This paper is the introduction to the volume. It gives an argumentative view of the philosophical landscape concerning incommensurability and incomparability. It argues that incomparability, not incommensurability, is the important phenomenon on which philosophers should be focusing and that the arguments for the existence of incomparability are so far not compelling.

A volume of philosophical studies, centred on problems of personal identity and extending to related topics in the philosophy of mind and moral philosophy.

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)

This paper argues that instrumental rationality is more permissive than expected utility theory. The most compelling instrumentalist argument in favour of separability, its core requirement, is that agents with non-separable preferences end up badly off by their own lights in some dynamic choice problems. I argue that once we focus on the question of whether agents’ attitudes to uncertain prospects help define their ends in their own right, or instead only assign instrumental value in virtue of the outcomes they may (...) lead to, we see that the argument must fail. Either attitudes to prospects assign non-instrumental value in their own right, in which case we cannot establish the irrationality of the dynamic choice behaviour of agents with non-separable preferences. Or they don’t, in which case agents with non-separable preferences can avoid the problematic choice behaviour without adopting separable preferences. (shrink)

The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might doubt (...) that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning the “independence” postulate. After all, if we grant that choice reveals preference, the anomalous choice patterns of the Allais and Ellsberg problems violate postulate P2 of Savage's system. The strategy of making room for new preference patterns by relaxing independence is adopted in each of the following works: Samuelson, Kahneman and Tversky's “Prospect Theory”, Allais and Hagen, Fishburn, Chew and MacCrimmon, McClennen, and in closely (...) argued essays by Machina. (shrink)

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

The following values have no corresponding Zotero field: PB - JSTOR.

Many philosophers have argued that agents must be irrational to lose out in a or . A number of different conclusions have been drawn from this claim. The has been one of the main arguments offered for the axioms of expected utility theory; it has been used to show that options cannot be incomparable or on a par; and it has been used to show that our past choices have normative significance for our subsequent choices. In this article, I argue (...) that the fact that someone loses out in a value pump provides no reason to believe that they are irrational. The VP is impotent. (shrink)

We tell a story where an agent who chooses in such a way as to make the greatest possible profit on each of an infinite series of transactions ends up worse off than an agent who chooses in such a way as to make the least possible profit on each transaction. That is, contrary to what one might suppose, it is not necessarily rational always to choose the option that yields the greatest possible profit on each transaction.

I sketch my general model of the roles of intentions in the planning of agents like us-agents with substantial resource limitations and with important needs for coordination. I then focus on the stability of prior intentions: their rational resistance to reconsideration. I emphasize the importance of cases in which one's nonreconsideration of a prior intention is nondeliberative and is grounded in relevant habits of reconsideration. Concerning such cases I argue for a limited form of two-tier consequentialism, one that is restricted (...) in ways that aim at blocking an analogue of Smart's concerns about rule-worship. I contrast this with the unrestricted two-tier consequentialism suggested by McClennen. I argue that my restricted approach is superior for a theory of the practical rationality of reflective, planning agents like us. But I also conjecture that an unrestricted two-tier consequentialism may be more appropriate for the AI project of specifying a high level architecture for a resource-bounded planner. (shrink)

This book, first published in 1991, offers an integrative approach to the study of formal models in the social and behavioural sciences. The theory presented here unifies both the representation of the social environment and the equilibrium concept. The theory requires that all alternatives that are available to the players be specified in an explicit and detailed manner, and this specification is defined as a social 'situation'. A situation, therefore, not only consists of the alternatives currently available to the players, (...) but also includes the set of opportunities that might be induced by the players from their current environment. The theory requires that all recommended alternatives be both internally and externally stable; the recommendation cannot be self-defeating and, at the same time, should account for alternatives that were not recommended. In addition to unifying the representation and the solution concept, the theory also extends the social environments accommodated by current game theory. (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in (...) the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (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)

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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)