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)

The value of knowledge can vary in that knowledge of important facts is more valuable than knowledge of trivialities. This variation in the value of knowledge is mirrored by a variation in evidential standards. Matters of greater importance require greater evidential support. But all knowledge, however trivial, needs to be evidentially certain. So on one hand we have a variable evidential standard that depends on the value of the knowledge, and on the other, we have the invariant standard of evidential (...) certainty. This paradox in the concept of knowledge runs deep in the history of philosophy. We approach this paradox by proposing a bet settlement theory of knowledge. Degrees of belief can be measured by the expected value of a bet divided by stake size, with the highest degree of belief being probability 1, or certainty. Evidence sufficient to settle the bet makes the expectation equal to the stake size and therefore has evidential probability 1. This gives us the invariant evidential certainty standard for knowledge. The value of knowledge relative to a bet is given by the stake size. We propose that evidential probability can vary with stake size, so that evidential certainty at low stakes does not entail evidential certainty at high stakes. This solves the paradox by allowing that certainty is necessary for knowledge at any stakes, but that the evidential standards for knowledge vary according to what is at stake. We give a Stake Size Variation Principle that calculates evidential probability from the value of evidence and the stakes. Stake size variant degrees of belief are probabilistically coherent and explain a greater range of preferences than orthodox expected utility theory, namely the Ellsberg and Allais preferences. The resulting theory of knowledge gives an empirically adequate, rationally grounded, unified account of evidence, value and probability. (shrink)

So-called money pump arguments aim to show that intransitive preferences are irrational because they will lead someone to accept a series of deals that leaves his/her financially worse off and better off in no respect. A common response to these arguments is the foresight response, which counters that the agent in question may see the exploitation coming, and refuse to trade at all. To obviate this response, I offer a “deluxe money pump argument” that applies dominance reasoning to a modified (...) money pump case. (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)

This is a collection of published and unpublished essays by distinguished philosopher Michael E. Bratman of Stanford University. They revolve around his influential theory, know as the "planning theory of intention and agency." Bratman's primary concern is with what he calls "strong" forms of human agency--including forms of human agency that are the target of our talk about self-determination, self-government, and autonomy. These essays are unified and cohesive in theme, and will be of interest to philosophers in ethics and metaphysics.

First published in 1903, this volume revolutionized philosophy and forever altered the direction of ethical studies. A philosopher’s philosopher, G. E. Moore was the idol of the Bloomsbury group, and Lytton Strachey declared that Principia Ethica marked the rebirth of the Age of Reason. This work clarifies some of moral philosophy’s most common confusions and redefines the science’s terminology. Six chapters explore: the subject matter of ethics, naturalistic ethics, hedonism, metaphysical ethics, ethics in relation to conduct, and the ideal. Moore's (...) simplicity of style and precise use of everyday language exercised an enormous influence on the development of analytic philosophy, and they contribute to the continuing resonance of his compelling arguments. (shrink)

What happens to our conception of mind and rational agency when we take seriously future-directed intentions and plans and their roles as inputs into further practical reasoning? The author's initial efforts in responding to this question resulted in a series of papers that he wrote during the early 1980s. In this book, Bratman develops further some of the main themes of these essays and also explores a variety of related ideas and issues. He develops a planning theory of intention. Intentions (...) are treated as elements of partial plans of action. These plans play basic roles in practical reasoning, roles that support the organization of our activities over time and socially. Bratman explores the impact of this approach on a wide range of issues, including the relation between intention and intentional action, and the distinction between intended and expected effects of what one intends. (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)

Most work in Kant’s epistemology focuses on what happens “upstream” from experience, prior to the formation of conscious propositional attitudes. By contrast, this essay focuses on what happens "downstream": the formation of assent (Fuerwahrhalten) in its various modes. The mode of assent that Kant calls "Belief" (Glaube) is the main topic: not only moral Belief but also "pragmatic" and "doctrinal" Belief as well. I argue that Kant’s discussion shows that we should reject standard accounts of the extent to which theoretical (...) reason can provide justified assent about things-in-themselves, in favor of one that is much more liberal. Interpretive benefits are not the only results of the discussion, however. I also hope it will become clear along the way that there is such a thing as Kantian Belief, and that we often have quite a lot of it. -/- . (shrink)

I describe in section 1 how cyclical preferences can arise. In section 2, I relate preference to judgments of choiceworthiness and distinguish between two kinds of preference cycles, vicious and benign. In section 3, I run through the standard money pump in order to show, in section 4, how this pump can be stopped by foresight, using backward induction. A new money pump that *cannot* be stopped by foresight is presented in section 5. This pump works even for agents with (...) benign cyclical preferences. What makes it work is persistency on the part of the would-be exploiter. In section 6, I compare this pump to a diachronic Dutch book that can be set up against someone whose probability assignments violate Reflection. Even in this case, the book only works if the bookie is assumed to be persistent. I use this comparison between preference cyclicity and violations of Reflection in order to question whether exploitability must be seen as a proof of irrationality. Finally, in section 7, I consider resolute choice as an alternative to the backward-induction procedure. While a resolute chooser cannot be exploited, I argue that resoluteness is not required by rationality. The argument is based on a suggestion that rationality, when it comes to actions, is a local rather than a global requirement. (shrink)

This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed "Reflection". This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that (...) violate Reflection; hence these principles are also requirements of rationality under suitable conditions, though not universal requirements of rationality. (shrink)

A critical examination of the Reflection principle in Bayesian epistemology, and of the diachronic Dutch-book-style arguments that have been invoked to support Reflection and Conditionalization.

My focus is on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch (...) Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. It is suggested that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, she can be exploited only if she is disunified in his decision-making, i.e., only if she makes decisions on various issues she confronts separately rather than jointly. In other words, exploitation is possible only if the decision problem has been framed in a certain way. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be quite costly and inconvenient diachronically, especially when the issues under consideration are widely spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Isaac Levis view of the status of pragmatic arguments is diametrically opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper. (shrink)

Levi’s work in decision theory has for many years been a major influence on the field. His writings have raised important new issues and opened new lines of inquiry. This collection of his papers brings out the range of his recent studies and the close bearing of his work on the work of others.

A compilation of all previously published writings on philosophy and the foundations of mathematics from the greatest of the generation of Cambridge scholars that included G.E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes.

Isaac Levi has long criticized causal decisiontheory on the grounds that it requiresdeliberating agents to make predictions abouttheir own actions. A rational agent cannot, heclaims, see herself as free to choose an actwhile simultaneously making a prediction abouther likelihood of performing it. Levi is wrongon both points. First, nothing in causaldecision theory forces agents to makepredictions about their own acts. Second,Levi's arguments for the ``deliberation crowdsout prediction thesis'' rely on a flawed modelof the measurement of belief. Moreover, theability of agents (...) to adopt beliefs about theirown acts during deliberation is essentialto any plausible account of human agency andfreedom. Though these beliefs play no part inthe rationalization of actions, they arerequired to account for the causalgenesis of behavior. To explain the causes ofactions we must recognize that (a) an agentcannot see herself as entirely free in thematter of A unless she believes herdecision to perform A will cause A,and (b) she cannot come to a deliberatedecision about A unless she adoptsbeliefs about her decisions. FollowingElizabeth Anscombe and David Velleman, I arguethat an agent's beliefs about her own decisionsare self-fulfilling, and that this can beused to explain away the seeming paradoxicalfeatures of act probabilities. (shrink)

In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction (BI). This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz (2000). There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more striking (...) than the modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action. (shrink)

Isaac Levi is one of the preeminent philosophers in the areas of pragmatic rationality and epistemology. This collection of essays constitutes an important presentation of his original and influential ideas about rational choice and belief. A wide range of topics is covered, including consequentialism and sequential choice, consensus, voluntarism of belief, and the tolerance of the opinions of others. The essays elaborate on the idea that principles of rationality are norms that regulate the coherence of our beliefs and values with (...) our rational choices. The norms impose minimal constraints on deliberation and inquiry, but they also impose demands well beyond the capacities of deliberating agents. This major collection will be eagerly sought out by a wide range of philosophers in epistemology, logic, and philosophy of science, as well as economists, decision theorists, and statisticians. (shrink)

My focus is on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch (...) Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. It is suggested that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, she can be exploited only if she is disunified in his decision-making, i.e., only if she makes decisions on various issues she confronts separately rather than jointly. In other words, exploitation is possible only if the decision problem has been framed in a certain way. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be quite costly and inconvenient diachronically, especially when the issues under consideration are widely spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Isaac Levis view of the status of pragmatic arguments is diametrically opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper. (shrink)

The paper's focus is on pragmatic arguments for various ‘rationality constraints’ on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which he will act to his guaranteed disadvantage. Dramatically put, he can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic (...) Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. The proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, he can be exploited only if he is disunified in his decision-making. Exploitation is possible only if the agent makes decisions on various issues he confronts one by one, rather than on all of them together. Unity in decision making may be quite costly and is often inconvenient, especially when it concerns opportunity packages that are spread over time. Therefore, pragmatic arguments should be seen as delivering conditional conclusions: “To afford being disunified as a decision maker, you’d better satisfy these constraints.” Arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Levi’s view of the status of pragmatic arguments (cf. Levi 2002) is diametrally opposed. According to him, only synchronic pragmatic arguments are valid (indeed, categorically valid). The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in the paper. (shrink)

According to the standard objection to backward induction in games, its application depends on highly questionable assumptions about the players' expectations as regards future counterfactual game developments. It seems that, in order to make predictions needed for backward reasoning, the players must expect each player to act rationally at each node that in principle could be reached in the game, and also to expect that this confidence in the future rationality of the players would be kept by each player come (...) what may: even at the game-nodes that could only be reached by irrational play. Both expectations seem to be rather unreasonable: a player's initial disposition to rational behaviour may be weakened by a long stretch of irrational play on his part and, even more importantly, his initial confidence in the other players' future rationality may be undermined by an irrational play on their part. For different formulations of this objection see Binmore, Reny and, Bicchieri, Pettit and Sugden. and Aumann and.). (shrink)

An agent whose preferences violate the Independence Axiom or for some other reason are not representable by an expected utility function, can avoid 'dynamic inconsistency' either by foresight ('sophisticated choice') or by subsequent adjustment of preferences to the chosen plan of action ('resolute choice'). Contrary to McClennen and Machina, among others, it is argued these two seemingly conflicting approaches to 'dynamic rationality' need not be incompatible. 'Wise choice' reconciles foresight with a possibility of preference adjustment by rejecting the two assumptions (...) that create the conflict: Separability of Preferences in the case of sophisticated choice and Reduction to Normal form in the case of resolute choice.. (shrink)

In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction. This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz. There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more striking than the (...) modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action. (shrink)

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU (...) preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

In a recent, thought-provoking paper Adam Elga argues against unsharp – e.g., indeterminate, fuzzy and unreliable – probabilities. Rationality demands sharpness, he contends, and this means that decision theories like Levi's, Gärdenfors and Sahlin's, and Kyburg's, though they employ different decision rules, face a common, and serious, problem. This article defends the rule to maximize minimum expected utility against Elga's objection.

The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not (...) coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A. (shrink)

The idea that rational agents should have acyclic preferences and should obey conditionalization has been defended on the grounds that otherwise an agent is threatened with becoming a “money pump.” This essay argues that such arguments fail to prove their claims.

It is a popular view thatpractical deliberation excludes foreknowledge of one's choice. Wolfgang Spohn and Isaac Levi have argued that not even a purely probabilistic self-predictionis available to thedeliberator, if one takes subjective probabilities to be conceptually linked to betting rates. It makes no sense to have a betting rate for an option, for one's willingness to bet on the option depends on the net gain from the bet, in combination with the option's antecedent utility, rather than on the offered (...) odds. And even apart from this consideration, assigning probabilities to the options among which one is choosing is futile since such probabilities could be of no possible use in choice. The paper subjects these arguments to critical examination and suggests that, appearances notwithstanding, practical deliberation need not crowd outself-prediction. (shrink)

I describe in section 1 how cyclical preferences can arise. In section 2, I relate preference to judgments of choiceworthiness and distinguish between two kinds of preference cycles, vicious and benign. In section 3, I run through the standard money pump in order to show, in section 4, how this pump can be stopped by foresight, using backward induction. A new money pump that *cannot* be stopped by foresight is presented in section 5. This pump works even for agents with (...) benign cyclical preferences. What makes it work is persistency on the part of the would-be exploiter. In section 6, I compare this pump to a diachronic Dutch book that can be set up against someone whose probability assignments violate Reflection. Even in this case, the book only works if the bookie is assumed to be persistent. I use this comparison between preference cyclicity and violations of Reflection in order to question whether exploitability must be seen as a proof of irrationality. Finally, in section 7, I consider resolute choice as an alternative to the backward-induction procedure. While a resolute chooser cannot be exploited, I argue that resoluteness is not required by rationality. The argument is based on a suggestion that rationality, when it comes to actions, is a local rather than a global requirement. (shrink)

Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will "see the dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really (...) no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened "sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through. (shrink)

For three centuries, philosophers have mounted defenses against the melan genie with an obsessive intensity comparable to the Reaganite determination to squander American wealth on defenses against a Communist threat. And for three centuries, skeptics have argued for the futility of the expenditure of conceptual effort with no more success than critics of the Pentagon have had in stemming the flow of funds to the military and its industrial minions. My own sympathies are with the skeptics. However, their own intense (...) involvement with the obsessions of the epistemological fear mongers and their failure to address the analogue of the problem of conversion from military to civilian industry in an acceptable manner often deprive the skeptical position of the subversive force it ought to have. (shrink)