Pascal’s Wager involves expected utilities. In this chapter, we examine the Wager in light of two main features of expected utility theory: utilities and probabilities. We discuss infinite and finite utilities, and zero, infinitesimal, extremely low, imprecise, and undefined probabilities. These have all come up in recent literature regarding Pascal’s Wager. We consider the problems each creates and suggest prospects for the Wager in light of these problems.

Maximize Expected Choiceworthiness (MEC) is a theory of decision-making under moral uncertainty. It says that we ought to handle moral uncertainty in the way that Expected Value Theory (EVT) handles descriptive uncertainty. MEC inherits from EVT the problem of fanaticism. Roughly, a decision theory is fanatical when it requires our decision-making to be dominated by low-probability, high-payoff options. Proponents of MEC have offered two main lines of response. The first is that MEC should simply import whatever are the best solutions (...) to fanaticism on offer in decision theory. The second is to propose statistical normalization as a novel solution on behalf of MEC. This paper argues that the first response is open to serious doubt and that the second response fails. As a result, MEC appears significantly less plausible when compared to competing accounts of decision-making under moral uncertainty, which are not fanatical. (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)

Moral latitude is only ever a matter of coincidence on the most popular decision procedure in the literature on moral uncertainty. In all possible choice situations other than those in which two or more options happen to be tied for maximal expected choiceworthiness, Maximize Expected Choiceworthiness implies that only one possible option is uniquely appropriate. A better theory of appropriateness would be more sensitive to the decision maker’s credence in theories that endorse agent-centred prerogatives. In this paper, we will develop (...) and defend a modified version of this view that allows for agent-centred prerogatives and supererogation as part of its verdicts about appropriateness. (shrink)

Critical-set views avoid the Repugnant Conclusion by subtracting some constant from the welfare score of each life in a population. These views are thus sensitive to facts about biographical identity: identity between lives. In this paper, I argue that questions of biographical identity give us reason to reject critical-set views and embrace the total view. I end with a practical implication. If we shift our credences towards the total view, we should also shift our efforts towards ensuring that humanity survives (...) for the long term. (shrink)

This paper presents a unifying diagnosis of a number of important problems facing existing models of rational choice under moral uncertainty and proposes a remedy. I argue that the problems of (i) severely limited scope, (ii) intertheoretic comparisons, and (iii) 'swamping’ all stem from the way in which values are assigned to options in decision rules such as Maximisation of Expected Choiceworthiness. By assigning values to options under a given moral theory by asking something like ‘how much do I desire (...) this option, supposing this theory is true?’ rather than ‘how much value does this theory assign to this option?’ these problems can be avoided, while the appealing features of these accounts can be preserved. This amendment provides a role for the preferences, desires, or goals of rational agents that is curiously absent from the existing discussion of what individuals rationally ought to do when they are uncertain about what they morally ought to do. (shrink)

In this article, we re-examine Pascal’s Mugging, and argue that it is a deeper problem than the St. Petersburg paradox. We offer a way out that is consistent with classical decision theory. Specifically, we propose a “many muggers” response analogous to the “many gods” objection to Pascal’s Wager. When a very tiny probability of a great reward becomes a salient outcome of a choice, such as in the offer of the mugger, it can be discounted on the condition that there (...) are other symmetric, non-salient rewards that one may receive if one chooses otherwise. (shrink)

The repugnant conclusion poses a conundrum in population ethics that has evaded satisfactory solution for four decades. In this article, I show that the repugnant conclusion can be avoided without sacrificing any moral intuitions. The resulting framework satisfies Parfit's requirements for `theory X'. This is achieved using non-Archimedean orders, which admit the possibility of pairs of goods for which no amount of one is better than a single unit of the other. I show that with minimal assumptions, not only are (...) such goods sensible, they are compulsory. I show that utilitarianism and expected utility theory in their canonical forms are not in general suitable in this setting, and using these tools naively can lead to ethical errors that are arbitrarily serious. Multi-dimensional lexicographic expected utility representations may be required. I use fuzzy sets to show that there needn't be a clear boundary separating goods that are not Archimedean equivalent. This may be unavoidable due to intrinsic physical limits on the ability to discriminate between different goods arising from e.g. quantum mechanics. Limited discriminatory power causes preferences to be non-transitive, which can resolve problems related to so-called `fanaticism' and `recklessness' wherein `rational' decision-makers counterintuitively prefer arbitrary long shot bets to a guaranteed lesser outcome. (shrink)

This thesis is about the moral reasons we have to do less than best. It consists of six chapters. Part I of the thesis proposes, extends, and defends reasons to do less than best. In Chapter One (“The Conditional Obligation”) I outline and reject two recent arguments from Joe Horton and Theron Pummer for the claim that we have a conditional obligation to bring about the most good. In Chapter Two (“Agglomeration and Agent-Relative Costs”) I argue that agent-relative costs can (...) justify permissions to less than best in a far greater range of decisions contexts than we currently believe. In Chapter Three (“Risk and Aggregation”) I discuss how anti-aggregative moral theories deal with risk, whilst proposing an argument in favour of ex-post moral theories. -/- In Part II of the thesis, I discuss longtermism, presenting a series of reasons to believe we have both significant permissions and obligations to prioritise those in the short-term. In Chapter Four (“Listening to Future People”) I criticise a recent argument presented by Andreas Mogensen for the claim we cannot have obligations grounded in the wellbeing of future people. I then show that, even permitting the existence of obligations to future people, we still have significant reasons to resist longtermism on the grounds of partiality. In Chapter Five (“The Complaints of Future People”) I argue that scepticism about aggregation is inconsistent with an obligation, or indeed even a permission, to help far future people. In Chapter Six (“Leaving the Present Behind”) I explore the moral significance of “dooming”, whilst arguing that we have a pro tanto reason of fairness to prioritise aiding those currently in existence. (shrink)

This thesis is about making decisions when we are uncertain about what will happen, how valuable it will be, and even how to make decisions. Even the most sure-footed amongst us are sometimes uncertain about all three, but surprisingly little attention has been given to the latter two. The three essays that constitute my thesis hope to do a small part in rectifying this problem. The first essay is about the value of finding out how to make decisions. Society spends (...) considerable resources funding people (like me) to research decision-making, so it is natural to wonder whether society is getting a good deal. This question is so shockingly underresearched that bedrock facts are readily discoverable, such as when this kind of information is valuable. My second essay concerns whether we can compare value when we are uncertain about value. Many people are in fact uncertain about value, and how we deal with this uncertainty hinges on these comparisons. I argue that value comparisons are only sometimes possible; I call this weak comparability. This essay is largely a synthesis of the literature, but I also present an argument which begins with a peculiar view of the self: it is as if each of us is a crowd of different people separated by time (but connected by continuity of experience). I’m not the first to endorse this peculiar view of the self, but I am the first to show how it supports the benign view that value is sometimes comparable. We may be uncertain of any decision rules, even those that would tell us how to act when we face uncertainty in decision rules. We may be uncertain of how to decide how to decide how to... And so on. If so, we might have to accept infinitely many decision rules just to make any mundane decision, such as whether to pick up a five-cent piece from the gutter. My third essay addresses this problem of regress. I think all of our decisions are forced: we must decide now or continue to deliberate. Surprisingly, this allows us to avoid the original problem. I call this solution “when forced, do your best”. (shrink)

Countenancing unbounded utility in ethics gives rise to deep puzzles in formal decision theory. Here, these puzzles are taken as an invitation to assess the most fundamental principles relating probability and value, with the aim of demonstrating that unbounded utility in ethics is compatible with a desirable decision theory. The resulting theory frames further discussion of Expected Utility Theory and of principles concerning symmetries of utility.

No existing normative decision theory adequately handles risk. Expected Utility Theory is overly restrictive in prohibiting a range of reasonable preferences. And theories designed to accommodate such preferences (for example, Buchak's (2013) Risk‐Weighted Expected Utility Theory) violate the Betweenness axiom, which requires that you are indifferent to randomizing over two options between which you are already indifferent. Betweenness has been overlooked by philosophers, and we argue that it is a compelling normative constraint. Furthermore, neither Expected nor Risk‐Weighted Expected Utility Theory (...) allow for stakes‐sensitive risk‐attitudes—they require that risk matters in the same way whether you are gambling for loose change or millions of dollars. We provide a novel normative interpretation of Weighted‐Linear Utility Theory that solves all of these problems. (shrink)

Decision theorists widely accept a stochastic dominance principle: roughly, if a risky prospect A is at least as probable as another prospect B to result in something at least as good, then A is at least as good as B. Recently, philosophers have applied this principle even in contexts where the values of possible outcomes do not have the structure of the real numbers: this includes cases of incommensurable values and cases of infinite values. But in these contexts the usual (...) formulation of stochastic dominance is wrong. We show this with several counterexamples. Still, the motivating idea behind stochastic dominance is a good one: it is supposed to provide a way of applying dominance reasoning in the stochastic context of probability distributions. We give two new formulations of stochastic dominance that are more faithful to this guiding idea, and prove that they are equivalent. (shrink)

Orthodox decision theory is fanatical in the way it treats small probabilities of enormous value, if unbounded utility functions are allowed. Some have suggested a fix, Nicolausian discounting, according to which outcomes with small enough probabilities should be ignored when making decisions. However, there are lotteries involving only small-probability outcomes, none of which should intuitively be ignored. So the Nicolausian discounter needs a procedure for distinguishing the problematic cases of small-probability outcomes from the unproblematic ones. In this paper, I present (...) a dilemma for Nicolausian discounting: the view must be coupled either with a procedure that delivers fanatical verdicts of its own, as bad as those of orthodox decision theory, or with one that entails intransitive cyclic preferences. (shrink)

Longtermists claim that what we ought to do is mainly determined by how our actions might affect the very long-run future. A natural objection to longtermism is that these effects may be nearly impossible to predict — perhaps so close to impossible that, despite the astronomical importance of the far future, the expected value of our present actions is mainly determined by near-term considerations. This paper aims to precisify and evaluate one version of this epistemic objection to longtermism. To that (...) end, I develop two simple models for comparing ‘longtermist’ and ‘neartermist’ interventions, incorporating the idea that it is harder to make a predictable difference to the further future. These models yield mixed conclusions: if we simply aim to maximize expected value, and don’t mind premising our choices on minuscule probabilities of astronomical payoffs, the case for longtermism looks robust. But on some prima facie plausible empirical worldviews, the expectational superiority of longtermist interventions depends heavily on these ‘Pascalian’ probabilities. So the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism. (shrink)

Should we make significant sacrifices to ever-so-slightly lower the chance of extremely bad outcomes, or to ever-so-slightly raise the chance of extremely good outcomes? *Fanaticism* says yes: for every bad outcome, there is a tiny chance of extreme disaster that is even worse, and for every good outcome, there is a tiny chance of an enormous good that is even better. I consider two related recent arguments for Fanaticism: Beckstead and Thomas's argument from *strange dependence on space and time*, and (...) Wilkinson's *Indology* argument. While both arguments are instructive, neither is persuasive. In fact, the general principles that underwrite the arguments (a *separability* principle in the first case, and a *reflection* principle in the second) are *inconsistent* with Fanaticism. In both cases, though, it is possible to rehabilitate arguments for Fanaticism based on restricted versions of those principles. The situation is unstable: plausible general principles tell *against* Fanaticism, but restrictions of those same principles (with strengthened auxiliary assumptions) *support* Fanaticism. All of the consistent views that emerge are very strange. (shrink)

We set out longtermist political philosophy as a research field by exploring the case for, and the implications of, ‘institutional longtermism’: the view that, when evaluating institutions, we should give significant weight to their very long-term effects. We begin by arguing that the standard case for longtermism may be more robust when applied to institutions than to individual actions or policies, both because institutions have large, broad, and long-term effects, and because institutional longtermism can plausibly sidestep various objections to individual (...) longtermism. We then address points of contact between longtermism and some central values of mainstream political philosophy, focusing on justice, equality, freedom, legitimacy, and democracy. While each value initially seems to conflict with institutional longtermism, we find that these conflicts are less clear-cut upon closer inspection, and that some political values might even provide independent support for institutional longtermism. We end with a grab bag of related questions that we lack space to explore here. (shrink)

Suppose we want to do the most good we can with a particular sum of money, but we cannot be certain of the consequences of different ways of making use of it. This article explores how our attitudes towards risk and ambiguity bear on what we should do. It shows that risk-avoidance and ambiguity-aversion can each provide good reason to divide our money between various charitable organizations rather than to give it all to the most promising one. It also shows (...) how different attitudes towards risk and ambiguity affect whether we should give to an organization which does a small amount of good for certain or to one which does a large amount of good with some small or unknown probability. (shrink)

A number of philosophers have argued that if you care about how much goodness your actions generate, or how good the state-of-affairs you actions bring about are, then your attention should be directed towards the very far future. But many don’t care about how much goodness their actions generate, nor do they care about things like “states-of-affairs”. Amongst a multitude of things, many people care about how their actions impact individuals. And they also care about the sorts of justifications they (...) are able to offer for those actions. One moral theory which captures this moral viewpoint is contractualism. In this chapter, I argue that contractualism is, in large part, incompatible with longtermism – the view that, in many contexts, we ought to do that which will most improve the prospects of future people. I then discuss what advice, if any at all, contractualism can offer to the longtermist. (shrink)

This paper considers questions that small animals and AI systems raise for utilitarianism. Specifically, if these beings have more welfare than humans and other large animals, then utilitarianism implies that we should prioritize them, all else equal. This could lead to a ‘rebugnant conclusion’, according to which we should, say, create large populations of small animals rather than small populations of large animals. It could also lead to a ‘Pascal’s bugging’, according to which we should, say, prioritize large populations of (...) small animals even if they have a low chance of being sentient. I suggest that utilitarians should accept these implications in theory but might be able to avoid some of them in practice. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

This thesis consists of a series of papers in population ethics: a subfield of normative ethics concerned with the distinctive issues that arise in cases where our actions can affect the identities or number of people of who ever exist. Each paper can be read independently of the others. In Chapter 1, I present a dilemma for Archimedean views in population axiology: roughly, those views on which adding enough good lives to a population can make that population better than any (...) other. In Chapter 2, I extend Gustaf Arrhenius’s famous impossibility theorems in population axiology into the domain of choices under risk. My risky impossibility theorems dispense with the assumption that welfare levels are finitely fine-grained, and so tell against lexical views in population axiology. In Chapter 3, I present objections to critical-level and critical-range views in population axiology. I then sketch out what I call the ‘Imprecise Exchange Rates View’ and argue that it is an attractive alternative. In Chapter 4, I address critical-level and critical-range views again. This time, I note that they are vulnerable to objections from biographical identity: identity between lives. I suggest that these objections give us reason to reject critical-level and critical-range views and embrace the Total View. In Chapter 5, I argue that objections of the same form – objections from personal identity – tell against person-affecting views in population ethics. In Chapter 6, I draw out some counterintuitive implications of two recent complaints-based theories of the procreation asymmetry. (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

Advocates of longtermism point out that interventions which focus on improving the prospects of people in the very far future will, in expectation, bring about a significant amount of good. Indeed, in expectation, such long-term interventions bring about far more good than their short-term counterparts. As such, longtermists claim we have compelling moral reason to prefer long-term interventions. In this paper, I show that longtermism is in conflict with plausible deontic scepticism about aggregation. I do so by demonstrating that, from (...) both an ex-ante and ex-post perspective, longtermist interventions – and, in particular, those which aim to mitigate catastrophic risk – typically generate extremely weak claims of assistance from future people. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

Longtermists claim that what we ought to do is mainly determined by how our actions might affect the very long-run future. A natural objection to longtermism is that these effects may be nearly impossible to predict -- perhaps so close to impossible that, despite the astronomical importance of the far future, the expected value of our present actions is mainly determined by near-term considerations. This paper aims to precisify and evaluate one version of this epistemic objection to longtermism. To that (...) end, I develop two simple models for comparing "longtermist" and "neartermist" interventions, incorporating the idea that it is harder to make a predictable difference to the further future. These models yield mixed conclusions: if we simply aim to maximize expected value, and don't mind premising our choices on minuscule probabilities of astronomical payoffs, the case for longtermism looks robust. But on some prima facie plausible empirical worldviews, the expectational superiority of longtermist interventions depends heavily on these "Pascalian" probabilities. So the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism. (shrink)

Various philosophers accept moral views that are impartial, additive, and risk-neutral with respect to moral betterness. But, if that risk neutrality is spelt out according to expected value theory alone, such views face a dire reductio ad absurdum. If the expected sum of value in humanity's future is undefined--if, e.g., the probability distribution over possible values of the future resembles the Pasadena game, or a Cauchy distribution--then those views say that no option is ever better than any other. And, as (...) I argue, this holds in practice: our evidence supports such a probability distribution. Indeed, it supports a probability distribution that cannot be evaluated even if we adopt one of the various extensions of expected value theory proposed in the literature. Must we therefore reject all impartial, additive, risk-neutral moral theories? It turns out that we need not. I develop an alternative solution: a new method of extending expected value theory, which allows us to deal with this distribution and to salvage those moral views. I also examine how this solution affects one of the most notable implications of those views--namely, longtermism. (shrink)

Can it be rational to be risk-averse? It seems plausible that the answer is yes—that normative decision theory should accommodate risk aversion. But there is a seemingly compelling class of arguments against our most promising methods of doing so. These long-run arguments point out that, in practice, each decision an agent makes is just one in a very long sequence of such decisions. Given this form of dynamic choice situation, and the (Strong) Law of Large Numbers, they conclude that those (...) theories which accommodate risk aversion end up delivering the same verdicts as risk-neutral theories in nearly all practical cases. If so, why not just accept a simpler, risk-neutral theory? The resulting practical verdicts seem to be much the same. In this paper, I show that these arguments do not in fact condemn those risk-aversion-accommodating theories. Risk aversion can indeed survive the long run. (shrink)

Suppose you found that the universe around you was infinite—that it extended infinitely far in space or in time and, as a result, contained infinitely many persons. How should this change your moral decision-making? Radically, it seems, according to some philosophers. According to various recent arguments, any moral theory that is ’minimally aggregative’ will deliver absurd judgements in practice if the universe is (even remotely likely to be) infinite. This seems like sound justification for abandoning any such theory. -/- My (...) goal in this thesis is simple: to demonstrate that we need not abandon minimally aggregative theories, even if we happen to live in an infinite universe. I develop and motivate an extension of such theories, which delivers plausible judgements in a range of realistic cases. I show that this extended theory can overcome key objections—both old and new—and that it succeeds where other proposals do not. With this proposal in hand, we can indeed retain minimally aggregative theories and continue to make moral decisions based on what will promote the good. (shrink)

Expected utility theory often falls silent, even in cases where the correct rankings of options seems obvious. For instance, it fails to compare the Pasadena game to the Altadena game, despite the latter turning out better in every state. Decision theorists have attempted to fill these silences by proposing various extensions to expected utility theory. As I show in this paper, such extensions often fall silent too, even in cases where the correct ranking is intuitively obvious. But we can extend (...) the theory further than has been done before---I offer a new extension, Invariant Value Theory, which deals neatly with those problem cases and also satisfies various desirable conditions. But other prima facie desirable conditions, including Independence, the theory violates. Is this a problem for the proposal? It may not be---in a new impossibility result, I show that no theory can satisfy Independence in full generality without violating several other conditions that together seem just as plausible. (shrink)

1. 1.1. Suffering is bad. This is why, ceteris paribus, there are strong moral reasons to prevent suffering. Moreover, typically, those moral reasons are stronger when the amount of suffering at st...

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)

Philosophers have spent a great deal of time debating whether intransitive preferences can be rational. I present a risky decision that poses a challenge for the defender of intransitivity. The defender of intransitivity faces a trilemma and must either: (i) reject the rationality of intransitive preferences, (ii) deny State-wise Dominance, or (iii) accept the bizarre verdict that you can be required to pay to relabel the tickets of a fair lottery. If we take the first horn, then we have a (...) synchronic refutation of intransitivity, an improvement on widely criticized diachronic arguments. I sketch possible responses that may rescue intransitivity and argue that each response is possible but generates an explanatory debt. I conclude by showing how the challenge here clarifies the foundations of decision theory without transitivity, conditional on some explanatory debt being payable. (shrink)