In hard cases of comparison, people are faced with two options neither of which is conceived of as better, worse, or equally good compared to the other. Most philosophers claim that hard cases can indeed be distinguished from cases in which two options are equally good, and can be characterized by a failure of transitive reasoning. It is a much more controversial matter and at the heart of an ongoing debate, whether the options in hard cases of comparison should be (...) interpreted as incomparable, on par, or roughly equal. So far, however, none of these claims and interpretations have been tested. This paper presents the first empirical investigation on hard cases, intransitive reasoning, and incomparability. Our results reveal that hard cases present real-world dilemmas in which a significant majority of people violate transitivity. After suggesting a way of operationalizing the notion of incomparability, we provide empirical evidence that the options in some hard cases are not considered to be incomparable. Theories of rough equality or parity seem to provide better interpretations of our results. (shrink)

All ordinary decisions involve some risk. If I go outside for a walk, I may trip and injure myself. But if I don’t go for a walk, I slightly increase my chances of cardiovascular disease. Typically, we disregard most small risks. When, for practical purposes, is it appropriate for one to ignore risk? This issue looms large because many activities performed by those in wealthy societies, such as driving a car, in some way risk contributing to climate harms. Are these (...) activities morally appropriate? -/- In this paper, I first summarize and respond to some arguments that purport to show that it is appropriate to ignore or discount very small risks. I argue that because our rationality is bounded, it is impossible for us to include every small risk in our decision-making process, and so we may reasonably use heuristics to guide many decisions. However, contrary to some thinkers, I argue that this does not violate the spirit of expected value theory; it merely shows that we should adopt a so-called "two-level" view. Our use of heuristics allows for the reasonable ignoring of some risks, and this perhaps explains why one might be inclined to think that individual climate-related risks are negligible. However, virtually all greenhouse-gas emitting activities in fact have some climate risk on the negative side of the ledger, and the use of heuristics does not permit the general ignoring of climate-change-related risk by individuals on grounds of expediency of judgment and decision-making. (shrink)

Ruth Chang and Joseph Raz have both drawn far-reaching consequences for agency from the phenomenon of incommensurability. After criticizing their arguments, I outline an alternative view: if incommensurability is vagueness, then there are no substantial implications for agency, except perhaps a limited form of naturalistic voluntarism if our reasons are provided by desires.

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the (...) Arrow–Sen framework for social choice to study grading in groups. (shrink)

This article articulates and defends a dissolution of the so-called repugnant conclusion, which focuses on the notion of life worth living figuring both in Parfit's formulation of the repugnant conclusion and in most responses to such a conclusion. The proposed dissolution demonstrates that the notion of life worth living is plagued by multiple ambiguities and that these ambiguities, in turn, hamper meaningful debate about both the issue of whether the repugnant conclusion can be avoided and the issue of whether the (...) repugnant conclusion is actually repugnant. This result does not exclude that some modified versions of the repugnant conclusion may yield valuable insights about the value of populations and the tenability of different axiological/ethical theories. Still, if the proposed dissolution is correct, then the repugnant conclusion rests on an ill-defined notion and we lack the information required to assess the merits of the repugnant conclusion. (shrink)

This introductory article describes the phenomena of incommensurability and incomparability, how they are related, and why they are important. Since incomparability is the more significant phenomenon, the paper takes that as its focus. It gives a detailed account of what incomparability is, investigates the relation between the incomparability of values and the incomparability of alternatives for choice, distinguishes incomparability from the related phenomena of parity, indeterminacy, and noncomparability, and, finally, defends a view about practical justification that vindicates the importance of (...) incomparability — assuming it exists — for practical reason. (shrink)

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)

In other work I have argued that items can be on a par, where being on a par is a fourth, basic, sui generis value relation beyond the usual trichotomy of ‘better than’, ‘worse than’, and ‘equally good’. In this paper, I aim to marshal non-technical, intuitive arguments for this view. First, I try to cast doubt on the leading source of intuitive resistance to parity, the conviction that if two items are comparable, one must be better than the other, (...) worse than it, or they must be equally good. Second, I explain how parity can arise by appealing to an uncontroversial distinction between quantity and quality of value. I propose both sufficient conditions for parity and a nontechnical model of the notion. My overall aim is to bring into view a simple and intuitive picture of value – and more generally of normativity – in which parity plays a significant role. (shrink)

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about what (...) it is to be a rational agent. (shrink)

The puzzle of the self-torturer raises intriguing questions concerning rationality, cyclic preferences, and resoluteness. Interestingly, what makes the case puzzling has not been clearly pinpointed. The puzzle, it seems, is that a series of rational choices foreseeably leads the self-torturer to an option that serves his preferences worse than the one with which he started. But this is a very misleading way of casting the puzzle. I pinpoint the real puzzle of the self-torturer and, in the process, reveal a neglected (...) but crucial dimension of instrumental rationality. (shrink)