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)

Abstract: The paper provides a general account of value relations. It takes its departure in a special type of value relation, parity, which according to Ruth Chang is a form of evaluative comparability that differs from the three standard forms of comparability: betterness, worseness and equal goodness. Recently, Joshua Gert has suggested that the notion of parity can be accounted for if value comparisons are interpreted as normative assessments of preference. While Gert's basic idea is attractive, the way he develops (...) it is flawed: His modeling of values by intervals of permissible preference strengths is inadequate. Instead, I provide an alternative modeling in terms of intersections of rationally permissible preference orderings. This yields a general taxonomy of all binary value relations. The paper concludes with some implications of this approach for rational choice. (shrink)

Some philosophers believe that two objects of value can be ‘roughly equal’, or ‘on a par’, or belong to the same ‘clump’ of value in a sense that is fundamentally different from that in which some objects are ‘better than’, ‘worse than’, or ‘equally as good as’ others. This article shows that if two objects are on a par, or belong to the same clump, then an agent accepting a few plausible premises can be exploited in a money-pump. The central (...) premise of the argument is that value is choice-guiding. If one object is more valuable than another, then it is not permitted to choose the less valuable object; and if two objects are equally valuable it is permitted to choose either of them; and if two objects are on a par or belong to the same clump it is also permitted to choose either of them. (shrink)

It is commonly assumed that moral deliberation requires that the alternatives available in a choice situation are evaluatively comparable. This comparability assumption is threatened by claims of incomparability, which is often established by means of the small improvement argument (SIA). In this paper I argue that SIA does not establish incomparability in a stricter sense. The reason is that it fails to distinguish incomparability from a kind of evaluative indeterminacy which may arise due to the vagueness of the evaluative comparatives (...) ‘better than,’ ‘worse than,’ and ‘equally as good as.’. (shrink)

This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

Politics, Philosophy & Economics, Volume 21, Issue 4, Page 347-371, November 2022. We sometimes have to choose between options that are seemingly incomparable insofar as they seem to be neither better than, worse than, nor equal to each other. This often happens when the available options are quite different from one another. For instance, consider a choice between prioritizing either criminal justice reform or healthcare reform as a public policy goal. Even after the relevant details of the goals and possible (...) reforms are filled in, it is plausible that neither goal is better than, worse than, nor equal to the other. Such seemingly incomparable options present a problem for rational choice since it is unclear how an agent might rationally choose between them. What we need are some principles to help govern rational choice when faced with seemingly incomparable options. I here present three such principles. While each principle is individually compelling, I show that they are jointly incompatible. I then argue that the correct response to this inconsistent triad is to reject the principle that rationally censures performing a sequence of choices one knows will result in a suboptimal outcome. The upshot is that when seeming incomparability is involved, an agent can money pump themselves without being less rational for it. (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)

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (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)

It is commonly assumed that preferences are determinate; that is, that an agent who has a preference knows that she has the preference in question and is disposed to act upon it. This paper argues the dubiousness of that assumption. An account of indeterminate preferences in terms of self-predicting subjective probabilities is given, and a decision rule for choices involving indeterminate preferences is proposed. Wolfgang Spohn’s and Isaac Levi ’s arguments against self-predicting probabilities are also considered, in light of Wlodek (...) Rabinowicz’s recent criticism. (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)

Repeatedly and successfully, the celebrated Harvard philosopher Robert Nozick has reached out to a broad audience beyond the confines of his discipline, addressing ethical and social problems that matter to every thoughtful person. Here Nozick continues his search for the connections between philosophy and "ordinary" experience. In the lively and accessible style that his readers have come to expect, he offers a bold theory of rationality, the one characteristic deemed to fix humanity's "specialness." What are principles for? asks Nozick. We (...) could act simply on whim, or maximize our self-interest and recommend that others do the same. As Nozick explores rationality of decision and rationality of belief, he shows how principles actually function in our day-to-day thinking and in our efforts to live peacefully and productively with each other. Throughout, the book combines daring speculations with detailed investigations to portray the nature and status of rationality and the essential role that imagination plays in this singular human aptitude. (shrink)

Probably many people have cyclic preferences: they prefer A to B, B to C and C to A for some objects of choice A, B and C. Recent work has resurrected the objection to cyclic preference that agents possessing them are open to exploitation by means of ‘money pumps’. The paper briefly reviews this work and proposes a general approach to problems of sequential choice that makes cyclic preference immune to exploitation by means of these new mechanisms.

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)

(No abstract is available for this citation).

Ethicists and economists commonly assume that if A is all things considered better than B, and B is all things considered better than C, then A is all things considered better than C. Call this principle Transitivity. Although it has great conceptual, intuitive, and empirical appeal, I argue against it. Larry S. Temkin explains how three types of ethical principle, which cannot be dismissed a priori, threaten Transitivity: (a) principles implying that in some cases different factors are relevant to comparing (...) A to C than to comparing A to B or B to C; (b) principles of limited scope; (c) principles implying that morally relevant differences in degree can amount to differences in kind. My counterexamples employ a principle of type (c): pleasures and pains enormously different in intensity differ in kind. Temkin has also endorsed this type of counterexample, using arguments based on earlier drafts of this paper. (shrink)

People are often faced with so called hard choices – also known as hard cases of comparison. In trying to characterize these hard choices, philosophers have made two central claims. First, failure of transitivity underlies hard cases of comparison. Second, using a random procedure is considered inappropriate in order to arrive at a decision in hard cases. While having some argumentative support, both claims primarily rely on expert intuitions. The results of the experiments we present in this paper challenge both (...) claims, as well as the representativeness of expert intuitions that support these claims, by showing that most people violate transitivity only if a hard choice is important, and find it appropriate to use a random procedure even in hard cases of comparison. (shrink)

Contemporary philosophers interested in value theory appear to be largely concerned with questions of the following sort:What is value?What is the meaning of the word ‘good’?Does the attribution of value to an object have a cognitive, or merely an emotive, significance?The first question is metaphysical; to ask it is analogous to asking in physics:What is matter?What is electricity?The others are generally treated as semantical questions; to ask them is analogous to asking in statistics:What is the meaning of the word ‘probable’?Does (...) an attribution of probability express an objective fact, or merely a subjective attitude? (shrink)

Gustafsson and Espinoza have recently argued that the ‘small-improvement argument’, against completeness as a rationality requirement for preference orderings, is defective. They claim that the two main premises of the argument conflict, and hence should not both be accepted. I show that this conflict can be avoided by modifying one of the premises.