There are 1,000 of us and one victim. We each increase the level at which a "discomfort machine" operates on the victim---leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the "no-difference argument" the answer is "yes" because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because if it is sound, similar arguments threaten (...) intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle---an objection that avoids challenges that have been brought against previous criticisms of the no difference argument. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

Ruth Chang and Joseph Raz have both drawn far-reaching consequences for agency from the phenomenon of incommensurability. After criticizing their arguments, I outline an alternative view: if incommensurability is vagueness, then there are no substantial implications for agency, except perhaps a limited form of naturalistic voluntarism if our reasons are provided by desires.

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.

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

Politics, Philosophy & Economics, Volume 21, Issue 4, Page 347-371, November 2022. We sometimes have to choose between options that are seemingly incomparable insofar as they seem to be neither better than, worse than, nor equal to each other. This often happens when the available options are quite different from one another. For instance, consider a choice between prioritizing either criminal justice reform or healthcare reform as a public policy goal. Even after the relevant details of the goals and possible (...) reforms are filled in, it is plausible that neither goal is better than, worse than, nor equal to the other. Such seemingly incomparable options present a problem for rational choice since it is unclear how an agent might rationally choose between them. What we need are some principles to help govern rational choice when faced with seemingly incomparable options. I here present three such principles. While each principle is individually compelling, I show that they are jointly incompatible. I then argue that the correct response to this inconsistent triad is to reject the principle that rationally censures performing a sequence of choices one knows will result in a suboptimal outcome. The upshot is that when seeming incomparability is involved, an agent can money pump themselves without being less rational for it. (shrink)

Sometimes it is indeterminate what an agent morally ought do. This generates a Decision Ought Challenge—to give moral guidance to agents in such a scenario. This article is a field guide to the options for a theory of the decision ought for cases of indeterminacy. Three categories of view are evaluated, and the best representative for each is identified.

Which is better: a guarantee of a modest amount of moral value, or a tiny probability of arbitrarily large value? To prefer the latter seems fanatical. But, as I argue, avoiding such fanaticism brings severe problems. To do so, we must decline intuitively attractive trade-offs; rank structurally identical pairs of lotteries inconsistently, or else admit absurd sensitivity to tiny probability differences; have rankings depend on remote, unaffected events ; and often neglect to rank lotteries as we already know we would (...) if we learned more. Compared to these implications, fanaticism is highly plausible. (shrink)

How should we make choices where the values we subscribe to give conflicting recommendations? I will be defending a reduction of decision making under conflict to decision making under indeterminacy, in the spirit of Broome. To defend this, I set out and endorse the basic features of decision making under conflict that Ruth Chang identifies. I show that we find exactly those features in cases of decision making under indeterminacy not involving conflicting values. Further, my theory of decision making under (...) indeterminacy predicts and explains these features. Particular attention will be paid to the aspect that Chang emphasizes as the decisive problem for the Broomean reduction: the resolutional residue, or angst, that decision making under conflict evinces. (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)

How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that worlds are made better if we increase the value in every region of space and time, or that they are made better if we (...) increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most. (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)

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)

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)

The endeavour to locate value in moral progress faces various substantive as well as more formal challenges. This paper focuses on challenges of the latter kind. After some preliminaries, Section 3 introduces two general kinds of “evaluative moral progress-claims”, and outlines a possible novel analysis of a descriptive notion of moral progress. While Section 4 discusses certain logical features of betterness in light of recent work in value theory which are pertinent to the notion of moral progress, Sections 5 and (...) 6 outline the ambiguous character of “making moral progress”. (shrink)

According to the mixed lexicographic/additive account of ‘better than’ and similar aggregative value comparatives like ‘healthier than’, values are multidimensional and different aspects of a value are aggregated into an overall assessment in a lexicographic way, based on an ordering of value aspects. It is argued that this theory can account for an acceptable definition of Chang’s notion of parity and that it also offers a solution to Temkin’s and Rachels’s Spectrum Cases without giving up the transitivity of overall betterness. (...) Formal details and proofs are provided in an “Appendix”. (shrink)

How should one understand comparisons in which neither of two alternatives is at least as good as the other? Much recent literature on comparability problems focuses on what the appropriate explanation of the phenomenon is. Is it due to vagueness or the possibility of non-conventional comparative relations such as parity? This paper argues that the discussions on how to best explain comparability problems has reached an impasse at which it is hard to make any progress. To advance the discussion we (...) suggest a new classification of comparability problems that focuses on the problems they cause for practical reasoning. (shrink)

Many consequentialists argue that you ought to do your part in collective action problems like climate change mitigation and ending factory farming because (i) all such problems are triggering cases, in which there is a threshold number of people such that the outcome will be worse if at least that many people act in a given way than if fewer do, and (ii) doing your part in a triggering case maximises expected value. I show that both (i) and (ii) are (...) false: Some triggering cases cannot be solved by appeal to expected value, since they involve infinities, and some collective action problems are not triggering cases, since they involve parity. However, I argue that consequentialism can still generally prohibit failure to do your part in those collective action problems where we believe that so acting would be impermissible. (shrink)

In “An Intrapersonal Addition Paradox,” Jacob Nebel provides a novel intrapersonal argument for the Repugnant Conclusion. The most controversial premise of Nebel’s argument is the “Probable Addition Principle,” on which it is better for individuals to receive additional chances of existence with a life worth living. I provide an alternative intrapersonal argument for the Repugnant Conclusion which does not assume the Probable Addition Principle. I also show that Pareto principles alone, when conjoined with very minimal principles of prudence, imply a (...) version of the Repugnant Conclusion. (shrink)

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (shrink)

Let’s say that you regard two things as on a par when you don’t prefer one to other and aren’t indifferent between them. What does rationality require of you when choosing between risky options whose outcomes you regard as on a par? According to Prospectism, you are required to choose the option with the best prospects, where an option’s prospects is a probability-distribution over its potential outcomes. In this paper, I argue that Prospectism violates a dominance principle—which I call The (...) Principle of Predominance—because it sometimes requires you to do something that’s no better than the alternatives and might be worse. I argue that this undermines the strongest argument that’s been given in favor of Prospectism. (shrink)

I argue that any plausible decision theory for agents with incomplete preferences which obeys the Never Worse Principle will violate Transitivity. The Never Worse Principle says that if one option never does worse than another, you shouldn’t disprefer it. Transitivity says that if you prefer X to Y and you prefer Y to Z, then you should prefer X to Z. Violating Transitivity allows one to be money pumped. Although agents with incomplete preferences are already, in virtue of having incomplete (...) preferences, vulnerable to being money pumped, I argue that the money pump argument for Transitivity is more serious than the one for Completeness. (shrink)

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about what (...) it is to be a rational agent. (shrink)

Metanormativists hold that moral uncertainty can affect how we ought, in some morally authoritative sense, to act. Many metanormativists aim to generalize expected utility theory for normative uncertainty. Such accounts face the “easy problem of intertheoretic comparisons”: the worry that distinct theories’ assessments of choiceworthiness are incomparable. The easy problem may well be resolvable, but another problem looms: while some moral theories assign cardinal degrees of choiceworthiness, other theories’ choiceworthiness assignments are merely ordinal. Expected choiceworthiness over such theories is undefined. (...) Call this the “hard problem of intertheoretic comparisons.” This paper argues that to solve the hard problem, we should model moral theories with imprecise choiceworthiness. Imprecise choiceworthiness assignments can model incomplete cardinal information about choiceworthiness, with precise cardinal choiceworthiness and merely ordinal choiceworthiness as limiting cases. Generalizing familiar decision theories for imprecise choiceworthiness to the case of moral uncertainty generates puzzles, however: natural generalizations seem to require reifying parts of the model that don’t correspond to anything in normative reality. I discuss three ways of addressing this problem: by demystifying the reified elements by using them as promiscuously as possible; by constructing alternative decision theories that don’t require the troublesome elements; and by employing an alternative model of metanormative decision problems, and of moral uncertainty generally. (shrink)

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)

ABSTRACTThis paper addresses the problem of opaque sweetening and argues that one should use stochastic dominance in comparing lotteries even when dealing with incomplete orderings that allow for non-comparable outcomes.

This paper argues that evidential decision theory is incompatible with options having objective values. If options have objective values, then it should always be rationally permissible for an agent to choose an option if they are certain that the option uniquely maximizes objective value. But, as we show, if options have objective values and evidential decision theory is true, then it is not always rationally permissible for an agent to choose an option if they are certain that the option uniquely (...) maximizes objective value. (shrink)

How should we weigh suffering against happiness? This paper highlights the existence of an argument from intuitively plausible axiological principles to the striking conclusion that in comparing different populations, there exists some depth of suffering that cannot be compensated for by any measure of well-being. In addition to a number of structural principles, the argument relies on two key premises. The first is the contrary of the so-called Reverse Repugnant Conclusion. The second is a principle according to which the addition (...) of any population of lives with positive welfare levels makes the outcome worse if accompanied by sufficiently many lives that are not worth living. I consider whether we should accept the conclusion of the argument and what we may end up committed to if we do not, illustrating the implications of the conclusions for the question of whether suffering in aggregate outweighs happiness among human and non-human animals, now and in future. GPI Working Paper No . 4-2022 . (shrink)

This thesis consists of several independent papers in population ethics. I begin in Chapter 1 by critiquing some well-known 'impossibility theorems', which purport to show there can be no intuitively satisfactory population axiology. I identify axiological vagueness as a promising way to escape or at least mitigate the effects of these theorems. In particular, in Chapter 2, I argue that certain of the impossibility theorems have little more dialectical force than sorites arguments do. From these negative arguments I move to (...) positive ones. In Chapter 3, I justify the use of a 'veil of ignorance', starting from three more basic normative principles. This leads to positive arguments for various kinds of utilitarianism - the best such arguments I know. But in general the implications of the veil depend on how one answers what I call 'the risky existential question': what is the value to an individual of a chance of non-existence? I chart out the main options, and raise some puzzles for non-comparativism, the view that life is incomparable to non-existence. Finally, in Chapter 4, I consider the consequences for population ethics of the idea that what is normatively relevant is not personal identity, but a degreed relation of psychological connectedness. In particular, I pursue a strategy based in population ethics for understanding the controversial 'time-relative interests' account of the badness of death. (shrink)

One of the main lines of research in algorithmic fairness involves individual fairness (IF) methods. Individual fairness is motivated by an intuitive principle, similar treatment, which requires that similar individuals be treated similarly. IF offers a precise account of this principle using distance metrics to evaluate the similarity of individuals. Proponents of individual fairness have argued that it gives the correct definition of algorithmic fairness, and that it should therefore be preferred to other methods for determining fairness. I argue that (...) individual fairness cannot serve as a definition of fairness. Moreover, IF methods should not be given priority over other fairness methods, nor used in isolation from them. To support these conclusions, I describe four in-principle problems for individual fairness as a definition and as a method for ensuring fairness: (1) counterexamples show that similar treatment (and therefore IF) are insufficient to guarantee fairness; (2) IF methods for learning similarity metrics are at risk of encoding human implicit bias; (3) IF requires prior moral judgments, limiting its usefulness as a guide for fairness and undermining its claim to define fairness; and (4) the incommensurability of relevant moral values makes similarity metrics impossible for many tasks. In light of these limitations, I suggest that individual fairness cannot be a definition of fairness, and instead should be seen as one tool among several for ameliorating algorithmic bias. (shrink)

This paper presents a decision problem called the holiday puzzle. The decision problem is one that involves incommensurable goods and sequences of choices. This puzzle points to a tension between three prima facie plausible, but jointly incompatible claims. I present a way out of the trilemma which demonstrates that it is possible for agents to have incomplete preferences and to be dynamically rational. The solution also suggests that the relationship between preference and rational permission is more subtle than standardly assumed.