We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk and uncertainty. For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased (...) uncertainty aversion for large-probability gains and for small-probability losses. (shrink)

A method for forcing norms onto individual agents in a multi-agent system is presented. The agents under study are supersoft agents: autonomous artificial agents programmed to represent and evaluate vague and imprecise information. Agents are further assumed to act in accordance with advice obtained from a normative decision module, with which they can communicate. Norms act as global constraints on the evaluations performed in the decision module and hence no action that violates a norm will be suggested to any agent. (...) Further constraints on action may then be added locally. The method strives to characterise real-time decision making in agents, in the presence of risk and uncertainty. (shrink)

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.

In a seminal paper, Aumann (1987, Econometrica 55, 1–18) showed how the choices of rational players could be analyzed in a unified state space framework. His innovation was to include the choices of the players in the description of the states, thus abolishing Savage’s (1954, The Foundations of Statistics. Wiley, New York) distinction between acts and consequences. But this simplification comes at a price: Aumann’s notion of Bayes rationality does not allow players to evaluate what would happen were they to (...) deviate from their actual choices. We show how the addition of a causal structure to the framework enables us to analyze such counterfactual statements, and use it to introduce a notion of causal rationality. Under a plausible causal independence condition, the two notions are shown to be equivalent. If we are prepared to accept this condition we can dispense with the causal apparatus and retain Aumann’s original framework. (shrink)

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

We argue that philosophers ought to distinguish epistemic decision theory and epistemology, in just the way ordinary decision theory is distinguished from ethics. Once one does this, the internalist arguments that motivate much of epistemic decision theory make sense, given specific interpretations of the formalism. Making this distinction also causes trouble for the principle called Propriety, which says, roughly, that the only acceptable epistemic utility functions make probabilistically coherent credence functions immodest. We cast doubt on this requirement, but then argue (...) that epistemic decision theorists should never have wanted such a strong principle in any case. (shrink)

Information is a force multiplier. Knowledge of the enemy's capability and intentions may be of far more value to a military force than additional troops or firepower. Situation assessment is the ongoing process of inferring relevant information about the forces of concern in a military situation. Relevant information can include force types, firepower, location, and past, present and future course of action. Situation assessment involves the incorporation of uncertain evidence from diverse sources. These include photographs, radar scans, and other forms (...) of image intelligence, or IMINT; electronics intelligence, or ELINT, derived from characteristics (e.g., wavelength) of emissions generated by enemy equipment; communications intelligence, or COMINT, derived from the characteristics of messages sent by the enemy; and reports from human informants (HUMINT). These sources must be combined to form a model of the situation. The sheer volume of data, the ubiquity of uncertainty, the number and complexity of hypotheses to consider, the high-stakes environment, the compressed time frame, and deception and damage from hostile forces, combine to present a staggeringly complex problem. Even if one could formulate a decision problem in reasonable time, explicit determination of an optimal decision policy exceeds any reasonable computational resources. While it is tempting to drop any attempt at rational analysis and rely purely on simple heuristics, we argue that this can lead to catastrophic outcomes. We present an architecture for a ``complex decision machine'' that performs rational deliberation to make decisions in real time. We argue that resource limits require such an architecture to be grounded in simple heuristic reactive processes. We thus argue that both simple heuristics and complex decision machines are required for effective decision making in real time for complex problems. We describe an implementation of our architecture applied to the problem of military situation assessment. (shrink)

Standard axioms of additively separable utility for choice over time and classic axioms of expected utility theory for choice under risk yield a generalized expected additively separable utility representation of risk-time preferences over probability distributions over sure streams of intertemporal outcomes. A dual approach is to use the analogues of the same axioms in a reversed order to obtain a generalized additively separable expected utility representation of time–risk preferences over intertemporal streams of probability distributions over sure outcomes. The paper proposes (...) an additional axiom, which is called risk-time reversal, for obtaining a special case of the two representations—expected discounted utility. The axiom of risk-time reversal postulates that if a risky lottery over streams of sure intertemporal outcomes and an intertemporal stream of risky lotteries yield the same probability distribution of possible outcomes in every point in time then a decision-maker is indifferent between the two. This axiom is similar to assumption 2 “reversal of order in compound lotteries” in Anscombe and Aumann :199–205, 1963, p. 201). (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new (...) elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

In binary choice between discrete outcome lotteries, an individual may prefer lottery L1 to lottery L2 when the probability that L1 delivers a better outcome than L2 is higher than the probability that L2 delivers a better outcome than L1. Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function (...) has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed. (shrink)

Uncertain or ambiguous events cannot be objectively measured by probabilities, i.e. different decision-makers may disagree about their likelihood of occurrence. This paper proposes a new decision-theoretical approach on how to measure ambiguity that is analogous to axiomatic risk measurement in finance. A decision-theoretical measure of ambiguity is a function from choice alternatives to non-negative real numbers. Our proposed measure of ambiguity is derived from a novel assumption that ambiguity of any choice alternative can be decomposed into a left-tail ambiguity and (...) a right-tail ambiguity. This decomposability assumption is combined with two standard assumptions: ambiguity sources are independent from outcomes and any elementary increase in uncertainty necessarily increases ambiguity. (shrink)

Evolution and Rationality marks the end of a three-year project, ‘Evolution, Cooperation, and Rationality’, directed at the University of Bristol by the book’s editors, Samir Okasha and Ken Binmore. The collection draws together the editors’ pick of the papers delivered at the conferences the project hosted, and covers a wide range of topics at the intersection of evolutionary theory and the social sciences. It is a splendid anthology: timely, interdisciplinary, thematically cohesive, and full of substantive and interesting disagreements between the (...) contributors. (shrink)

The standard Bayesian recipe for selecting the rational choice is presented. A familiar example in which the recipe fails to produce any definite result is introduced. It is argued that a generalization of Gärdenfors’ and Sahlin’s theory of unreliable probabilities — which itself does not guarantee a solution to the problem — offers the best available approach. But a number of challenges to this approach are also presented and discussed.

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} by assigning it a number π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} (...) as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document}. The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility. (shrink)

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...) reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction. (shrink)

Frank Knight (1921) famously distinguished the epistemic modes of certainty, risk, and uncertainty in order to characterize situations where deterministic, probabilistic or possibilistic foreknowledge is available. Because our probabilistic knowledge is limited, i.e. because many systems, e.g. the global climate, cannot be described and predicted probabilistically in a reliable way, Knight's third category, possibilistic foreknowledge, is not simply swept by the probabilistic mode. This raises the question how to justify possibilistic predictionsincluding the identication of the worst case. The development of (...) such a modal methodology is particularly vital with respect to predictions of climate change. I show that a methodological dilemma emerges when possibilistic predictions are framed in traditional terms and argue that a more nuanced conceptual framework, distinguishing dierent types of possibility, should be used in order to convey our uncertain knowledge about the future. The new conceptual scheme, however, questions the applicability of standard rules of rational decision-making, thus generating new challenges. (shrink)

This paper reflects on the notion of partial ambiguity. Using a framework decomposing ambiguity into distinct layers of analysis, among which are risk and model uncertainty, and allowing for different attitudes toward these layers, I show that partial ambiguity may prove less desirable than full ambiguity, even under ambiguity aversion. This observation poses difficulties for interpreting the notion of partial ambiguity in relation to the partial information available to determine the potential compositions of an ambiguous urn. Two Ellsberg-style thought experiments (...) are described to challenge the meaning of partial ambiguity further, and an alternative interpretation, based on a more ambiguous relation, is discussed. (shrink)

Most decisions concerning insurance and self-protection have to be taken in situations in which the effort exerted precedes the moment uncertainty realizes, and the probabilities of future states of the world are not perfectly known. By integrating these two characteristics in a simple theoretical framework, this paper derives plausible conditions under which ambiguity aversion raises the demand for insurance and self-protection. In particular, it is shown that in most usual situations where the level of ambiguity does not increase with the (...) level of effort, a simple condition of ambiguity prudence known as decreasing absolute ambiguity aversion is sufficient to give a clear and positive answer to the question: Does ambiguity aversion raise the optimal level of effort? (shrink)

This critical notice explores the distinction central to analytic philosophy between the logical study of the normative principles governing rational thought and the psychological study of the processes of thinking. Thomas Nagel maintains (1) that the fundamental principles of reasoning have normative force and make claims to universal validity; (2) that the fundamental principles of reasoning cannot be construed as the expression of contingent forms of life; and (3) that the identification of fundamental principles of reasoning should be completely independent (...) of psychological facts about how people reason. The notice draws upon intuitionist critiques of classical logic and the Allais paradox in expected utility theory to argue that (1) can be consistently combined with the denial of (2) and (3). (shrink)

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

The notion of supererogation—going above and beyond the call of duty—is typically discussed in a moral context. However, in this paper we argue for the existence of rationally supererogatory actions: that is, actions that go above and beyond the call of rational duty. In order to establish the existence of such actions, we first need to overcome the so-called paradox of supererogation: we need to provide some explanation for why, if some act is rationally optimal, it is not the case (...) that we are rationally required to carry out that act. We argue that a response to this ‘paradox’ can be found by reflecting on normative conflicts: cases where what is best according to some normative domain is different from what is best according to some other normative domain. (shrink)

It is natural to regard understanding as having a rational dimension, in the sense that understanding seems to require having justification for holding certain beliefs about the world. Some philosophers however argue that justification is not required to gain understanding of phenomena. In the present paper, my intention is to provide a critical examination of the arguments that have been offered against the view that understanding requires justification in order to show that, contrary to what they purport to establish, justification (...) remains a plausible requirement on understanding. (shrink)

A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents that, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the present discussion are to show that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality, since they render a certain sort of (...) arrogance rationally mandatory. (shrink)

This paper discusses the conditions under which an agent is rationally permitted to leave some uncertain propositions relevant to her decision out of her deliberation. By relying on the view that belief involves a defeasible disposition to treat a proposition as true in one’s reasoning, we examine the conditions under which such a disposition can be overridden and under which an agent should take into account her uncertainty as to a proposition she believes in the course of a particular deliberation. (...) We argue that, in some contexts, an agent can be faced with the choice of either accepting or not accepting a proposition she believes in the course of her deliberation. We provide a description of such higher-order deliberations within the framework of expected utility theory and draw conclusions regarding the phenomenon of pragmatic encroachment on knowledge. (shrink)

Scholars disagree about the plausibility of preference purification. Some see it as a familiar phenomenon. Others denounce it as conceptually incoherent, postulating that it relies on the psychologically implausible assumption of an inner rational agent. I argue that different notions of rationality can be leveraged to advance the debate: procedural rationality and structural rationality. I explicate how structural rationality, in contrast to procedural rationality, allows us to offer an account of the guiding idea behind preference purification that avoids inner rational (...) agents. Afterward, I address two pressing challenges against preference purification that emerge under the structural rationality account. (shrink)

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...) assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (shrink)

This paper provides a general framework for analyzing self-confirming policies. We study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. We characterize stationary monetary policies in a linear-quadratic setting.

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of (...) judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals. (shrink)

We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)

A person’s epistemic goals sometimes clash with pragmatic ones. At times, rational agents will degrade the quality of their epistemic process in order to satisfy a goal that is knowledge-independent (for example, to gain status or at least keep the peace with friends.) This is particularly so when the epistemic quest concerns an abstract political or economic theory, where evidence is likely to be softer and open to interpretation. Before wide-scale adoption of the Internet, people sought out or stumbled upon (...) evidence related to a proposition in a more random way. And it was difficult to aggregate the evidence of friends and other similar people to the exclusion of others, even if one had wanted to. Today, by contrast, the searchable Internet allows people to simultaneously pursue social and epistemic goals.This essay shows that the selection effect caused by a merging of social and epistemic activities will cause both polarization in beliefs and devaluation of expert testimony. This will occur even if agents are rational Bayesians and have moderate credences before talking to their peers. What appears to be rampant dogmatism could be just as well explained by the nonrandom walk in evidence-gathering. This explanation better matches the empirical evidence on how people behave on social media platforms. It also helps clarify why media outlets (not just the Internet platforms) might have their own pragmatic reasons to compromise their epistemic goals in today’s competitive and polarized information market. Yet, it also makes policy intervention much more difficult, since we are unlikely to neatly separate individuals’ epistemic goals from their social ones. (shrink)

We propose simple behavioral definitions of comparative uncertainty aversion for a single agent towards different sources of uncertainty. Our definitions allow for the comparison of utility curvature for different sources if the agent’s choices satisfy subjective expected utility towards each source. We discuss how our definitions can be applied to investigate ambiguity aversion in Klibanoff et al.’s :1849–1892, 2005) smooth ambiguity model, to study the effects of learning and situational factors on uncertainty preferences, and to compare uncertainty preferences between different (...) agents. (shrink)

State-dependent utility is a problem for the behavioural branch of decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This article gives grounds to reject these two views. The various models of beliefs can be shown to be unequally exposed to the problem of (...) state-dependent utility. The problem can be argued to be solved even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed. (shrink)

In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need to (...) be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper. (shrink)

This paper examines the preference-based approach to the identification of beliefs. It focuses on the main problem to which this approach is exposed, namely that of state-dependent utility. First, the problem is illustrated in full detail. Four types of state-dependent utility issues are distinguished. Second, a comprehensive strategy for identifying beliefs under state-dependent utility is presented and discussed. For the problem to be solved following this strategy, however, preferences need to extend beyond choices. We claim that this a necessary feature (...) of any complete solution to the problem of state-dependent utility. We also argue that this is the main conceptual lesson to draw from it. We show that this lesson is of interest to both economists and philosophers. (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)

Decision theory is founded on the principle that we ought to take the action that has the maximum expected value from among actions we are in a position to take. But prior to the notion of expected value is the notion of the actual value of that action: roughly, a measure of the good outcomes you would in fact procure if you were to take it. Surprisingly many decision theories operate without an analysis of actual value. I offer a definition (...) of actual value, and show that a form of decision theory due to Stalnaker can be reformulated so as to be in line with the edict to maximize expected value. By contrast, I show that there is no quantity — given by my definition or otherwise — that plays the role of actual value in Jeffrey's decision theory. (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)

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

Ockham’s razor is the idea that simpler hypotheses are to be preferred over more complex ones. In the context of medical diagnosis, this is taken to mean that when a patient has multiple symptoms, a single diagnosis should be sought that accounts for all the clinical features, rather than attributing a different diagnosis to each. This paper examines whether diagnostic parsimony can be justified by reference to probability theory. I argue that while attempts to offer universal justifications of diagnostic parsimony (...) fail, a more constrained use of this diagnostic principle can be supported. (shrink)

We study a class of representation mechanisms, based on reports made by a random subset of agents, called representatives, in a collective choice problem with quasi-linear utilities. We do not assume the existence of a common prior probability describing the distribution of preference types. In addition, there is no benevolent planner. Decisions will be carried out by an individual who cannot be assumed impartial, a self-interested executive. These assumptions impose new constraints on Mechanism Design. A robust mechanism is defined as (...) maximizing expected welfare under a vague prior probability distribution, and over a set of mechanisms which is at the same time immune from opportunistic manipulations by the executive, and compatible with truthful revelation of preferences by representatives. Robust mechanisms are characterized and their existence is shown. Sampling Groves mechanisms are shown to be robust. (shrink)

A general theory of acts leads to a theory of cognition distinguishing between formation of apriorical knowledge about values, norms, and cognitive beliefs, based on conditioning by means of rewards and punishments, and formation of aposteriorical knowledge based on conscious, theoretical analysis of observations. The latter, rational layer of consciousness can be built on the former, irrational layer only, if certain conditions are fulfilled. It is shown that rational cognition of values presupposes a notion of aposteriorical value, which challenges some (...) conventions of the 'value-free' social science, in particular, the so called guillotine of Hume. (shrink)