Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and multi-stage (...) aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three. (shrink)

Is the overall value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say 'yes', but non-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction appears to be practically important: among other things, additive axiologies generally assign great importance to large changes in population size, and therefore tend to strongly prioritize the long-term survival of humanity over (...) the interests of the present generation. Non-additive axiologies, on the other hand, need not assign great importance to large changes in population size. We show, however, that when there is a large enough `background population' unaffected by our choices, a wide range of non-additive axiologies converge in their implications with additive axiologies—for instance, average utilitarianism converges with critical-level utilitarianism and various egalitarian theories converge with prioritarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from the scale of potential future populations for the astronomical importance of avoiding existential catastrophe, and other arguments in practical ethics that seem to presuppose additive separability, may succeed in practice whether or not we accept additive separability as a basic axiological principle. (shrink)

Standard decision theory has trouble handling cases involving acts without finite expected values. This paper has two aims. First, building on earlier work by Colyvan (2008), Easwaran (2014), and Lauwers and Vallentyne (2016), it develops a proposal for dealing with such cases, Difference Minimizing Theory. Difference Minimizing Theory provides satisfactory verdicts in a broader range of cases than its predecessors. And it vindicates two highly plausible principles of standard decision theory, Stochastic Equivalence and Stochastic Dominance. The second aim is to (...) assess some recent arguments against Stochastic Equivalence and Stochastic Dominance. If successful, these arguments refute Difference Minimizing Theory. This paper contends that these arguments are not successful. (shrink)

Is the overall value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say 'yes', but non-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction is practically important: additive axiologies support 'arguments from astronomical scale' which suggest (among other things) that it is overwhelmingly important for humanity to avoid premature extinction and ensure the existence of a (...) large future population, while non-additive axiologies need not. We show, however, that when there is a large enough 'background population' unaffected by our choices, a wide range of non-additive axiologies converge in their implications with some additive axiology -- for instance, average utilitarianism converges to critical-level utilitarianism and various egalitarian theories converge to prioritiarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from astronomical scale, and other arguments in practical ethics that seem to presuppose additive separability, may be truth-preserving in practice whether or not we accept additive separability as a basic axiological principle. (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)

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely _infinitely large_, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value so, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. (...) This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is _relative_. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute. So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. (shrink)

Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “Direct Difference Taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...) a proposal offered by Arntzenius :31–58, 2014). I argue that while Arntzenius’s proposal has many attractive features, it runs into a number of problems which Direct Difference Taking avoids. (shrink)

Suppose that an altruistic agent who is uncertain between evidential and causal decision theory finds herself in a situation where these theories give conflicting verdicts. We argue that even if she has significantly higher credence in CDT, she should nevertheless act in accordance with EDT. First, we claim that the appropriate response to normative uncertainty is to hedge one's bets. That is, if the stakes are much higher on one theory than another, and the credences you assign to each of (...) these theories are not very different, then it is appropriate to choose the option that performs best on the high-stakes theory. Second, we show that, given the assumption of altruism, the existence of correlated decision makers will increase the stakes for EDT but leave the stakes for CDT unaffected. Together these two claims imply that whenever there are sufficiently many correlated agents, the appropriate response is to act in accordance with EDT. (shrink)

It is widely assumed that a literal understanding of someone’s self-deception that p yields the following contradiction. Qua self-deceiver, she does not believe that p, yet – qua self-deceived – she does believe that p. I argue that this assumption is ill-founded. Literalism about self-deception – the view that self-deceivers literally self-deceive – is not committed to this contradiction. On the contrary, properly understood, literalism excludes it.

We show that in infinite worlds the following three conditions are incompatible: The spatiotemporal ordering of individuals is morally irrelevant. All else being equal, the act of bringing about a good outcome with a high probability is better than the act of bringing about the same outcome with a low probability. One act is better than another only if there is a nonzero probability that it brings about a better outcome. The impossibility of combining these conditions shows that it is (...) more costly to endorse than has been previously acknowledged. (shrink)

Our universe is both chaotic and (most likely) infinite in space and time. But it is within this setting that we must make moral decisions. This presents problems. The first: due to our universe's chaotic nature, our actions often have long-lasting, unpredictable effects; and this means we typically cannot say which of two actions will turn out best in the long run. The second problem: due to the universe's infinite dimensions, and infinite population therein, we cannot compare outcomes by simply (...) adding up their total moral values - those totals will typically be infinite or undefined. Each of these problems poses a threat to aggregative moral theories. But, for each, we have solutions: a proposal from Greaves let us overcome the problem of chaos, and proposals from the infinite aggregation literature let us overcome the problem of infinite value. But a further problem emerges. If our universe is both chaotic and infinite, those solutions no longer work - outcomes that are infinite and differ by chaotic effects are incomparable, even by those proposals. In this paper, I show that we can overcome this further problem. But, to do so, we must accept some peculiar implications about how aggregation works. (shrink)

How should an agent decide what to do when she is uncertain not just about morally relevant empirical matters, like the consequences of some course of action, but about the basic principles of morality itself? This question has only recently been taken up in a systematic way by philosophers. Advocates of moral hedging claim that an agent should weigh the reasons put forward by each moral theory in which she has positive credence, considering both the likelihood that that theory is (...) true and the strength of the reasons it posits. The view that it is sometimes rational to hedge for one's moral uncertainties, however, has recently come under attack both from those who believe that an agent should always be guided by the dictates of the single moral theory she deems most probable and from those who believe that an agent's moral beliefs are simply irrelevant to what she ought to do. Among the many objections to hedging that have been pressed in the recent literature is the worry that there is no non-arbitrary way of making the intertheoretic comparisons of moral value necessary to aggregate the value assignments of rival moral theories into a single ranking of an agent's options. -/- This dissertation has two principal objectives: First, I argue that, contra these recent objections, an agent's moral beliefs and uncertainties are relevant to what she rationally ought to do, and more particularly, that agents are at least sometimes rationally required to hedge for their moral uncertainties. My principal argument for these claims appeals to the enkratic conception of rationality, according to which the requirements of practical rationality derive from an agent's beliefs about the objective, desire-independent value or choiceworthiness of her options. Second, I outline a new general theory of rational choice under moral uncertainty. Central to this theory is the idea of content-based aggregation, that the principles according to which an agent should compare and aggregate rival moral theories are grounded in the content of those theories themselves, including not only their value assignments but also the metaethical and other non-surface-level propositions that underlie, justify, or explain those value assignments. (shrink)