Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

Joe Horton argues that partial aggregation yields unacceptable verdicts in cases with risk and multiple decisions. I begin by showing that Horton’s challenge does not depend on risk, since exactly similar arguments apply to riskless cases. The underlying conflict Horton exposes is between partial aggregation and certain principles of diachronic choice. I then provide two arguments against these diachronic principles: they conflict with intuitions about parity, prerogatives, and cyclical preferences, and they rely on an odd assumption about diachronic choice. Finally, (...) I offer an explanation, on behalf of partial aggregation, for why these diachronic principles fail. (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)

The much-discussed ‘Argument from Small Improvement’ has been advanced both as a reason to reject (tripartite) Completeness, one of the standard axioms of decision theory, and to accept the possibility of rationally incomparable choices. But this form of argument cannot be an effective basis for either of these conclusions, unless one already has some prior, independent reason to prefer Transitivity to Completeness as a constraint on rational preferences (or rational values). In particular, I show how a reverse argument from small (...) improvement can be constructed, starting from the assumption of tripartite Completeness, to the conclusion that Transitivity fails. I conclude that this form of argument as it has been standardly presented in the literature is a kind of ‘red herring’. We can only make progress here by evaluating the reasons independent of either such argument to prefer one or other of Transitivity or Completeness. (shrink)

Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we (...) interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology. (shrink)

According to the Welfare Diffusion Objection, we should reject Prioritarianism because it implies the ‘desirability of welfare diffusion’: the claim that it can be better for there to be less total wellbeing spread thinly between a larger total number of people, rather than for there to be more total wellbeing, spread more generously between a smaller total number of people. I argue that while Prioritarianism does not directly imply the desirability of welfare diffusion, Prioritarians are nevertheless implicitly committed to certain (...) principles for comparing different-number populations which, together with the Prioritarian same-person axiology, imply the desirability of welfare diffusion. (shrink)

In this article, I examine the consequences of Mamou’s recent solution to the so-called problem of reindividuation. The problem is first proposed by John Broome as an argument against the Humean view of rationality and subjective decision theory. Essentially, Broome argues that the reindividuation of outcomes must be constrained in some way if the axioms of rationality are not to be vacuous, but the constraints on individuation cannot be consistent with the Humean view of rationality. Mamou offers an elegant Humean (...) solution to this problem. We do not need such rules for reindividuation since the subjective decision theory operates under the assumption of maximal relevance of description, and only under that assumption do the axioms tell anything. Thus the problem of reindividuation dissolves in a quite natural and simple way. However, I argue that if we connect this solution to the topic of justification for the requirements of rationality, problems arise. I examine the influence of the solution on the common argument for the axioms of decision theory, the so-called money-pump arguments. These arguments are a staple in the justification of the axioms of subjective decision theory. I argue that they are in collision with Mamou’s solution. This collision brings us to the dilemma: either accept Broome’s conclusions or lose the money-pump arguments as an effective tool for justification of the axioms. I conclude that neither of the options is really good for the defenders of the Humean view of rationality. (shrink)

A straightforward way to handle moral uncertainty is simply to follow the moral theory in which you have most credence. This approach is known as My Favourite Theory. In this paper, I argue that, in some cases, My Favourite Theory prescribes choices that are, sequentially, worse in expected moral value than the opposite choices according to each moral theory you have any credence in. In addition this, problem generalizes to other approaches that avoid intertheoretic comparisons of value, such as My (...) Favourite Option, the Borda Rule, Variance Normalization, and the Principle of Maximizing Expected Normalized Moral Value. (shrink)