This article explores the main similarities and differences between Derek Parfit’s notion of imprecise comparability and a related notion I have proposed of parity. I argue that the main difference between imprecise comparability and parity can be understood by reference to ‘the standard view’. The standard view claims that 1) differences between cardinally ranked items can always be measured by a scale of units of the relevant value, and 2) all rankings proceed in terms of the trichotomy of ‘better than’, (...) ‘worse than’, and ‘equally good’. Imprecise comparability, which can be understood in terms of the more familiar notions of cardinality and incommensurability, rejects only the first claim while parity rejects both claims of the standard view. -/- I then argue that insofar as those attracted to imprecise comparability assume that all rankings are trichotomous, as Parfit appears to, the view should be rejected. This is because imprecise equality is not a form of equality but is a sui generis ‘fourth’ basic way in which items can be ranked. We should, I argue, understand imprecise equality as parity, and imprecise comparability as entailing ‘tetrachotomy’ – that if two items are comparable, one must better than, worse than, equal to, or on a par with the other. Thus those attracted to the idea that cardinality can be imprecise should abandon trichotomy and accept parity and tetrachotomy instead. -/- Finally, I illustrate the difference between Parfit’s trichotomous notion of imprecise comparability and parity by examining how each notion might be employed in different solutions to the problem posed by the Repugnant Conclusion in population ethics. I suggest that parity provides the arguably more ecumenical solution to the problem. (shrink)

Suppose that A and B are two kinds of goods such that more of each is better than less. A is strongly superior to B if any amount of A is better than any amount of B. It is weakly superior to B if some amount of A is better than any amount of B. There are many examples of these relations in the literature, sometimes under the labels “higher goods” and “discontinuity.” The chapter gives a precise and generalized statement (...) of Strong and Weak Superiority and discusses different ways in which these relations can be relevant to the aggregation of welfare. It also proves a number of general results. One of the results gives rise to a dilemma: It can be used as an argument against the existence of value superiority or, alternatively, as an argument against the view that superiority entails a radical difference in value. (shrink)

Recently, in his Rolf Schock Prize Lecture, Derek Parfit has suggested a novel way of avoiding the Repugnant Conclusion by introducing what he calls “imprecision” in value comparisons. He suggests that in a range of important cases, populations of different sizes are only imprecisely comparable. Parfit suggests that this feature of value comparisons opens up a way of avoiding the Repugnant Conclusion without implying other counterintuitive conclusions, and thus solves one of the major challenges in ethics. In this article, I (...) try to clarify Parfit's proposal and evaluate whether it will help us with the paradoxes in population ethics. (shrink)

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The (...) underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes. (shrink)

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The (...) underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes. (shrink)

According to the Repugnant Conclusion: Compared with the existence of many people who would all have some very high quality of life, there is some much larger number of people whose existence would be better, even though these people would all have lives that were barely worth living. I suggest some ways in which we might be able to avoid this conclusion. I try to defend a strong form of lexical superiority.

James Griffin has considered a form of superiority in value that is weaker than lexical priority as a possible remedy to the Repugnant Conclusion. In this article, I demonstrate that, in a context where value is additive, this weaker form collapses into the stronger form of superiority. And in a context where value is non-additive, weak superiority does not amount to a radical value difference at all. These results are applied on one of Larry Temkin's cases against transitivity. I demonstrate (...) that Temkin appeals to two conflicting notions of aggregation. I then spell out the consequences of these results for different interpretations of Griffin's suggestion regarding population ethics. None of them comes out very successful, but perhaps they nevertheless retain some interest. (shrink)

If A is better than B and B is better than C, then A is better than C, right? Larry Temkin and Stuart Rachels say: No! Betterness is nontransitive, they claim. In this paper, I discuss the central type of argument advanced by Temkin and Rachels for this radical idea, and argue that, given this view very likely has sceptical implications for practical reason, we would do well to identify alternative responses. I propose one such response, which employs the idea (...) that rational agents might regard some options as incommensurate in value, and will reasonably employ a heuristic of status quo maintenance to avoid suboptimal choices from incommensurate goods. (shrink)

The spectrum argument purports to show that the better-than relation is not transitive, and consequently that orthodox value theory is built on dubious foundations. The argument works by constructing a sequence of increasingly less painful but more drawn-out experiences, such that each experience in the spectrum is worse than the previous one, yet the final experience is better than the experience with which the spectrum began. Hence the betterness relation admits cycles, threatening either transitivity or asymmetry of the relation. This (...) paper examines recent attempts to block the spectrum argument, using the idea that it is a mistake to affirm that every experience in the spectrum is worse than its predecessor: an alternative hypothesis is that adjacent experiences may be incommensurable in value, or that due to vagueness in the underlying concepts, it is indeterminate which is better. While these attempts formally succeed as responses to the spectrum argument, they have additional, as yet unacknowledged costs that are significant. In order to effectively block the argument in its most typical form, in which the first element is radically inferior to the last, it is necessary to suppose that the incommensurability is particularly acute: what might be called radical incommensurability. We explain these costs, and draw some general lessons about the plausibility of the available options for those who wish to save orthodox axiology from the spectrum argument. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations \is better than" and \is as good as". This eld has been riddled with para- doxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek (...) Par t's Repugnant Conclusion. Moreover, some theorists have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. As I shall show in this chapter, however, one can replace avoid- ance of the Repugnant Conclusion with a logically weaker and intuitively more convincing condition. The resulting theorem involves, to the best of my knowledge, logically weaker and intuitively more compelling con- ditions than the other theorems presented in the literature. As such, it challenges the very existence of a satisfactory population ethics. (shrink)