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)

Why should ‘better than’ be transitive? The leading answer in ethics is that values do not change with context. But this cannot be the entire source of transitivity, I argue, since transitivity can fail even if values never change, so long as they are complex, with multiple dimensions combined non-additively. I conclude by exploring a new hypothesis: that all alleged cases of nontransitive betterness, such as Parfit’s Repugnant Conclusion, can and should be modelled as the result of complexity, not context-relativity.

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...) assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (shrink)

John Taurek argues that, in a choice between saving the many or the few, the numbers should not count. Some object that this view clashes with the transitivity of ‘better than’; others insist the clash can be avoided. I defend a middle ground: Taurek cannot have transitivity, but that doesn’t doom his view, given a suitable conception of value. I then formalize and explore two conceptions: one context-sensitive, one multidimensional.

According to the mixed lexicographic/additive account of ‘better than’ and similar aggregative value comparatives like ‘healthier than’, values are multidimensional and different aspects of a value are aggregated into an overall assessment in a lexicographic way, based on an ordering of value aspects. It is argued that this theory can account for an acceptable definition of Chang’s notion of parity and that it also offers a solution to Temkin’s and Rachels’s Spectrum Cases without giving up the transitivity of overall betterness. (...) Formal details and proofs are provided in an “Appendix”. (shrink)

The voting paradox occurs when a democratic society seeking to aggregate individual preferences into asocialpreference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for anindividualaggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and (...) economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified. (shrink)

This thesis discusses the possibility of limited moral trade-offs between different people’s welfare. In chapter 2, I introduce the two central limited trade-off conditions. First, according to minimal infinite superiority, significantly benefiting one person matters more than slightly benefiting each of any number of better-off people. Second, according to minimal finite superiority, significantly benefiting many people matters more than slightly benefiting one person. I consider both axiological and deontic interpretations of these conditions. However, I explain why none of the simple (...) classic moral principles—the simple total and the maximin principles—satisfy both conditions. Furthermore, in chapter 3, I strengthen several proved impossibility results according to which no moral theory satisfies weak interpretations of these central trade-off conditions and several other seemingly plausible minimal conditions. I show that giving up structural axiological and deontic conditions is not a satisfactory solution to these paradoxes. In chapter 4, I discuss the modification of a background assumption of these impossibility results on the measurement of welfare. I show that, given a modification that allows for lexicographically ordered welfare components, a total principle can satisfy all the conditions of the impossibility results. However, I argue that such a modification is not entirely satisfactory because it does not apply in certain instances of the paradoxes. In chapter 5, I discuss a further weakening of minimal infinite superiority. However, I show that a suggested possibility result based on this modification is not valid and that further moral conditions, such as minimal finite superiority, need to be modified. Moreover, I argue that these modified conditions and the principle suggested in the possibility proof—a minimax complaint principle—do not capture the basic idea of the two central limited trade-off conditions sufficiently well. In chapter 6, I argue that other principles suggested for the task—the total claim principles—share the same fate as the simple total principles or the minimax complaint principle. In chapter 7, I propose new principles that take their structural roots from voting theory. I show that, in contrast to the other principles discussed, these principles give plausible verdicts where the other principles failed. Finally, in chapter 8, I consider possible objections levelled against this proposal, and I suggest solutions and avenues for future research. (shrink)

Temkin's Essentially Comparative View of moral ideals says that goodness is comparison set dependent: the goodness of an outcome is relativized to a set of outcomes. This view does not entail that betterness is intransitive; indeed, it provides the resources for maintaining transitivity. However, it does entail that the structure of goodness is more complex than is standardly supposed. It thereby demands a modification of the standard connection between goodness and decision. I set out this challenge, canvas some options, and (...) show that Temkin vacillates between two of them. (shrink)