated to addressing them. It is based on several of their recent publications, but it also summarizes and critiques the work of other scholars. Thus, in addition to a cogent and concise statement of the authors’ own views, it functions as a good introduction to the literature. Overall, it is informative, insightful and enjoyable to read. The writing is admirably clear, crisp and precise. The arguments are mostly persuasive and sometimes surprising. The central innovation is the application of tools from normative economic theory to moral philosophy. I think this strategy has great promise; indeed, my main criticisms (below) are that the authors perhaps do not take it far enough.

The book packs a lot of interesting material into two hundred pages. Due to length constraints, this review will mainly discuss the parts of the book where I feel most qualified to comment. Chapter 1 argues that moral uncertainty is important and we should take it seriously in our ethical reasoning, contra writers who have argued it is irrelevant, leads to infinite regress, or yields absurd conclusions regarding moral responsibility. Chapter 2 argues that, under certain assumptions, the correct response to moral uncertainty is to maximize expected choiceworthiness.

Chapter 2 assumes choiceworthiness is interval-scale measurable and can be compared between theories (so its ‘expected value’ is meaningful). Chapter 3 relaxes both assumptions, and considers a situation where choiceworthiness is purely ordinal, and does not admit intertheoretic comparisons. The authors make an analogy between moral uncertainty and social choice theory: moral theories are ‘voters’, and the aggregation of their conflicting recommendations is analogous to the aggregation of voters’ conflicting preferences via a weighted voting rule, where credences play the role of ‘voting weights’. Thus, to optimally cope with moral uncertainty, we must find the optimal voting rule. After considering alternatives, they conclude that the Borda rule is optimal.

Chapter 4 supposes choiceworthiness is interval-scale measurable, but not intertheoretically comparable. If there is no objectively correct way to compare choiceworthiness between moral theories, is there at least a ‘natural’ or ‘reasonable’ way to do this? The authors advocate the variance voting rule originally proposed by Owen Cotton-Barratt in the context of social choice: the scale of choiceworthiness within each theory should be renormalized so that its variance is the same for all theories. The authors justify this rule on the grounds that it equalizes the ‘distance’ of all moral theories to the totally indifferent moral theory, and thereby gives them all equal ‘influence’ over the decision.

Chapter 4 then addresses two problems that affect both the variance voting rule and the Borda rule. The first is that the decision may depend on how options are individuated. For example, suppose I want to donate €1200 per year to one of charities A, B, C or D. When I apply the variance voting rule, A is the winner. But now suppose I learn that I can also decide between one yearly payment to charity C, or twelve monthly payments (call these options C ₁ and C ₂). When I apply the variance voting rule, B might now be the winner.Footnote ¹ Clearly, this is absurd. The Borda rule suffers from a similar problem. The authors respond by introducing a probability measure on the set of options. The variance and Borda rules can be reformulated in terms of this measure. This measure is not a credence; it is just an ‘accounting device’, designed to make the decision invariant to different ways of individuating options. For example, suppose I assigned measure 0.25 to each of A, B, C and D. If I introduce the yearly vs. monthly distinction, and assign measure 0.125 to each of C ₁ and C ₂, then it can be shown that my final decision will still be A –so it is unaffected by how I individuate options. Introducing such a measure also has two other benefits: the voting rules can be applied to menus with infinitely many options, and the measure can always be chosen to guarantee that the variance is finite (so renormalization is possible).

The second problem for both the variance and Borda rules is that the outcome may be menu-dependent. Suppose I learn of a fifth charity, E. When I add E to the menu, my decision may change from A to B. This seems absurd. It violates the axiom of Contraction Consistency, as well as Arrow’s axiom of Independence of Irrelevant Alternatives. One ‘solution’ is to always include all possible options in the menu – following Amartya Sen, the authors refer to this as the Broad Account. But this may be impractical or even infeasible. So the authors favour the Narrow Account, where the menu is restricted to only those options relevant to a particular choice situation. They argue that Contraction Consistency is not really important anyway. Chapter 4 ends with a proposal for how to manage moral uncertainty when some theories are interval-scale and comparable, others are interval-scale and non-comparable, and others are purely ordinal.

Chapter 5 examines the problem of intertheoretic comparisons. After rejecting several approaches, it advocates an account based on an analogy with the metaphysics of physical quantities like mass and length. Chapter 6 grapples with ‘fanaticism’ and ‘infectious incomparability’. (The former is the moral uncertainty version of Pascal’s Wager. The latter arises because some moral theories treat certain moral objectives as incommensurable.) Chapter 7 reviews several attempts to develop non-cognitivist accounts of moral uncertainty, and concludes none of them succeed. Chapter 8 considers the implications of moral uncertainty for practical ethics, and shows they are not as one-sided as has been claimed by some scholars. Finally, Chapter 9 estimates the value of acquiring moral knowledge, and concludes that, under reasonable assumptions, we should be willing to invest considerable resources in this activity.

The authors strive to be ecumenical regarding ethical and meta-ethical claims – as is appropriate for a book which takes as its starting point our uncertainty about such claims. For example, to avoid any hint of consequentialism, they eschew terms such as ‘utility’ in favour of the neologism ‘choiceworthiness’. Furthermore, they focus on the choiceworthiness of acts rather than consequences. Thus, although ‘consequentialist’ in inspiration, the decision procedures outlined in this book are compatible with many deontological moralities. This is clearest in Chapter 3, which deals with ordinal theories. But Chapter 3 still supposes deontological theories rank actions by choiceworthiness, even if this is only an ordinal ranking. It is not clear that all deontologies admit such an ordinal description. Some simply put actions into two categories: permissible and forbidden. Suppose I assign non-zero credence to five such deontological theories V, W, X, Y and Z, which assess the permissibility of actions A, B, C, D and E as follows.

Presumably, I should choose the action permitted by the largest total credence among the theories. In this example, this is A, which is permitted by Theories Y and Z, together claiming 65% credence. This is an application of the Approval Voting rule (Brams and Fishburn Reference Brams and Fishburn1983). As this example shows, Approval Voting may sometimes be more appropriate for managing deontological uncertainty than the Borda rule advocated in the book.

Deontological ethics often grounds moral judgements in concepts such as ‘rights’, ‘dignity’ and ‘responsibility’. Often, the key issue is not only which actions are permissible/forbidden, but why they are permissible/forbidden in terms of these more foundational concepts. A typical syllogism takes the form, ‘P and Q, therefore R’, where statements P and Q refer to rights, dignity, etc., and R is some conclusion about moral permissibility. For example, P might assert, ‘Human genetic modification violates human dignity’, while Q asserts, ‘It is immoral to violate human dignity’, entailing R: ‘Human genetic modification is immoral’. Different deontologies may disagree about P, Q and R. This leads to a situation as in the following table.

Theories X, Y and Z have different views about rights, dignity, responsibility, etc. Each is logically consistent: it is compatible with the syllogism (P&Q)⇒R. But when we aggregate these theories by taking a credence-weighted majority vote for each of P, Q and R, we get a logically inconsistent theory. The obvious solution is to not use majority vote, but aggregate truth-values in some other way. But any ‘simple’ way of aggregating truth-values across a system of logically interconnected statements yields logical inconsistencies (List Reference List2012; Mongin Reference Mongin2012). There are attractive rules that guarantee logical consistency, but they are not simple (see e.g. Nehring and Pivato Reference Nehring and Pivato2019).

These examples show that applications of social choice theory to deontological moral uncertainty go far beyond ordinal preference aggregation. But even if we confine ourselves to deontologies that yield ordinal rankings (as assumed in Chapter 3), the authors’ adoption of the Borda rule seems premature and insufficiently justified. There are many ordinal preference aggregation rules, with different strengths and weaknesses. None is ideal, but some have at least as many arguments in their favour as the Borda rule.Footnote ²

A similar criticism can be levelled against the focus on variance voting in Chapter 4. There are many ways to measure the ‘dispersion’ of a real-valued function defined over a measure space. Variance is only one of them.Footnote ³ Variance normalization is elegant and mathematically natural, because of its intimate connections with Euclidean geometry and Hilbert space. But elegance and mathematical naturalness do not necessarily yield the best solution to a normative problem. The arguments for variance voting in Section 4.IV of the book are suggestive, but far from conclusive.

There is another problem. As noted earlier, to obviate the problem of option-individuation, Chapter 4 introduces a probability measure on the set of options. This is a totally arbitrary mathematical gadget, without any motivation or justification; its only role is to make the theory ‘work’. The authors do not specify how to choose such a measure, or why one choice is more natural than any other. In my opinion, this arbitrary ingredient is the weakest part of their whole framework.

Fortunately, there are at least two ways to make this measure less arbitrary. First, ‘option individuation’ is only an issue because some options seem very similar to others. ‘Donate €1200 to C once a year’ and ‘Denote €100 to C once a month’ are just variants of the same action. We could introduce a metric on the space of options to codify this notion of ‘similarity’. For any metric, there is a canonical measure: the Hausdorff measure. If this Hausdorff measure is finite, then it can be renormalized to a probability measure.

The second approach is to use Bolker–Jeffrey decision theory. In this theory, the space of outcomes is equipped with a primordial probability distribution, describing how things will turn out unless the decision-maker intervenes. An ‘action’ selects some subset of the outcome space and ‘makes it true’, but otherwise does not modify the primordial probability. If the Borda and variance voting rules of Chapter 3 and 4 were reformulated in this Bolker–Jeffrey framework, then the primordial probability measure would provide a natural solution to the option-individuation problem.

But these two solutions have a price. The choiceworthiness of a moral theory over an infinite set of options could have infinite variance. Section 4.V of the book circumvents this by choosing a suitable measure on the option space. But the two solutions above impose a non-choosable measure. So if infinite variance rears its ugly head, it cannot be eliminated.

Furthermore, in some moral decisions, there is no natural probability measure on the space of options. Consider the following simplified model of population ethics. Suppose every human life falls into one of five classes: Excellent, Good, Mediocre, Bad or Horrible; current policies determine how many human lives of each kind there will be in the future. Any policy is described by a vector (X,G,M,B,H), where X is the number of future Excellent lives, etc. These numbers can be arbitrarily large. So the set of options is countably infinite. There is no ‘uniformly distributed’ probability measure on a countably infinite set. So any probability measure must give some vectors greater ‘weight’ than other vectors. But there is no good reason why one vector should have different weight than another. Any probability measure on this space is entirely arbitrary.

Finally, notwithstanding its status as the ‘gold standard’ of rational decision-making, the maximization of expected value itself is open to re-examination. Expected choiceworthiness requires a credence on the space of moral theories. How should we obtain this credence? How can we even apprehend the underlying space of possibilities? Decision theory offers two lines of research in response to such concerns. Sometimes it is impossible or inappropriate to describe uncertainty with a single probability measure; this has engendered decision models that use sets of probability measures (Gilboa and Schmeidler Reference Gilboa and Schmeidler1989) or second-order probabilities (Klibanoff et al. Reference Klibanoff, Marinacci and Mukerji2005), inter alia. Meanwhile, models of decision-making with unawareness explicitly recognize that the agent might be ignorant of certain possibilities (e.g. Karni and Vierø Reference Karni and Vierø2017; Dietrich Reference Dietrich2018). Both of these research lines could be highly relevant to moral uncertainty.

The import of these critiques depends on how we understand the project of this book: is it merely proposing a way to manage moral uncertainty, or is it asserting the way to manage moral uncertainty? The authors sometimes take the former position; for example, they describe the Borda rule and variance voting as ‘a way of coming to a principled decision in the face of incomparable theories’ when ‘there isn’t a fact of the matter’ about intertheoretic comparisons (103). They make similar remarks with respect to an obviously arbitrary scheme they propose to combine Borda scores and variance-voting scores (108). In this case, my critiques just suggest possible future enhancements to the theory.

But the authors sometimes make a more ambitious claim. In their concluding remarks (211), they refer to expected choiceworthiness, Borda and variance voting each as ‘the correct theory’. (The phrase appears three times in one paragraph.) Perhaps this was merely rhetorical overreach. But if the authors really want to defend the claim that this book articulates the correct theory of moral uncertainty, then they will need to address these critiques, and others.

In any case, this book is an impressive achievement. It may not be the complete and final theory of moral uncertainty, but it provides a superb foundation upon which future scholars will undoubtedly build. It will be an important part of the library of every moral philosopher.