Purists think that changes in our practical interests can’t affect what we know unless those changes are truth-relevant with respect to the propositions in question. Impurists disagree. They think changes in our practical interests can affect what we know even if those changes aren’t truth-relevant with respect to the propositions in question. I argue that impurists are right, but for the wrong reasons, since they haven’t appreciated the best argument for their own view. Together with “Minimalism and the Limits of (...) Warranted Assertability Maneuvers,” “The Pragmatic Encroachment Debate,” and “Anti-Intellectualism” (below), this paper constitutes my attempt to refute the entire pragmatic encroachment debate. As I show in this paper, there is an argument for impurism sitting in plain sight that is considerably more plausible than any extant argument for pragmatism. (shrink)

Some early phase clinical studies of candidate HIV cure and remission interventions appear to have adverse medical risk–benefit ratios for participants. Why, then, do people participate? And is it ethically permissible to allow them to participate? Recent work in decision theory sheds light on both of these questions, by casting doubt on the idea that rational individuals prefer choices that maximise expected utility, and therefore by casting doubt on the idea that researchers have an ethical obligation not to enrol (...) participants in studies with high risk–benefit ratios. This work supports the view that researchers should instead defer to the considered preferences of the participants themselves. This essay briefly explains this recent work, and then explores its application to these two questions in more detail. (shrink)

The paper summarizes expected utility theory, both in its original von Neumann-Morgenstern version and its later developments, and discusses the normative claims to rationality made by this theory.

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's (...) Thesis. I suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a (...) strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

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)

An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.

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)

Suppose that it is rational to choose or intend a course of action if and only if the course of action maximizes some sort of expectation of some sort of value. What sort of value should this definition appeal to? According to an influential neo-Humean view, the answer is “Utility”, where utility is defined as a measure of subjective preference. According to a rival neo-Aristotelian view, the answer is “Choiceworthiness”, where choiceworthiness is an irreducibly normative notion of a course of (...) action that is good in a certain way. The neo-Humean view requires preferences to be measurable by means of a utility function. Various interpretations of what exactly a “preference” is are explored, to see if there is any interpretation that supports the claim that a rational agent’s “preferences” must satisfy the “axioms” that are necessary for them to be measurable in this way. It is argued that the only interpretation that supports the idea that the rational agent’s preferences must meet these axioms interprets “preferences” as a kind of value-judgment. But this turns out to be version of the neo-Aristotelian view, rather than the neo-Humean view. Rational intentions maximize expected choiceworthiness, not expected utility. (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)

This paper examines how the concepts of utility, impartiality, and universality worked together to form the foundation of Adam Smith's jurisprudence. It argues that the theory of utility consistent with contemporary rational choice theory is insufficient to account for Smith's use of utility. Smith's jurisprudence relies on the impartial spectator's sympathetic judgment over whether third parties are injured, and not individuals' expected utility associated with individuals' expected gains from rendering judgments over innocence or guilt.

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to (...) consequences. Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background (...) uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (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)

Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions interpreted as expressing high conditional probabilities. In the present article, we investigate four prominent LP systems (namely, systems O, P, Z, and QC) by means of computer simulations. The results reported here extend our previous work in this area, and evaluate the four systems in terms of the expected utility of the dispositions to act that derive from the conclusions that the systems license. In addition to conforming to the (...) dominant paradigm for assessing the rationality of actions and decisions, our present evaluation complements our previous work, since our previous evaluation may have been too severe in its assessment of inferences to false and uninformative conclusions. In the end, our new results provide additional support for the conclusion that (of the four systems considered) inference by system Z offers the best balance of error avoidance and inferential power. Our new results also suggest that improved performance could be achieved by a modest strengthening of system Z. (shrink)

It is widely held that the influence of risk on rational decisions is not entirely explained by the shape of an agent’s utility curve. Buchak (Erkenntnis, 2013, Risk and rationality, Oxford University Press, Oxford, in press) presents an axiomatic decision theory, risk-weighted expected utility theory (REU), in which decision weights are the agent’s subjective probabilities modified by his risk-function r. REU is briefly described, and the global applicability of r is discussed. Rabin’s (Econometrica 68:1281–1292, 2000) calibration theorem strongly (...) suggests that plausible levels of risk aversion cannot be fully explained by concave utility functions; this provides motivation for REU and other theories. But applied to the synchronic preferences of an individual agent, Rabin’s result is not as problematic as it may first appear. Theories that treat outcomes as gains and losses (e.g. prospect theory and cumulative prospect theory) account for risk sensitivity in a way not available to REU. Reference points that mark the difference between gains and losses are subject to framing, many instances of which cannot be regarded as rational. However, rational decision theory may recognize the difference between gains and losses, without endorsing all ways of fixing the point of reference. In any event, REU is a very interesting theory. (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)

According to epistemic utility theory, epistemic rationality is teleological: epistemic norms are instrumental norms that have the aim of acquiring accuracy. What’s definitive of these norms is that they can be expected to lead to the acquisition of accuracy when followed. While there’s much to be said in favor of this approach, it turns out that it faces a couple of worrisome extensional problems involving the future. The first problem involves credences about the future, and the second problem (...) involves future credences. Examining prominent solutions to a different extensional problem for this approach reinforces the severity of the two problems involving the future. Reflecting on these problems reveals the source: the teleological assumption that epistemic rationality aims at acquiring accuracy. (shrink)

A cursory glance at the list of Nobel Laureates for Economics is sufficient to confirm Stanovich’s description of the project to evaluate human rationality as seminal. Herbert Simon, Reinhard Selten, John Nash, Daniel Kahneman, and others, were awarded their prizes less for their work in economics, per se, than for their work on rationality, as such. Although philosophical works have for millennia attempted to describe, explicate and evaluate individual and collective aspects of rationality, new impetus was brought (...) to this endeavor over the last century as mathematical logic along with the social and behavioral sciences emerged. Yet more recently, over the last several decades, propelled by the emergence of artificial intelligence, cognitive science, evolutionary psychology, neuropsychology, and related fields, even more sophisticated approaches to the study of rationality have emerged. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our (...) theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

In this chapter, we explore some ways in which reasoning based on mysticism can be rational, focusing on the episode “The Fortuneteller,” in which Aang, Katara, and Sokka save a village from a volcanic eruption. Throughout this episode, Sokka advocates a purely empirical approach to reasoning. The villagers, however, believe that no source of knowledge is more reliable than Aunt Wu, the local fortuneteller. At several points in the episode, Sokka claims that the villagers’ reliance on Aunt Wu is irrational. (...) The villagers claim otherwise: since Aunt Wu has never led them astray, it is rational to rely on her. As we will see, the villagers are right. Their approach to reasoning – based on Aunt Wu’s fortunetelling – is more rational than it initially seems to be. Roughly put, despite their belief in the mystical, the villagers behave in accord with a standard philosophical theory of rational decision-making, a theory of what makes some decisions rational and other decisions not. So Sokka is wrong to claim that the villagers’ reliance on Aunt Wu is irrational. The villagers behave quite rationally. (shrink)

This paper introduces a model for evidence denial that explains this behavior as a manifestation of rationality and it is based on the contention that social values (measurable as utilities) often underwrite these sorts of responses. Moreover, it is contended that the value associated with group membership in particular can override epistemic reason when the expected utility of a belief or belief system is great. However, it is also true that it appears to be the case that it (...) is still possible for such unreasonable believers to reverse this sort of dogmatism and to change their beliefs in a way that is epistemically rational. The conjecture made here is that we should expect this to happen only when the expected utility of the beliefs in question dips below a threshold where the utility value of continued dogmatism and the associated group membership is no longer sufficient to motivate defusing the counter-evidence that tells against such epistemically irrational beliefs. (shrink)

This article argues that Lara Buchak’s risk-weighted expected utility (REU) theory fails to offer a true alternative to expected utility theory. Under commonly held assumptions about dynamic choice and the framing of decision problems, rational agents are guided by their attitudes to temporally extended courses of action. If so, REU theory makes approximately the same recommendations as expected utility theory. Being more permissive about dynamic choice or framing, however, undermines the theory’s claim to capturing a steady choice (...) disposition in the face of risk. I argue that this poses a challenge to alternatives to expected utility theory more generally. (shrink)

Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the (...) objections and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, (...) Harman 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

The orthodox theory of instrumental rationality, expected utility (EU) theory, severely restricts the way in which risk-considerations can figure into a rational individual's preferences. It is argued here that this is because EU theory neglects an important component of instrumental rationality. This paper presents a more general theory of decision-making, risk-weighted expected utility (REU) theory, of which expected utility maximization is a special case. According to REU theory, the weight that each outcome gets in decision-making (...) is not the subjective probability of that outcome; rather, the weight each outcome gets depends on both its subjective probability and its position in the gamble. Furthermore, the individual's utility function, her subjective probability function, and a function that measures her attitude towards risk can be separately derived from her preferences via a Representation Theorem. This theorem illuminates the role that each of these entities plays in preferences, and shows how REU theory explicates the components of instrumental rationality. (shrink)

With the growing focus on prevention in medicine, studies of how to describe risk have become increasing important. Recently, some researchers have argued against giving patients “comparative risk information,” such as data about whether their baseline risk of developing a particular disease is above or below average. The concern is that giving patients this information will interfere with their consideration of more relevant data, such as the specific chance of getting the disease (the “personal risk”), the risk reduction the treatment (...) provides, and any possible side effects. I explore this view and the theories of rationality that ground it, and I argue instead that comparative risk information can play a positive role in decision-making. The criticism of disclosing this sort of information to patients, I conclude, rests on a mistakenly narrow account of the goals of prevention and the nature of rational choice in medicine. (shrink)

Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox asa normative argument, concerned with ‘the rational man’ and not the ‘real man’, to use his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, being concerned not so (...) much with therationality of choicesas with therationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. While not denying that this use of the paradox was fruitful in many ways, we propose another use that turns out also to be compatible with an experimental perspective. Following Allais’s hints on ‘the experimental definition of rationality’, this new use consists inletting the experiment itself speak of the rationality or otherwise of the subjects. In the 1970s, a short sequence of papers inspired by Allais implemented original ways of eliciting the reasons guiding the subjects’ choices, and claimed to be able to draw relevant normative consequences from this information. We end by reviewing this forgotten experimental avenue not simply historically, but with a view to recommending it for possible use by decision theorists today. (shrink)

The Lockean Thesis says that you must believe p iff you’re sufficiently confident of it. On some versions, the 'must' asserts a metaphysical connection; on others, it asserts a normative one. On some versions, 'sufficiently confident' refers to a fixed threshold of credence; on others, it varies with proposition and context. Claim: the Lockean Thesis follows from epistemic utility theory—the view that rational requirements are constrained by the norm to promote accuracy. Different versions of this theory generate different versions of (...) Lockeanism; moreover, a plausible version of epistemic utility theory meshes with natural language considerations, yielding a new Lockean picture that helps to model and explain the role of beliefs in inquiry and conversation. Your beliefs are your best guesses in response to the epistemic priorities of your context. Upshot: we have a new approach to the epistemology and semantics of belief. And it has teeth. It implies that the role of beliefs is fundamentally different than many have thought, and in fact supports a metaphysical reduction of belief to credence. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Standard decision theory, or rational choice theory, is often interpreted to be a theory of instrumental rationality. This dissertation argues, however, that the core requirements of orthodox decision theory cannot be defended as general requirements of instrumental rationality. Instead, I argue that these requirements can only be instrumentally justified to agents who have a desire to have choice dispositions that are stable over time and across different choice contexts. Past attempts at making instrumentalist arguments for the core requirements (...) of decision theory fail due to a pervasive assumption in decision theory, namely the assumption that the agent’s preferences over the objects of choice – be it outcomes or uncertain prospects – form the standard of instrumental rationality against which the agent’s actions are evaluated. I argue that we should instead take more basic desires to be the standard of instrumental rationality. But unless agents have a desire to have stable choice dispositions, according to this standard, instrumental rationality turns out to be more permissive than orthodox decision theory. (shrink)

We use a theorem from M. J. Schervish to explore the relationship between accuracy and practical success. If an agent is pragmatically rational, she will quantify the expected loss of her credence with a strictly proper scoring rule. Which scoring rule is right for her will depend on the sorts of decisions she expects to face. We relate this pragmatic conception of inaccuracy to the purely epistemic one popular among epistemic utility theorists.

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance (...) condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, (...) but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

Neoclassical economists use expected utility theory to explain, predict, and prescribe choices under risk, that is, choices where the decision-maker knows---or at least deems suitable to act as if she knew---the relevant probabilities. Expected utility theory has been subject to both empirical and conceptual criticism. This chapter reviews expected utility theory and the main criticism it has faced. It ends with a brief discussion of subjective expected utility theory, which is the theory neoclassical economists use to (...) explain, predict, and prescribe choices under uncertainty, that is, choices where the decision-maker cannot act on the basis of objective probabilities but must instead consult her own subjective probabilities. (shrink)

According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which states (...) that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ i, assigns an equal or higher weight to another agent, $$\hbox {j}$$ j,, he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely rational and (...) sympathetic $$\hbox {j}$$ j choose for him whether to accept a bet with positive expected utility. If $$\hbox {i}$$ i assigns a lower weight to $$\hbox {j}$$ j than to himself, he must not be willing to pay any positive price for letting $$\hbox {j}$$ j choose for him. Respecting the constraint entails, we show, that the impact of disagreement on one’s degree of belief is not independent of what the disagreement is discovered to be. (shrink)

When you are indifferent between two options, it’s rationally permissible to take either. One way to decide between two such options is to flip a fair coin, taking one option if it lands heads and the other if it lands tails. Is it rationally permissible to employ such a tie-breaking procedure? Intuitively, yes. However, if you are genuinely risk-averse—in particular, if you adhere to risk-weighted expected utility theory (Buchak in Risk and rationality, Oxford University Press, 2013) and have (...) a strictly convex risk-function—the answer will often be no: the REU of deciding by coin-flip will be lower than the REU of choosing one of the options outright (so long as at least one of the options is a nondegenerate gamble). This turns out to be a significant worry for risk-weighted expected utility theory. I argue that it adds real bite to established worries about diachronic consistency afflicting views, like risk-weighted expected utility theory, that violate Independence. And that, while these worries might be surmountable, surmounting them comes at a price. (shrink)

Self-interest voting is irrational when it has even a small cost, but it can be rational for those who care about others; its expected utility (EU) may exceed its cost. For cosmopolitan voters (those who care about outsiders), the EU of voting increases with the number of affected others. The EU of voting for the good of the world now and in the future can thus be large. In some cases, the EU of parochial voting (e.g., considering only one's (...) nation) may not cross the cost threshold, but cosmopolitan voting can cross it. I apply these principles to various kinds of voting. And I compare voting to charity. Voting has the advantage of enlisting the coercive power of the state, but charity can be more focused on effective policies. I discuss campaign contributions, and I conclude with a discussion of the existence of utilitarian voters. (shrink)

Instability occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. In decision theory: An act is stable iff given that it is actually performed, its expected utility is maximal. When there is no stable choice available, the resulting instability can seem to pose a dilemma of practical rationality. A structurally very similar kind of instability, which occurs in cases of anti-expertise, can likewise seem to (...) create dilemmas of epistemic rationality. One possible line of response to such cases of instability, suggested by both Jeffrey (1983) and Sorensen (1987), is to insist that a rational agent can simply refuse to accept that such instability applies to herself in the first place. According to this line of thought it can be rational for a subject to discount even very strong empirical evidence that the anti-expertise condition obtains. I present a new variety of anti-expertise condition where no particular empirical stage-setting is required, since the subject can deduce a priori that an anti-expertise condition obtains. This kind of anti-expertise case is therefore not amenable to the line of response that Jeffrey and Sorensen recommend. (shrink)

According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and probability functions. The main (...) problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is defined over chance propositions (i.e., propositions describing objective probability distributions) as well as ordinary (non-chance) ones, and argue that one should explain different risk attitudes in terms of different forms of the utility function over such propositions. (shrink)

Decision theory requires agents to assign probabilities to states of the world and utilities to the possible outcomes of different actions. When agents commit to having the probabilities and/or utilities in a decision problem defined by objective features of the world, they may find themselves unable to decide which actions maximize expected utility. Decision theory has long recognized that work-around strategies are available in special cases; this is where dominance reasoning, minimax, and maximin play a role. Here we describe (...) a different work around, wherein a rational decision about one decision problem can be reached by ‘interpolating’ information from another problem that the agent believes has already been rationally solved. (shrink)

This article critically discusses the concept of economic rationality, arguing that it is too narrow and specific to encompass the full concept of practical rationality. Economic rationality is identified here with the use of the optimizing model of decision, as well as of expected utility apparatus to deal with uncertainty. To argue that practical rationality is broader than economic rationality, the article claims that practical rationality includes bounded rationality as a particular case, (...) and that bounded rationality cannot be reduced to economic rationality as defined here. (shrink)

Several philosophers have proposed Knowledge-Based Decision Theories (KDTs)—theories that require agents to maximize expected utility as yielded by utility and probability functions that depend on the agent’s knowledge. Proponents of KDTs argue that such theories are motivated by Knowledge-Reasons norms that require agents to act only on reasons that they know. However, no formal derivation of KDTs from Knowledge-Reasons norms has been suggested, and it is not clear how such norms justify the particular ways in which KDTs relate knowledge (...) and rational action. In this paper, I suggest a new axiomatic method for justifying KDTs and providing them with stronger normative foundations. I argue that such theories may be derived from constraints on the relation between knowledge and preference, and that these constraints may be evaluated relative to intuitions regarding practical reasoning. To demonstrate this, I offer a representation theorem for a KDT proposed by Hawthorne and Stanley (2008) and briefly evaluate it through its underlying axioms. -/- In section 1, I present knowledge-based decision theories generally and the versions of such theories suggested in the literature. In section 2, I argue that KDTs and theories of practical reasoning conjoined with Knowledge-Reasons norms generate constraints on the same relation—the relation between knowledge and preference. In section 3, I present a formal framework in which constraints on this relation may be expressed and from which KDTs may be derived. In section 4, I present a representation theorem for a specific KDT. In section 5, I briefly evaluate the axioms of the theory, and in section 6, I conclude. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with (...) infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter we review these different answers, with a special focus on the latter answer and the debate it has generated. (shrink)

In philosophical action theory there is a wide agreement that intentions, often understood in terms of plans, play a major role in the deliberation of rational agents. Planning accounts of rational agency challenge game- and decision-theoretical accounts in that they allow for rationality of actions that do not necessarily maximize expected utility but instead aim at satisfying long-term goals. Another challenge for game-theoretical understanding of rational agency has recently been put forth by the theory of team reasoning in (...) which the agents select their actions by doing their parts in the collective action that is best for the group. Both planning and team reasoning can be seen as instances of a similar type of reasoning in which actions are selected on the basis of an evaluation of a larger unit than an individual’s momentary act. In recent theories of collective agency, both planning and team reasoning have been defended against orthodox game theory, but, interestingly, by different authors: Raimo Tuomela has defended team reasoning in his theory of group agency, but he ignores temporally extended planning in this context. Michael Bratman has extended his theory of planning to the case of shared agency, but he does not seem to see a role for team reasoning in understanding shared intentional activities. In this paper, we argue that both accounts suffer from this one-sidedness. We aim to combine the main insights of Tuomela’s we-mode approach and Bratman’s planning approach into a fruitful synthesis that we think is necessary for understanding the nature of group agency. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a (...) result, we should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Pascal’s wager uses decision theory to argue that it is rational to attempt to nurture belief in God, based on the expected utility of believing (infinite happiness) compared to not believing (at best, only finite happiness). A belief in an eternal conscious torment in hell (infinite suffering) for non-believers makes the differences in expected utility even more apparent, strengthening the argument. Similar reasoning can also be used to calculate the expected moral value of actions, including procreation. Under (...) theism, if possible future children might suffer eternal conscious torment, the expected moral value of procreation is extremely negative. This implies that theists have a moral obligation not to procreate, which for most theists, entails a moral obligation to be celibate or to undergo sterilisation surgery. (shrink)

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an (...) agent's attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)