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.

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)

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)

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.

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)

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)

Fanaticism is the view that, for every finite good x and every positive probability p, there is a finite good y such that getting y with probability p is better than getting x for sure. I develop a neglected argument for a form of fanaticism limited to life saving scenarios. I explain how my argument is compatible with some forms of small-probability discounting, imprecise probabilism, risk-aversion and aggregation scepticism. I also try to respond to theoretical problems that fanatical arguments encounter (...) in cases that involve infinitely many possible people. I also suggest why, even if fanaticism is true, we might often be warranted in our intuitive reluctance to accept fanatical conclusions. (shrink)

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)

Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti‐fanatics say you should not. Anti‐fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti‐fanaticism can be turned into a positive argument (...) for a weak version of fanaticism, but only from significantly more contentious premises. In combination, these facts suggest that those who find fanaticism counterintuitive should favor not anti‐fanaticism, but an intermediate position that permits agents to have incomplete preferences that are neither fanatical nor anti‐fanatical. (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)

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)

Various decision theories share a troubling implication. They imply that, for any finite amount of value, it would be better to wager it all for a vanishingly small probability of some greater value. Counterintuitive as it might be, this _fanaticism_ has seemingly compelling independent arguments in its favour. In this paper, I consider perhaps the most _prima facie_ compelling such argument: an _Egyptology argument_ (an analogue of the Egyptology argument from population ethics). I show that, despite recent objections from Russell (...) (Noûs, 2023) and Goodsell (Analysis 81(3):420–426, 2021), the argument’s premises can be justified and defended, and the argument itself remains compelling. (shrink)