As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally represent their beliefs about the world. However, this field currently lacks a unified theoretical foundation to underpin the study of belief in LLMs. This article begins filling this gap by proposing adequacy conditions for a representation in an LLM to count as belief-like. We argue that, while the project of belief (...) measurement in LLMs shares striking features with belief measurement as carried out in decision theory and formal epistemology, it also differs in ways that should change how we measure belief. Thus, drawing from insights in philosophy and contemporary practices of machine learning, we establish four criteria that balance theoretical considerations with practical constraints. Our proposed criteria include accuracy, coherence, uniformity, and use, which together help lay the groundwork for a comprehensive understanding of belief representation in LLMs. We draw on empirical work showing the limitations of using various criteria in isolation to identify belief representations. (shrink)

Philosophers’ two favorite accounts of rational choice, Evidential Decision Theory (EDT) and Causal Decision Theory (CDT), each face a number of serious objections. Especially troubling are the recent charges that these theories are dynamically inconsistent. I note here that, under the epistemic assumptions that validate these charges, every decision theory that satisfies a pair of attractive postulates is doomed to a similar fate and then survey various lessons rational choice theorists might opt to draw from this.

This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would (...) mean the end of human inquiry, so that won’t be attempted here. Rather I will follow tradition and merely investigate which sets of partial beliefs are coherent. -/- The standard answer to this question, what is commonly called the Bayesian answer, says that degrees of belief are coherent iff they form a probability function. I disagree with the way this is usually justified, but subject to an important qualification I accept the answer. The important qualification is that degrees of belief may be imprecise, or vague. Part one of the dissertation, chapters 1 to 6, looks largely at the consequences of this qualification for the semantic and epistemological questions already mentioned. It turns out that when we allow degrees of belief to be imprecise, we can discharge potentially fatal objections to some philosophically attractive theses. Two of these, that probability is degree of reasonable belief and that the probability calculus provides coherence constraints on partial beliefs, have been mentioned. Others include the claim, defended in chapter 4, that chance is probability given total history. -/- As well as these semantic and epistemological questions, studies of the foundations of probability usually include a detailed discussion of decision theory. For reasons set out in chapter 2, I deny we can gain epistemological insights from decision theory. Nevertheless, it is an interesting field to study on its own, and it might be expected that there would be decision theoretic consequences of allowing imprecise degrees of belief. As I show in part two, this expectation seems to be mistaken. Chapter 9 shows that there aren’t interesting consequences of this theory for decision theory proper, and chapters 10 and 11 show that Keynes’s attempt to use imprecision in degrees of belief to derive a distinctive theory of interest rates is unsound. -/- Chapters 7 and 8 provide a link between these two parts. In chapter 7 I look at some previous philosophical investigations into the effects of imprecision. In chapter 8 I develop what I take to be the best competitor to the theory defended here – a constructivist theory of probability. On this view degrees of belief are precise, but the relevant coherence constraint is a constructivist probability calculus. This view is, I think, mistaken, but the calculus has some intrinsic interest, and there are at least enough arguments for it to warrant a chapter-length examination. (shrink)

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons (...) to be uncertain about updating, rationality can require you to prefer ignorance. (shrink)

Suppose an agent is choosing between rescuing more people with a lower probability of success, and rescuing fewer with a higher probability of success. How should they choose? Our moral judgments about such cases are not well-studied, unlike the closely analogous non-moral preferences over monetary gambles. In this paper, I present an empirical study which aims to elicit the moral analogues of our risk preferences, and to assess whether one kind of evidence—concerning how they depend on outcome probabilities—can debunk them. (...) I find significant heterogeneity in our moral risk preferences—in particular, moral risk-seeking and risk-neutrality are surprisingly popular. I also find that subjects’ judgments aren't probability-dependent, thus providing an empirical defense against debunking arguments from probability dependence. (shrink)

No existing normative decision theory adequately handles risk. Expected Utility Theory is overly restrictive in prohibiting a range of reasonable preferences. And theories designed to accommodate such preferences (for example, Buchak's (2013) Risk‐Weighted Expected Utility Theory) violate the Betweenness axiom, which requires that you are indifferent to randomizing over two options between which you are already indifferent. Betweenness has been overlooked by philosophers, and we argue that it is a compelling normative constraint. Furthermore, neither Expected nor Risk‐Weighted Expected Utility Theory (...) allow for stakes‐sensitive risk‐attitudes—they require that risk matters in the same way whether you are gambling for loose change or millions of dollars. We provide a novel normative interpretation of Weighted‐Linear Utility Theory that solves all of these problems. (shrink)

This paper aims to address the question of how one ought to choose when one is uncertain about what outcomes will result from one’s choices, but when one can nevertheless assign probabilities to the different possible outcomes. These choices are commonly referred to as choices (or decisions) under risk. I assume in this paper that one ought to make instrumentally rational choices—more precisely, one ought to adopt suitable means to one’s morally permissible ends. Expected utility (EU) theory is generally accepted (...) as a normative theory of rational choice under risk, or, more specifically, as a theory of instrumental rationality. According to EU theory, when faced with a decision under risk, one ought to rank one’s options (from least to most choiceworthy) according to their EU and one ought to choose whichever option carries the greatest EU (or one of them in the event that several alternatives are tied). The EU of an option is a probability-weighted sum of each of its possible utilities. In this paper, I argue that EU theory is not the correct theory of instrumental rationality. In its place, I argue for a new theory of instrumental rationality, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this principle, I then argue, roughly speaking, that for any agent, S, faced with any decision under risk, S ought to rank her options (in terms of how choiceworthy they are) according to their ECU and S ought to choose whichever option carries the greatest ECU (or one of them in the event that several alternatives are tied). For any option, a, a’s ECU is a probability‐weighted sum of a’s comparative utilities across the various possible states of the world. In this paper, I show that in some commonplace decisions under risk, ECU theory delivers different verdicts from those of EU theory. (shrink)

Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we (...) interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology. (shrink)

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...) conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

The critics of rational choice theory frequently claim that RCT is self-defeating in the sense that agents who abide by RCT’s prescriptions are less successful in satisfying their preferences than they would be if they abided by some normative theory of choice other than RCT. In this paper, I combine insights from philosophy of action, philosophy of mind and the normative foundations of RCT to rebut this often-made criticism. I then explicate the implications of my thesis for the wider philosophical (...) debate concerning the normativity of RCT for both ideal agents who can form and revise their intentions instantly without cognitive costs and real-life agents who have limited control over the formation and the dynamics of their own intentions. (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)

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

A choice function C is rational iff: if it allows a path through a sequence of decisions with a particular outcome, then that outcome is amongst the ones that C would have chosen from amongst all the possible outcomes of the sequence. This implies, and it is the strongest definition that implies, that anyone who is irrational could be talked out of their own preferences. It also implies weak but non-vacuous constraints on choices over ends. These do not include alpha (...) or beta. (shrink)

On a view implicitly endorsed by many, a concept is epistemically better than another if and because it does a better job at ‘carving at the joints', or if the property corresponding to it is ‘more natural' than the one corresponding to another. This chapter offers an argument against this seemingly plausible thought, starting from three key observations about the way we use and evaluate concepts from en epistemic perspective: that we look for concepts that play a role in explanations (...) of things that cry out for explanation; that we evaluate not only ‘empirical' concepts, but also mathematical and perhaps moral concepts from an epistemic perspective; and that there is much more complexity to the concept/property relation than the natural thought seems to presuppose. These observations, it is argued, rule out giving a theory of conceptual evaluation that is a corollary of a metaphysical ranking of the relevant properties. -/- conceptual ethics, explanation, naturalness, epistemic value, concept/property, semantic internalism. (shrink)

I offer an explanation for why certain sequences of decisions strike us as irrational while others do not. I argue that we have a standing desire to tell flattering yet plausible narratives about ourselves, and that cases of diachronic behavior that strike us as irrational are those in which you had the opportunity to hide something unflattering and failed to do so.

This monographic chapter explains how expected utility (EU) theory arose in von Neumann and Morgenstern, how it was called into question by Allais and others, and how it gave way to non-EU theories, at least among the specialized quarters of decion theory. I organize the narrative around the idea that the successive theoretical moves amounted to resolving Duhem-Quine underdetermination problems, so they can be assessed in terms of the philosophical recommendations made to overcome these problems. I actually follow Duhem's recommendation, (...) which was essentially to rely on the passing of time to make many experiments and arguments available, and evebntually strike a balance between competing theories on the basis of this improved knowledge. Although Duhem's solution seems disappointingly vague, relying as it does on "bon sens" to bring an end to the temporal process, I do not think there is any better one in the philosophical literature, and I apply it here for what it is worth. In this perspective, EU theorists were justified in resisting the first attempts at refuting their theory, including Allais's in the 50s, but they would have lacked "bon sens" in not acknowledging their defeat in the 80s, after the long process of pros and cons had sufficiently matured. This primary Duhemian theme is actually combined with a secondary theme - normativity. I suggest that EU theory was normative at its very beginning and has remained so all along, and I express dissatisfaction with the orthodox view that it could be treated as a straightforward descriptive theory for purposes of prediction and scientific test. This view is usually accompanied with a faulty historical reconstruction, according to which EU theorists initially formulated the VNM axioms descriptively and retreated to a normative construal once they fell threatened by empirical refutation. From my historical study, things did not evolve in this way, and the theory was both proposed and rebutted on the basis of normative arguments already in the 1950s. The ensuing, major problem was to make choice experiments compatible with this inherently normative feature of theory. Compability was obtained in some experiments, but implicitly and somewhat confusingly, for instance by excluding overtly incoherent subjects or by creating strong incentives for the subjects to reflect on the questions and provide answers they would be able to defend. I also claim that Allais had an intuition of how to combine testability and normativity, unlike most later experimenters, and that it would have been more fruitful to work from his intuition than to make choice experiments of the naively empirical style that flourished after him. In sum, it can be said that the underdetermination process accompanying EUT was resolved in a Duhemian way, but this was not without major inefficiencies. To embody explicit rationality considerations into experimental schemes right from the beginning would have limited the scope of empirical research, avoided wasting resources to get only minor findings, and speeded up the Duhemian process of groping towards a choice among competing theories. (shrink)

My thesis explores alternatives to the orthodox model of decision theory. I criticise it by focusing on motivations that, for different reasons, I believe should not be labelled as a consequence. I start by describing what I call the orthodox theory of choice. I describe both the theories proposed by Von Neumann and Morgenstern, and Savage. This is followed by a discussion of the individuation strategy, and, in particular, John Broome’s proposal of an individuation by justifiers ). I then focus (...) on the Allais’s problem, and on how individuation can be employed to solve the problematic situation in which it puts orthodox decision theory. I argue against the practice of using this strategy as a general solution to cases such as the Allais’s problem. I then extend the concerns raised by the Allais’s problem to motivations that do not concern probabilities. I focus on dynamic decision making, and on a property of certain actions that arises from the passage of time: hope. This is interesting because it is no longer the probabilities that affect the decision maker, but an element that is not even represented in the standard model, namely time. I then describe the Kreps and Porteus’s model ) for a preference for the timing of the resolution of uncertainty, where a preference for either early or late resolution of uncertainty is modelled explicitly. I show how making time an explicit part of the model allows one to model utility as depending on something other than consequences, while not violating dynamic consistency. I use the above case to claim that in some contexts - for example, if the decision maker is deciding for herself, and time is passing - it is preferable to model concerns that do not quite fit the label of a consequence explicitly, because the benefits of doing so surpass the costs. This seems to indicate that decision theory should be moving towards a pluralist approach, where different models are used depending on the decision context. (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.

This volume presents research that integrates decision making and creativity within the social contexts in which these processes occur. The volume is an essential addition to and expansion of recent approaches to decision making. Such approaches attempt to incorporate more of the psychological and socio-cultural context in which human decision making takes place. The authors come from different disciplines and also belong to a broad spectrum of research traditions. They present innovative chapters dealing with both theoretical and empirical aspects of (...) decision making in different personal and organizational contexts. All chapters are written from the perspective that human decision making is inherently social and more or less creative. The volume addresses fundamental questions about the nature of human decision making as it occurs in different social contexts. Thereby, it becomes essential reading for researchers in decision making and for advanced students in psychology, management science, informatics, and related disciplines. (shrink)

I have claimed that risk-weighted expected utility maximizers are rational, and that their preferences cannot be captured by expected utility theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and that my original (...) claims still stand. However, their arguments do highlight some costs of REU theory. (shrink)

According to a simple form of consequentialism, we should base decisions on our judgments about their consequences for achieving our goals. Our goals give us reason to endorse consequentialism as a standard of decision making. Alternative standards invariably lead to consequences that are less good in this sense. Yet some people knowingly follow decision rules that violate consequentialism. For example, they prefer harmful omissions to less harmful acts, they favor the status quo over alternatives they would otherwise judge to be (...) belter, they provide third-party compensation on the basis of the cause of an injury rather than the benefit from the compensation, they ignore deterrent effects in decisions about punishment, and they resist coercive reforms they judge to be beneficial. I suggest that nonconsequentialist principles arise from overgeneralizing rules that are consistent with consequentialism in a limited set of cases. Commitment to such rules is detached from their original purposes. The existence of such nonconsequentialist decision biases has implications for philosophical and experimental methodology, the relation between psychology and public policy, and education. (shrink)

This note considers the conceptual part of Sen’s «Internal Consistency of Choice». Amongst the various claims this paper features, two are singled out. A first, negative, claim is that no formal condition of choice consistency is normatively compelling without exception. A second, positive, claim, is that a formal condition of choice consistency is normatively compelling only under some assumptions involving preference. Here, the puzzling choices Sen puts forward are scrutinized and it is argued that such a scrutiny leads to question (...) the negative claim, but in a subtle way, so that the positive claim is comforted, even strengthened. -/- Cette note examine la partie conceptuelle d’un article de Sen, «Internal Consistency of Choice». Elle isole deux thèses parmi celles que Sen défend. Une première, négative, est qu’aucune condition formelle de cohérence du choix n’est normativement valable sans exception. Une seconde, positive, est qu’une condition formelle de cohérence du choix n’est normativement valable que sous des suppositions faisant intervenir la préférence. Nous procédons à une analyse détaillée des choix énigmatiques dont Sen prend argument et affirmons que cet examen mène à remettre en cause la thèse négative, mais d’une manière subtile qui confirme — même renforce — la thèse positive. (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)

There are two distinct views on how to formulate an objective consequentialist account of the deontic status of actions, actualism and possibilism. On an actualist account, what matters to the deontic status of actions is only the value of the outcome an action would have, if performed. By contrast, a possibilist account also takes into account the value of the outcomes that an action could have. These two views come apart in their deontic verdicts when an agent is imperfect in (...) an avoidable way, viz., when agent brings about less good than she could. In this paper, I offer an argument against actualism that draws on the connection between moral obligation and practical reasons. (shrink)

The paper will show how one may rationalize one-boxing in Newcomb's problem and drinking the toxin in the Toxin puzzle within the confines of causal decision theory by ascending to so-called reflexive decision models which reflect how actions are caused by decision situations (beliefs, desires, and intentions) represented by ordinary unreflexive decision models.

Adrian Piper argues that the Humean conception can be made to work only if it is placed in the context of a wider and genuinely universal conception of the self, whose origins are to be found in Kant’s Critique of Pure Reason. This conception comprises the basic canons of classical logic, which provide both a model of motivation and a model of rationality. These supply necessary conditions both for the coherence and integrity of the self and also for unified agency. (...) The Kantian conception solves certain intractable problems in decision theory by integrating it into classical predicate logic, and provides answers to longstanding controversies in metaethics concerning moral motivation, rational final ends, and moral justification that the Humean conception engenders. In addition, it sheds light on certain kinds of moral behavior – for example, the whistleblower – that the Humean conception is at a loss to explain. (shrink)

This paper argues that the interest-relativity of knowledge cannot be explained by the interest-relativity of belief. The discussion starts with an argument that knowledge plays a key pair of roles in decision theory. It is then argued that knowledge cannot play that role unless knowledge is interest-relative. The theory of the interest-relativity of belief is reviewed and revised. That theory can explain some of the cases that are used to suggest knowledge is interest-relative. But it can’t explain some cases involving (...) ignorance, or mistake, about the odds at which a bet is offered. The paper ends with an argument that these cases require positing interest-relative defeaters, which affect whether an agent knows something without affecting whether she believes it, or is justified in believing it. (shrink)

Expected-utility theory has been a popular and influential theory in philosophy, law, and the social sciences. While its original developers, von Neumann and Morgenstern, presented it as a purely predictive theory useful to the practitioners of economic science, many subsequent theorists, particularly those outside of economics, have come to endorse EU theory as providing us with a representation of reason. But precisely in what sense does EU theory portray reason? And does it do so successfully? There are two strikingly different (...) answers to these questions in the literature. On the one hand, there is the view of people such as David Gauthier that EU theory is an implementation of the idea that reason's only role is instrumental. On the other hand, there is the view suggested by Leonard Savage that the theory is a “formal” and noninstrumental characterization of our reasoning process. (shrink)

This paper examines the relationship between Savage's sure thing principle and the value of information. We present two classes of results. First, we show that, under a consequentialist axiom, the sure-thing principle is neither sufficient nor necessary for perfect information to be always desirable: specifically, under consequentialism, the sure thing principle is not implied by the condition that perfect information is always valuable; moreover, the joint imposition of the sure thing principle, consequentialism and either one of two state independence axioms (...) does not imply that perfect information is always desirable. Second, we demonstrate that, under consequentialism, the sure thing principle is necessary for a nonnegative value of possibly imperfect information (though of course the principle is still not sufficient). One implication of these results is that the sure thing principle, under consequentialism, plays a somewhat different role in ensuring dynamic consistency in decision making under uncertainty than does the independence axiom in decision making under risk. (shrink)

According to decision theory, the rational initial action in a sequential decision-problem may be found by backward induction or folding back. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the depth of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, first, that (...) the traditional solutions of certain games depend on knowledge which exceeds depth limits, and that these solutions therefore cannot be shown rational in the usual sense. Then, for that related reason even folding back solutions of one-person problems cannot be! A revision of our notion of rational choice is proposed, analogous to the reliabilist account of knowledge of Goldman and others, by which this paradox is resolved. (shrink)

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion (...) on Independence generalizes to other views that also violate Independence. (shrink)

One of the main contributions of Richard Bradley’s book is an elegant extension of Jeffrey’s Logic of Decision that countenances the evaluation of conditional prospects. This extension offers a promising new setting in which to model dynamic choice. In Bradley’s framework, plans can be understood as conditionals of an appropriate sort, while dynamic consistency can be viewed as providing a constraint on the evaluation of conditionals across time. In this paper, we study connections between planning conditionals and dynamic consistency.

Consequentialists often assume rational monism: the thesis that options are always made rationally permissible by the maximization of the selfsame quantity. This essay argues that consequentialists should reject rational monism and instead accept rational pluralism: the thesis that, on different occasions, options are made rationally permissible by the maximization of different quantities. The essay then develops a systematic form of rational pluralism which, unlike its rivals, is capable of handling both the Newcomb problems that challenge evidential decision theory and the (...) unstable problems that challenge causal decision theory. (shrink)

Towards the end of Decision Theory with a Human Face, Richard Bradley discusses various ways a rational yet human agent, who, due to lack of evidence, is unable to make some fine-grained credibility judgments, may nonetheless make systematic decisions. One proposal is that such an agent can simply “reach judgments” on the fly, as needed for decision making. In effect, she can adopt a precise probability function to serve as proxy for her imprecise credences at the point of decision, and (...) then subsequently abandon the proxy as she proceeds to learn more about the world. Contra Bradley, I argue that an agent who employs this strategy does not necessarily act like a precise Bayesian, since she is not necessarily immune to sure loss in diachronic, as well as synchronic, settings. I go on to suggest a method for determining a proxy probability function whereby the agent does act like a precise Bayesian, so understood. (shrink)

Risk-weighted expected utility theory permits preferences which violate the Sure-Thing Principle. But preferences that violate the STP can lead to bad decisions in sequential choice problems. In particular, they can lead decision-makers to adopt a strategy that is dominated – i.e. a strategy such that some available alternative leads to a better outcome in every possible state of the world.