Is an outcome where many people are saved and one person dies better than an outcome where the one is saved and the many die? According to the standard utilitarian justification, the former is better because it has a greater sum total of well-being. This justification involves a controversial form of moral aggregation, because it is based on a comparison between aggregates of different people's well-being. Still, an alternative justification-the Argument for Best Outcomes-does not involve moral aggregation. I extend the (...) Argument for Best Outcomes to show that any utilitarian evaluation can be justified without moral aggregation. (shrink)

Critical-Range Utilitarianism is a variant of Total Utilitarianism which can avoid both the Repugnant Conclusion and the Sadistic Conclusion in population ethics. Yet Standard Critical-Range Utilitarianism entails the Weak Sadistic Conclusion, that is, it entails that each population consisting of lives at a bad well-being level is not worse than some population consisting of lives at a good well-being level. In this paper, I defend a version of Critical-Range Utilitarianism which does not entail the Weak Sadistic Conclusion. This is made (...) possible by a fourth category of absolute value in addition to goodness, badness, and neutrality. (shrink)

One of the principles on how to act under moral uncertainty, My Favourite Theory, says roughly that a morally conscientious agent chooses an option that is permitted by the most credible moral theory. In defence of this principle, we argue that it prescribes consistent choices over time, without relying on intertheoretic comparisons of value, while its main rivals are either plagued by moral analogues of money pumps or in need of a method for making non-arbitrary intertheoretic comparisons. We rebut the (...) arguments that have been levelled against My Favourite Theory and offer some arguments against intertheoretic comparisons of value. (shrink)

The small-improvement argument is usually considered the most powerful argument against comparability, viz the view that for any two alternatives an agent is rationally required either to prefer one of the alternatives to the other or to be indifferent between them. We argue that while there might be reasons to believe each of the premises in the small-improvement argument, there is a conflict between these reasons. As a result, the reasons do not provide support for believing the conjunction of the (...) premises. Without support for the conjunction of the premises, the small-improvement argument for incomparability fails. (shrink)

In this paper, I argue against defining either of ‘good’ and ‘better’ in terms of the other. According to definitions of ‘good’ in terms of ‘better’, something is good if and only if it is better than some indifference point. Against this approach, I argue that the indifference point cannot be defined in terms of ‘better’ without ruling out some reasonable axiologies. Against defining ‘better’ in terms of ‘good’, I argue that this approach either cannot allow for the incorruptibility of (...) intrinsic goodness or it breaks down in cases where both of the relata of ‘better’ are bad. (shrink)

Joshua Gert and Wlodek Rabinowicz have developed frameworks for value relations that are rich enough to allow for non-standard value relations such as parity. Yet their frameworks do not allow for any non-standard preference relations. In this paper, I shall defend a symmetry between values and preferences, namely, that for every value relation, there is a corresponding preference relation, and vice versa. I claim that if the arguments that there are non-standard value relations are cogent, these arguments, mutatis mutandis, also (...) show that there are non-standard preference relations. Hence frameworks of Gert and Rabinowicz's type are either inadequate since there are cogent arguments for both non-standard value and preference relations and these frameworks deny this, or they lack support since the arguments for non-standard value relations are unconvincing. Instead, I propose a simpler framework that allows for both non-standard value and preference relations. (shrink)

Moral obligation and permissibility are usually thought to be interdefinable. Following the pattern of the duality definitions of necessity and possibility, we have that something’s being permissible could be defined as its not being obligatory to not do it. And that something’s being obligatory could be defined as its not being permissible to not do it. In this paper, I argue that neither direction of this alleged interdefinability works. Roughly, the problem is that a claim that some act is obligatory (...) or permissible entails that there is a moral law, whereas a negative claim that some act is not obligatory or not permissible does not. Nevertheless, one direction of the interdefinability can potentially be salvaged. I argue that, if we do not require the conceptual possibility of moral dilemmas, then there is a way to plausibly define obligation in terms of permissibility. I conclude that permissibility is the only feasible deontic primitive. (shrink)

The standard argument for the claim that rational preferences are transitive is the pragmatic money-pump argument. However, a money-pump only exploits agents with cyclic strict preferences. In order to pump agents who violate transitivity but without a cycle of strict preferences, one needs to somehow induce such a cycle. Methods for inducing cycles of strict preferences from non-cyclic violations of transitivity have been proposed in the literature, based either on offering the agent small monetary transaction premiums or on multi-dimensional preferences. (...) This paper argues that previous proposals have been flawed and presents a new approach based on the dominance principle. (shrink)

Prioritarianism is a variant of utilitarianism. It differs from utilitarianism in that benefiting individuals matters more the worse off these individuals are. On this view, there are two standard ways of handling risky prospects: Ex-Post Prioritarianism adjusts for prioritizing the worse off in final outcomes and then values prospects by the expectation of the sum total of those adjusted values, whereas Ex-Ante Prioritarianism adjusts for prioritizing the worse off on each individual’s expectation and then values prospects by the sum total (...) of those adjusted expectations. A standard objection to Ex-Post Prioritarianism is that it violates Ex-Ante Pareto, that is, it prescribes choices that worsen the expectations for everyone. In this paper, I argue that Ex-Ante Prioritarianism suffers from much the same problem: It violates a sequential version of Ex-Ante Pareto, that is, it prescribes sequences of choices that worsen the expectations for everyone. (shrink)

A standard liberal claim is that freedom of choice is not only instrumentally valuable but also intrinsically valuable, that is, valuable for its own sake. I argue that each one of five conditions is plausible if freedom of choice is intrinsically valuable. Yet there exists a counter-example to the conjunction of these conditions. Hence freedom of choice is not intrinsically valuable.

A compelling requirement on normative theories is that they should be satisfiable, that is, in every possible choice situation with a finite number of alternatives, there should be at least one performable act such that, if one were to perform that act, one would comply with the theory. In this paper, I argue that, given some standard assumptions about free will and counterfactuals, Objective Act Consequentialism violates this requirement.

This article develops a new measure of freedom of choice based on the proposal that a set offers more freedom of choice than another if, and only if, the expected degree of dissimilarity between a random alternative from the set of possible alternatives and the most similar offered alternative in the set is smaller. Furthermore, a version of this measure is developed, which is able to take into account the values of the possible options.

In the 1960’s, Lars Bergström and Hector-Neri Castañeda noticed a problem with alternative acts and consequentialism. The source of the problem is that some performable acts are versions of other performable acts and the versions need not have the same consequences as the originals. Therefore, if all performable acts are among the agent’s alternatives, act consequentialism yields deontic paradoxes. A standard response is to restrict the application of act consequentialism to certain relevant alternative sets. Many proposals are based on some (...) variation of maximalism, that is, the view that act consequentialism should only be applied to maximally specific acts. In this paper, I argue that maximalism cannot yield the right prescriptions in some cases where one can either (i) form at once the intention to do an immediate act and form at a later time the intention to do a succeeding act or (ii) form at once the intention to do both acts and where the consequences of (i) and (ii) differ in value. Maximalism also violates normative invariance, that is, the condition that if an act is performable in a situation, then the normative status of the act does not depend on what acts are performed in the situation. Instead of maximalism, I propose that the relevant alternatives should be the exhaustive combinations of acts the agent can jointly perform without performing any other act in the situation. In this way, one avoids the problem of act versions without violating normative invariance. Another advantage is that one can adequately differentiate between possibilities like (i) and (ii). (shrink)

Given reductionism about people, personal persistence must fundamentally consist in some kind of impersonal continuity relation. Typically, these continuity relations can hold from one to many. And, if they can, the analysis of personal persistence must include a non-branching clause to avoid non-transitive identities or multiple occupancy. It is far from obvious, however, what form this clause should take. This paper argues that previous accounts are inadequate and develops a new proposal.

Moral wrongness comes in degrees. On a consequentialist view of ethics, the wrongness of an act should depend, I argue, in part on how much worse the act's consequences are compared with those of its alternatives and in part on how difficult it is to perform the alternatives with better consequences. I extend act consequentialism to take this into account, and I defend three conditions on consequentialist theories. The first is consequentialist dominance, which says that, if an act has better (...) consequences than some alternative act, then it is not more wrong than the alternative act. The second is consequentialist supervenience, which says that, if two acts have equally good consequences in a situation, then they have the same deontic status in the situation. And the third is consequentialist continuity, which says that, for every act and for any difference in wrongness δ greater than zero, there is an arbitrarily small improvement of the consequences of the act which would, other things being equal, not change the wrongness of that act or any alternative by more than δ. I defend a proposal that satisfies these conditions. (shrink)

Erik Carlson puts forward a new way of defining monadic value predicates, such as ‘good’, in terms of dyadic value relations, such as ‘better’. Earlier definitions of this kind have the unwanted feature that they rule out some reasonable axiologies by conceptual fiat. Carlson claims that his definitions do not have this drawback. In this paper, I argue that they do.

In this article, I argue that the small-improvement argument fails since some of the comparisons involved in the argument might be indeterminate. I defend this view from two objections by Ruth Chang, namely the argument from phenomenology and the argument from perplexity. There are some other objections to the small-improvement argument that also hinge on claims about indeterminacy. John Broome argues that alleged cases of value incomparability are merely examples of indeterminacy in the betterness relation. The main premise of his (...) argument is the much-discussed collapsing principle. I offer a new counterexample to this principle and argue that Broome's defence of the principle is not cogent. On the other hand, Nicolas Espinoza argues that the small-improvement argument fails as a result of the mere possibility of evaluative indeterminacy. I argue that his objection is unsuccessful. (shrink)

© Mind Association 2017In a choice between saving five people or saving another person, is it better to save the five, other things being equal? According to utilitarianism, it would be better to save the five if the combined gain in well-being for them would be greater than the loss for the one. A standard objection is that adding up the gains or losses of different people in this manner is a problematic form of interpersonal aggregation. It is far from (...) clear, however, what more precisely is supposed to be problematic about utilitarian aggregation. The aggregation critics—that is, among others, John Rawls, Robert Nozick, Thomas Nagel, John M. Taurek, and T. M. Scanlon—have not offered a clear criterion for what counts as a morally problematic form of aggregation and what does not. Hence it is hard to know what to make of this objection. In Moral Aggregation, Iwao... (shrink)

John Locke’s account of personal identity is usually thought to have been proved false by Thomas Reid’s simple ‘Gallant Officer’ argument. Locke is traditionally interpreted as holding that your having memories of a past person’s thoughts or actions is necessary and sufficient for your being identical to that person. This paper argues that the traditional memory interpretation of Locke’s account is mistaken and defends a memory continuity view according to which a sequence of overlapping memories is necessary and sufficient for (...) personal identity. On this view Locke is not vulnerable to the Gallant Officer argument. (shrink)

Derek Parfit’s argument against the platitude that identity is what matters in survival does not work given his intended reading of the platitude, namely, that what matters in survival to some future time is being identical with someone who is alive at that time. I develop Parfit’s argument so that it works against the platitude on this intended reading.

In an alleged counter-example to the completeness of rational preferences, a career as a clarinettist is compared with a career in law. It seems reasonable to neither want to judge that the law career is at least as preferred as the clarinet career nor want to judge that the clarinet career is at least as preferred as the law career. The two standard interpretations of examples of this kind are, first, that the examples show that preferences are rationally permitted to (...) be incomplete and, second, that the examples show that preferences are rationally permitted to be indeterminate. In this paper, I shall argue that the difference between these interpretations is crucial for the money-pump argument for transitivity, which is the standard argument that rational preferences are transitive. I shall argue that the money-pump argument for transitivity fails if preferences are rationally permitted to be incomplete but that it works if preferences are rationally permitted to be indeterminate and rationally required to be complete. (shrink)

In this paper we shed new light on the Argument from Disagreement by putting it to test in a computer simulation. According to this argument widespread and persistent disagreement on ethical issues indicates that our moral opinions are not influenced by any moral facts, either because no such facts exist or because they are epistemically inaccessible or inefficacious for some other reason. Our simulation shows that if our moral opinions were influenced at least a little bit by moral facts, we (...) would quickly have reached consensus, even if our moral opinions were affected by factors such as false authorities, external political shifts, and random processes. Therefore, since no such consensus has been reached, the simulation gives us increased reason to take seriously the Argument from Disagreement. Our conclusion is however not conclusive; the simulation also indicates what assumptions one has to make in order to reject the Argument from Disagreement. The simulation algorithm we use builds on the work of Hegselmann and Krause (J Artif Soc Social Simul 5(3); 2002, J Artif Soc Social Simul 9(3), 2006). (shrink)

According to the Psychological-Continuity Account of What Matters, you are justified in having special concern for the well-being of a person at a future time if and only if that person will be psychologically continuous with you as you are now. On some versions of the account, the psychological continuity is required be temporally ordered, whereas, on other versions, it is allowed to be temporally unordered. In this paper, I argue that the account is implausible if the psychological continuity is (...) allowed to be temporally unordered. I also argue that, if the psychological continuity is required to be temporally ordered, it cannot plausibly be purely psychological (in the sense that the psychological continuity is not required to be caused through spatio-temporal continuity of a brain). The upshot is that no plausible version of the Psychological-Continuity Account of What Matters is purely psychological. So psychological continuity is not what matters in survival. (shrink)

Andy Egan argues that neither evidential nor causal decision theory gives the intuitively right recommendation in the cases The Smoking Lesion, The Psychopath Button, and The Three-Option Smoking Lesion. Furthermore, Egan argues that we cannot avoid these problems by any kind of ratificationism. This paper develops a new version of ratificationism that gives the right recommendations. Thus, the new proposal has an advantage over evidential and casual decision theory and standard ratificationist evidential decision theory.

The aim of the Consequence Argument is to show that, if determinism is true, no one has, or ever had, any choice about anything. In the stock version of the argument, its two premisses state that no one is, or ever was, able to act so that the past would have been different and no one is, or ever was, able to act so that the laws of nature would have been different. This stock version fails, however, because it requires (...) an invalid inference rule. The standard response is to strengthen both premisses by replacing ‘would’ with ‘might’. While this response ensures validity, it weakens the argument, since it strengthens the premisses. I show that we can do better: We can keep the weak reading of one premiss and just strengthen the other. This provides two versions of the Consequence Argument which are stronger than the standard revision. (shrink)

The money-pump argument is the standard argument for the acyclicity of rational preferences. The argument purports to show that agents with cyclic preferences are in some possible situations forced to act against their preference. In the usual, diachronic version of the money-pump argument, such agents accept a series of trades that leaves them worse off than before. Two stock objections are (i) that one may get the drift and refuse the trades and (ii) that one may adopt a plan to (...) only accept some of the trades. This article argues that these objections are irrelevant. If the diachronic money-pump argument is cogent, so is a more direct synchronic argument. The upshot is that the standard objections to the diachronic money-pump argument do not affect this simpler synchronic argument. Hence the standard objections to the money-pump argument for acyclicity are irrelevant. (shrink)

John Rawls argues that the Difference Principle would be chosen by parties trying to advance their individual interests behind the Veil of Ignorance. Behind this veil, the parties do not know who they are and they are unable to assign or estimate probabilities to their turning out to be any particular person in society. Much discussion of Rawls’s argument concerns whether he can plausibly rule out the parties’ having access to probabilities about who they are. Nevertheless, I argue that, even (...) if the parties lacked access to probabilities about who they are in society, they would still reject the Difference Principle. I argue that there are cases where it is still clear to the parties that it is not in any of their individual interests that the Difference Principle is adopted. (shrink)

If ‘F’ is a predicate, then ‘Fer than’ or ‘more F than’ is a corresponding comparative relational predicate. Concerning such comparative relations, John Broome’s Collapsing Principle states that, for any x and y, if it is false that y is Fer than x and not false that x is Fer than y, then it is true that x is Fer than y. Luke Elson has recently put forward two alleged counter-examples to this principle, allegedly showing that it yields contradictions if (...) there are borderline cases. In this paper, I argue that the Collapsing Principle does not rule out borderline cases, but I also argue that it is implausible. (shrink)

Any theory that analyses personal identity in terms of phenomenal continuity needs to deal with the ordinary interruptions of our consciousness that it is commonly thought that a person can survive. This is the bridge problem. The present paper offers a novel solution to the bridge problem based on the proposal that dreamless sleep need not interrupt phenomenal continuity. On this solution one can both hold that phenomenal continuity is necessary for personal identity and that persons can survive dreamless sleep.

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

The Levelling-Down Objection is a standard objection to monistic egalitarian theories where equality is the only thing that has intrinsic value. Most egalitarians, however, are value pluralists; they hold that, in addition to equality being intrinsically valuable, the egalitarian currency in which we are equal or unequal is also intrinsically valuable. In this paper, I shall argue that the Levelling-Down Objection still minimizes the weight that the intrinsic badness of inequality could have in the overall intrinsic evaluation of outcomes, given (...) a certain way of measuring the badness of inequality, namely, the Additive Individual-Complaints Measure. (shrink)

Jeremy Bentham is often interpreted as defending a satisficing, rather than maximizing, version of utilitarianism, where an act is right as long as it produces more pleasure than pain. This lack of maximization is surprising given Bentham’s maximizing slogan ‘the greatest happiness of the greatest number’. Against the satisficing interpretation, I argue that Bentham consistently defends a maximizing version of utilitarianism, where an act’s consequences are compared to those of not performing the act. I show that following this version of (...) utilitarianism requires that one realizes the greatest happiness for all affected individuals. (shrink)

One might think that money pumps directed at agents with cyclic preferences can be avoided by foresight. This view was challenged two decades ago by the discovery of a money pump with foresight, which works against agents who use backward induction. But backward induction implausibly assumes that the agent would act rationally and retain her trust in her future rationality even at choice nodes that could only be reached if she were to act irrationally. This worry does not apply to (...) BI-terminating decision problems, where at each choice node backward induction prescribes a move that terminates further action. For BI-terminating decision problems, it is enough to assume that rationality and trust in rationality are retained at choice nodes reachable by rational moves. The old money pump with foresight was not BI-terminating. In this paper, we present a new money pump with foresight, one that is both BI-terminating and considerably simpler. (shrink)

According to T. M. Scanlon’s anti-aggregation principle, it is wrong to save a larger number of people from minor harms rather than a smaller number from much more serious harms. This principle is a central part of many influential and anti-utilitarian ethical theories. According to the sequential-dominance principle, one does something wrong if one knowingly performs a sequence of acts whose outcome would be worse for everyone than the outcome of an alternative sequence of acts. The intuitive appeal of the (...) sequential-dominance principle should be obvious; everyone is knowingly made worse off if it is violated. In this paper, I present a number of cases where one is forced to violate either the anti-aggregation principle or the sequential-dominance principle. I show that these principles conflict regardless of whether one accepts a counterfactual or a temporal, worsening view of harm. Moreover, I show that this result holds regardless of how much worse a harm has to be in order to count as a much more serious harm. (shrink)

Daniel C. Dennett has long maintained that the Consequence Argument for incompatibilism is confused. In a joint work with Christopher Taylor, he claims to have shown that the argument is based on a failure to understand Logic 101. Given a fairly plausible account of having the power to cause something, they claim that the argument relies on an invalid inference rule. In this paper, I show that Dennett and Taylor’s refutation does not work against a better, more standard version of (...) the Consequence Argument. Therefore, Dennett and Taylor’s alleged refutation fails. (shrink)

Kurt Gödel’s version of the Ontological Proof derives rather than assumes the crucial Possibility Claim: the claim that it is possible that something God-like exists. Gödel’s derivation starts off with a proof of the Possible Instantiation of the Positive: the principle that, if a property is positive, it is possible that there exists something that has that property. I argue that Gödel’s proof of this principle relies on some implausible axiological assumptions but it can be patched so that it only (...) relies on plausible principles. But Gödel’s derivation of the Possibility Claim also needs a substantial axiological assumption, which is still open to doubt. (shrink)

In order to account for non-traditional preference relations the present paper develops a new, richer framework for preference relations. This new framework provides characterizations of non-traditional preference relations, such as incommensurateness and instability, that may hold when neither preference nor indifference do. The new framework models relations with swaps, which are conceived of as transfers from one alternative state to another. The traditional framework analyses dyadic preference relations in terms of a hypothetical choice between the two compared alternatives. The swap (...) framework extends this approach by analysing dyadic preference relations in terms of two hypothetical choices: the choice between keeping the first of the compared alternatives or swapping it for the second; and the choice between keeping the second alternative or swapping it for the first. (shrink)

This thesis consists of an introduction and five essays on decision theory.

In order to account for non-traditional preference relations the present paper develops a new, richer framework for preference relations. This new framework provides characterizations of non-traditional preference relations, such as incommensurateness and instability, that may hold when neither preference nor indifference do. The new framework models relations with swaps, which are conceived of as transfers from one alternative state to another. The traditional framework analyses dyadic preference relations in terms of a hypothetical choice between the two compared alternatives. The swap (...) framework extends this approach by analysing dyadic preference relations in terms of two hypothetical choices: the choice between keeping the first of the compared alternatives or swapping it for the second; and the choice between keeping the second alternative or swapping it for the first. (shrink)

The Repugnant Conclusion served an important purpose in catalyzing and inspiring the pioneering stage of population ethics research. We believe, however, that the Repugnant Conclusion now receives too much focus. Avoiding the Repugnant Conclusion should no longer be the central goal driving population ethics research, despite its importance to the fundamental accomplishments of the existing literature.

In order to account for non-traditional preference relations the present paper develops a new, richer framework for preference relations. This new framework provides characterizations of non-traditional preference relations, such as incommensurateness and instability, that may hold when neither preference nor indifference do. The new framework models relations with swaps, which are conceived of as transfers from one alternative state to another. The traditional framework analyses dyadic preference relations in terms of a hypothetical choice between the two compared alternatives. The swap (...) framework extends this approach by analysing dyadic preference relations in terms of two hypothetical choices: the choice between keeping the first of the compared alternatives or swapping it for the second; and the choice between keeping the second alternative or swapping it for the first. (shrink)

In a recently published paper entitled, “The Difference Principle Would Not Be Chosen behind the Veil of Ignorance”, Johan E. Gustafsson attempts to demonstrate that the parties in Rawls’s original position would not choose the difference principle. Gustafsson’s main strategy was to show that Rawls’s difference principle in both of its ex post and ex ante versions imply counterintuitive distributional prescriptions in a few contrived examples. The purpose of this paper is to precisely demonstrate exactly how (...) class='Hi'>Gustafsson’s arguments have failed to show that the difference principle would not be chosen behind the veil of ignorance. (shrink)

In “The Difference Principle Would Not Be Chosen behind the Veil of Ignorance,” Johan E. Gustafsson argues that the parties in the Original Position would not choose the Difference Principle to regulate their society’s basic structure. In reply to this internal critique, we provide two arguments. First, his choice models do not serve as a counterexample to the choice of the difference principle, as the models must assume that individual rationality scales to collective contexts in a way that (...) begs the question in favor of utilitarianism. Second, the choice models he develops are incompatible with the constraints of fairness that apply in the OP, which by design subordinates claims of rationality to claims of impartiality. When the OP is modeled correctly the difference principle is indeed entailed by the conditions of the OP. (shrink)

In “The Irrelevance of the Diachronic Money-Pump Argument for Acyclicity,” The Journal of Philosophy CX, 8 (August 2013), 460-464, Johan E. Gustafsson contends that if Davidson, McKinsey and Suppes’ diachronic money-pump argument in their "Outlines of a Formal Theory of Value, I," Philosophy of Science 22 (1955), 140-160 is valid, so is the synchronic argument Gustafsson himself offers. He concludes that the latter renders irrelevant diachronic choice considerations in general, and the two best-known diachronic solutions to the (...) money pump problem in particular. I argue here that this reasoning is incorrect, and that Gustafsson’s synchronic argument is faulty on independent grounds. Specifically, it is based on a false analogy between the derivation of a synchronic ordinal ranking from a transitive series of pairwise comparisons, and the putative derivation of such a ranking from an intransitive series. The latter is not possible under the assumption of revealed preference theory, and is highly improbable even if that assumption is rejected. Moreover, Gustafsson’s argument raises issues of fidelity to the historical texts that must be addressed. I conclude that the money pump, and cyclical choice more generally, are necessarily diachronic; and therefore that the two best-known diachronic solutions to the money pump problem remain relevant. (shrink)