I present a new puzzle about choice under uncertainty for agents whose preferences are sensitive to multiple dimensions of outcomes in such a way as to be incomplete. In response, I develop a new theory of choice under uncertainty for incomplete preferences. I connect the puzzle to central questions in epistemology about the nature of rational requirements, and ask whether it shows that preferences are rationally required to be complete.

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure (...) subjective probability for partly irrational agents. (shrink)

Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases in (...) which agents have incomplete preferences or imprecise credences). The problem with the all of the decision theories that have been defended to account for parity is that they are committed to a claim I call unanimity: when all of the functions in the set agree that an agent ought to do A, then an agent ought to do A. A decision theory committed to unanimity violates the constraint I defend in this paper. Thus, if parity exists, a new approach to decision theory is necessary. (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.

In an influential paper, L. A. Paul argues that one cannot rationally decide whether to have children. In particular, she argues that such a decision is intractable for standard decision theory. Paul's central argument in this paper rests on the claim that becoming a parent is ``epistemically transformative''---prior to becoming a parent, it is impossible to know what being a parent is like. Paul argues that because parenting is epistemically transformative, one cannot estimate the values of the various outcomes of (...) a decision whether to become a parent. In response, we argue that it is possible to estimate the value of epistemically transformative experiences. Therefore, there is no special difficulty involved in deciding whether to undergo epistemically transformative experiences. Insofar as major life decisions do pose a challenge to decision theory, we suggest that this is because they often involve separate, familiar 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)

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)

We defend three controversial claims about preference, credence, and choice. First, all agents (not just rational ones) have complete preferences. Second, all agents (again, not just rational ones) have real-valued credences in every proposition in which they are confident to any degree. Third, there is almost always some unique thing we ought to do, want, or believe.

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)

Pareto principles are at the core of ethics and decision theory. The Strong Pareto principle says that if one thing is better than another for someone and at least as good for everyone else, then the one is overall better than the other. But a host of famous figures express it differently, with ‘not worse’ in place of ‘at least as good.’ In the presence of parity (or incommensurability), this results in a strictly stronger Pareto principle, which I call Super‐Strong (...) Pareto. Super‐Strong Pareto, however, yields cyclic betterness and is therefore false. I point out a number of influential arguments—concerning population ethics, collective action problems, and decision‐making in the face of parity and uncertainty—that crucially rely on Super‐Strong Pareto and are therefore unsound. I then turn to the most influential argument against the possibility of parity—Broome's collapsing argument—and argue that it likewise relies on Super‐Strong Pareto reasoning and is therefore question‐begging. Finally, I turn to the much‐neglected question of how to justify Strong Pareto. The answer I arrive at, which emphasizes tie‐breaking, yields a striking insight, namely that Super‐Strong Pareto amounts to the denial of insensitivity to mild sweetening. That is what makes it problematic in the presence of parity. (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)

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 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)

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)

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)

A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences.

Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists, and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...) assess several different criteria for individuating and formally representing agents’ choice options. (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)

Moral options are permissions to do less than best, impartially speaking. In this paper, we investigate the challenge of reconciling moral options with the ideal of justifiability to each individual. We examine ex-post and ex-ante views of moral options and show how they might conflict with this ideal in single-choice and sequential-choice cases, respectively. We consider some ways of avoiding this conflict in sequential-choice cases, showing that they face significant problems.

Expected value maximization gives plausible guidance for moral decision‐making under uncertainty in many situations. But it has unappetizing implications in ‘Pascalian’ situations involving tiny probabilities of extreme outcomes. This paper shows, first, that under realistic levels of ‘background uncertainty’ about sources of value independent of one's present choice, a widely accepted and apparently innocuous principle—stochastic dominance—requires that prospects be ranked by the expected value of their consequences in most ordinary choice situations. But second, this implication does not hold when differences (...) in expected value are driven by tiny probabilities of extreme outcomes. Stochastic dominance therefore lets us draw a surprisingly principled line between ‘ordinary’ and ‘Pascalian’ situations, providing a powerful justification for de facto expected value maximization in the former context while permitting deviations in the latter. Drawing this distinction is incompatible with an in‐principle commitment to maximizing expected value, but does not require too much departure from decision‐theoretic orthodoxy: it is compatible, for instance, with the view that moral agents must maximize the expectation of a utility function that is an increasing function of moral value. (shrink)

Some worry that advanced artificial agents may resist being shut down. The Incomplete Preferences Proposal (IPP) is an idea for ensuring that doesn't happen. A key part of the IPP is using a novel 'Discounted REward for Same-Length Trajectories (DREST)' reward function to train agents to (1) pursue goals effectively conditional on each trajectory-length (be 'USEFUL'), and (2) choose stochastically between different trajectory-lengths (be 'NEUTRAL' about trajectory-lengths). In this paper, we propose evaluation metrics for USEFULNESS and NEUTRALITY. We use a (...) DREST reward function to train simple agents to navigate gridworlds, and we find that these agents learn to be USEFUL and NEUTRAL. Our results thus suggest that DREST reward functions could also train advanced agents to be USEFUL and NEUTRAL, and thereby make these advanced agents useful and shutdownable. (shrink)

How should you evaluate your choices when you’re unsure what their outcomes will be? One popular answer is to rank your options in terms of their expected utilities. But what should you do when you think that the value of their respective outcomes might be incommensurable? In the face of incommensurable values, it no longer makes sense to speak of ranking your options according to expected utility. Are there any general principles to guide us when facing decisions of this kind? (...) If only! This chapter develops an impossibility result: it holds that there are a handful of independently plausible constraints that no such decision theory can jointly satisfy. The result, while depressing, can be used to helpfully classify extant approaches based on which of the constraints they violate. (shrink)

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)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter, we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter, we review these different answers, with a special focus on the latter answer and the debate it has generated. (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)