This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

Newcomb's problem and similar cases show the need to incorporate causal distinctions into the theory of rational decision; the usual noncausal decision theory, though simpler, does not always give the right answers. I give my own version of causal decision theory, compare it with versions offered by several other authors, and suggest that the versions have more in common than meets the eye.

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion (...) on Independence generalizes to other views that also violate Independence. (shrink)

In this article it is argued that the standard theoretical account of risk in the contemporary literature, which is cast along probabilistic lines, is flawed, in that it is unable to account for a particular kind of risk. In its place a modal account of risk is offered. Two applications of the modal account of risk are then explored. First, to epistemology, via the defence of an anti-risk condition on knowledge in place of the normal anti-luck condition. Second, to legal (...) theory, where it is shown that this account of risk can cast light on the debate regarding the extent to which a criminal justice system can countenance the possibility of wrongful convictions. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

One of the great difficulties with Kant’s moral philosophy is that it seems to imply that our moral obligations leave us powerless in the face of evil. Kant’s theory sets a high ideal of conduct and tells us to live up to that ideal regardless of what other persons are doing. The results may be very bad. But Kant says that the law "remains in full force, because it commands categorically" (G, 438-39/57).* The most weI1—known example of...

When is it morally acceptable to expose others to risk? Most moral philosophers have had very little to say in answer to that question, but here is a moral philosopher who puts it at the centre of his investigations.

Consider the following claim: given the choice between saving a life and preventing any number of people from temporarily experiencing a mild headache, you should always save the life. Many moral theorists accept this claim. In doing so, they commit themselves to some form of ‘moral absolutism’: the view that there are some moral considerations that cannot be outweighed by any number of lesser moral considerations. In contexts of certainty, it is clear what moral absolutism requires of you. However, what (...) does it require of you when deciding under risk? What ought you to do when there is a chance that, say, you will not succeed in saving the life? In recent years, various critics have argued that moral absolutism cannot satisfactorily deal with risk and should, therefore, be abandoned. In this paper, we show that moral absolutism can answer its critics by drawing on—of all things—orthodox expected utility theory. (shrink)

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B p|E (T), for (...) every E such that p(E) > 0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The "Lockean" rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1-2):221-262, 1975; Alchourrón et al., J Symb Log 50:510-530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987). (shrink)

This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities (...) assigned to them)? The paper first outlines a certain simple response to the Pasadena game and identifies two problems with this response, the second of which is that it leads to a wholesale violation of evaluative compositionality. I then argue that rationality does not require decision makers to factor in outcomes of arbitrarily low probability. A method for making decisions which flows from this basic idea is then developed, and it is shown that this decision method (Truncation) leads to a limited — as opposed to wholesale — violation of evaluative compositionality. The paper then argues that the truncation method yields solutions to the problems posed by the Pasadena game and its relatives that are both attractive in themselves and superior to those yielded by alternative proposals in the literature. (shrink)

Decision theory has at its core a set of mathematical theorems that connect rational preferences to functions with certain structural properties. The components of these theorems, as well as their bearing on questions surrounding rationality, can be interpreted in a variety of ways. Philosophy’s current interest in decision theory represents a convergence of two very different lines of thought, one concerned with the question of how one ought to act, and the other concerned with the question of what action consists (...) in and what it reveals about the actor’s mental states. As a result, the theory has come to have two different uses in philosophy, which we might call the normative use and the interpretive use. It also has a related use that is largely within the domain of psychology, the descriptive use. This essay examines the historical development of decision theory and its uses; the relationship between the norm of decision theory and the notion of rationality; and the interdependence of the uses of decision theory. (shrink)

Deontologists have long been upbraided for lacking an account of justified decision- making under risk and uncertainty. One response is to develop a deontological decision theory—a set of necessary and sufficient conditions for an act’s being permissible given an agent’s imperfect information. In this article, I show that deontologists can make more use of regular decision theory than some might have thought, but that we must adapt decision theory to accommodate agent- centered options—permissions to favor or sacrifice our own interests, (...) when doing so is overall morally worse. Accommodating options requires more than just amend- ing the decision-theoretic ‘value function’. We must change the decision rule as well. (shrink)

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) proposition, the higher her confidence in the truth of that proposition. For instance, Sophia’s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief. (shrink)

University of Alberta Forthcoming in Utilias Consider Lives for Headaches: there is some number of headaches such that the relief of those headaches is sufficient to outweigh the good life of an innocent person. Lives for Headaches is unintuitive, but difficult to deny. The argument leading to Lives for Headaches is valid, and appears to be constructed out of firmly entrenched premises. In this paper, I advocate one way to reject Lives for Headaches; I defend a form of lexical superiority (...) between values. Based on an inquiry into the notion of human well-being, I argue that no amount of headaches is sufficient to outweigh the disvalue of the loss of a good life. Though this view has been thought subject to devastating objections, these objections are not dispositive against the form of value superiority I advance here. (shrink)

In this paper we explore the connections between ethics and decision theory. In particular, we consider the question of whether decision theory carries with it a bias towards consequentialist ethical theories. We argue that there are plausible versions of the other ethical theories that can be accommodated by “standard” decision theory, but there are also variations of these ethical theories that are less easily accommodated. So while “standard” decision theory is not exclusively consequentialist, it is not necessarily ethically neutral. Moreover, (...) even if our decision-theoretic models get the right answers vis-`a-vis morally correct action, the question remains as to whether the motivation for the non-consequentialist theories and the psychological processes of the agents who subscribe to those ethical theories are lost or poorly represented in the resulting models. (shrink)

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we (...) project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty. (shrink)

Many philosophers think that given the choice between saving the life of an innocent person and averting any number of minor ailments or inconveniences, it would be better to save the life. How, then, should one compare the risk of an innocent person’s life to such minor ailments and inconveniences? If lives are infinitely more important than insignificant factors then any risk cannot be outweighed, and that is untenable. An alternative approach seems more promising: let the values of such insignificant (...) factors be bounded, as then there will be well-behaved tradeoffs between insignificant things and the risk to an innocent life. We argue, however, that bounding the values of insignificant factors poses myriad problems. (shrink)

Some theories of practical reasons incorporate a lexical priority structure, according to which some practical reasons have infinitely greater weight than others. This includes absolute deontological theories and axiological theories that take some goods to be categorically superior to others. These theories face problems involving cases in which there is a non-extreme probability that a given reason applies. In view of such cases, lexical-priority theories are in danger of becoming irrelevant to decision-making, becoming absurdly demanding, or generating paradoxical cases in (...) which each of a pair of actions is permissible yet the pair is impermissible. (shrink)

It is plausible to think that it is wrong to cure many people’s headaches rather than save someone else’s life. On the other hand, it is plausible to think that it is not wrong to expose someone to a tiny risk of death when curing this person’s headache. I will argue that these claims are inconsistent. For if we keep taking this tiny risk then it is likely that one person dies, while many others’ headaches are cured. In light of (...) this inconsistency, there is a conflict in our intuitions about beneficence and chance. This conflict is perplexing. And I have not been able to find a satisfactory way of resolving it. Perhaps you can do better? (shrink)

Three philosophical accounts of risk dominate the contemporary literature. On the probabilistic account, risk has to do with the probability of a disvaluable event obtaining; on the modal account, it has to do with the modal closeness of that event obtaining; on the normic account, it has to do with the normalcy of that event obtaining. The debate between these accounts has proceeded via counterexample-trading, with each account having some cases it explains better than others, and some cases that it (...) cannot explain at all. In this article, we attempt to break the impasse between the three accounts of risk through a shift in methodology. We investigate the concept of risk via the method of conceptual reverse-engineering, whereby a theorist reconstructs the need that a concept serves for a group of agents in order to illuminate the shape of the concept: its intension and extension. We suggest that risk functions to meet our need to make decisions that reduce disvalue under conditions of uncertainty. Our project makes plausible that risk is a pluralist concept: meeting this need requires that risk takes different forms in different contexts. But our pluralism is principled: each of these different forms are part of one and the same concept, that has a ‘core-to-periphery’ structure, where the form the concept takes in typical cases (at its ‘core’) explains the form it takes in less typical cases (at its ‘periphery’). We then apply our findings to epistemic risk, to resolve an ambiguity in how ‘epistemic risk’ is standardly understood. (shrink)

Normative ethical theories owe us an account of how to evaluate decisions under risk and uncertainty. Deontologists seem at a disadvantage here: our best decision theories seem tailor-made for consequentialism. For example, decision theory enjoins us to always perform our best option; deontology is more permissive. In this paper, we discuss and defend the idea that, when some pro-tanto wrongful act is all-things considered permissible, because it is a ‘lesser evil’, it is often merely permissible, by the lights of deontology. (...) We show that this raises new problems for deontological decision theory, and we show that to resolve them, we need to take a more innovative approach to morally evaluating decision-making under risk and uncertainty. (shrink)

In this paper I examine the prospects for a rights-based approach to the morality of pure risk-imposition. In particular, I discuss a practical challenge to proponents of the thesis that we have a right against being imposed a risk of harm. According to an influential criticism, a right against risk-imposition will rule out all ordinary activities. The paper examines two strategies that rights theorists may follow in response to this “Paralysis Problem”. The first strategy introduces a threshold for when a (...) risk-imposition is a rights violation. The second strategy drops the claim that rights are absolute and maintains that all rights infringements generate compensation duties. It is argued that both strategies face significant practical problems of their own and that the Paralysis Problem seems fatal for a right against risk-imposition in the absence of an adequate account of the morally relevant threshold risk. (shrink)

Many moral theories are committed to the idea that some kinds of moral considerations should be respected, whatever the cost to ‘lesser’ types of considerations. A person's life, for instance, should not be sacrificed for the trivial pleasures of others, no matter how many would benefit. However, according to the decision-theoretic critique of lexical priority theories, accepting lexical priorities inevitably leads us to make unacceptable decisions in risky situations. It seems that to operate in a risky world, we must reject (...) lexical priorities altogether. This paper argues that lexical priority theories can, in fact, offer satisfactory guidance in risky situations. It does so by equipping lexical priority theories with overlooked resources from decision theory. (shrink)

In his famous Wager, Blaise Pascal offers the reader an argument that it is rational to strive to believe in God. Philosophical debates about this classic argument have continued until our own times. This volume provides a comprehensive examination of Pascal's Wager, including its theological framework, its place in the history of philosophy, and its importance to contemporary decision theory. The volume starts with a valuable primer on infinity and decision theory for students and non-specialists. A sequence of chapters then (...) examines topics including the Wager's underlying theology, its influence on later philosophical figures, and contemporary analyses of the Wager including Alan Hájek's challenge to its validity, the many gods objection, and the ethics of belief. The final five chapters explore various ways in which the Wager has inspired contemporary decision theory, including questions related to infinite utility, imprecise probabilities, and infinitesimals. (shrink)

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult (...) to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: as we argue, continuity for easy cases gives rise to a sorites. (shrink)