We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We (...) show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs. (shrink)

On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering points as higher-order abstractions from regions. Over the years, such theories have focused almost exclusively on the topological and geometric structure of space. We introduce to region-based theories of space a new primitive binary relation (‘qualitative probability’) that is tied (...) to _measure_. It expresses that one region is _smaller than or equal in size_ to another. Algebraic models of our theory are _separation_ _σ_-_algebras with qualitative probability_: \((\mathbb {B}, \ll, \preceq )\), where \(\mathbb {B}\) is a Boolean _σ_-algebra, ≪ is a separation relation on \(\mathbb {B}\), and ≼ is a qualitative probability on \(\mathbb {B}\). We show that from algebraic models of this kind we can, in an interesting class of cases, recover a compact Hausdorff topology _X_, together with a countably additive measure _μ_ on a _σ_-field of Borel subsets of that topology, and that \((\mathbb {B}, \ll, \preceq )\) is isomorphic to a ‘standard model’ arising out of the pair (_X_, _μ_). It follows from one of our main results that any closed ball in Euclidean space, \(\mathbb {R}^{n}\), together with Lebesgue measure arises in this way from a separation _σ_-algebra with qualitative probability. (shrink)

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (shrink)

In both axiomatic theories and the practice of extensive measurement, it is assumed that a series of replicas of any given object can be found. The replicas give rise to a standard series, the "multiples" of the given object. The numerical value assigned to any object is determined, approximately, by comparisons with members of a suitable standard series. This prescription introduces unspecified errors, if the comparison process is somewhat insensitive, so that "replicas" are not really equivalent. In this paper, it (...) is assumed that the comparison process leads only to a semiorder, which allows for such insensitivity. It is shown that, nevertheless, extensive measurement can be carried out, provided that a certain set of (plausible) axioms is valid. Approximate measures, and their limits of error, can be derived from finite sets of semiorder observations. These approximate measures converge to ratio-scale exact measurement. (shrink)

Despite the ubiquity of uncertainty, scientific attention has focused primarily on probabilistic approaches, which predominantly rely on the assumption that uncertainty can be measured and expressed numerically. At the same time, the increasing amount of research from a range of areas including psychology, economics, and sociology testify that in the real world, people’s understanding of risky and uncertain situations cannot be satisfactorily explained in probabilistic and decision-theoretical terms. In this article, we offer a theoretical overview of an alternative approach to (...) uncertainty developed in the framework of the ecological rationality research program. We first trace the origins of the ecological approach to uncertainty in Simon’s bounded rationality and Brunswik’s lens model framework and then proceed by outlining a theoretical view of uncertainty that ensues from the ecological rationality approach. We argue that the ecological concept of uncertainty relies on a systemic view of uncertainty that features it as a property of the organism–environment system. We also show how simple heuristics can deal with unmeasurable uncertainty and in what cases ignoring probabilities emerges as a proper response to uncertainty. (shrink)

Recently, much attention has been paid to ‘rational requirements’ and, especially, to what I call ‘rational requirements of formal coherence as such’. These requirements are satisfied just when our attitudes are formally coherent: for example, when our beliefs do not contradict each other. Nevertheless, these requirements are puzzling. In particular, it is unclear why we should satisfy them. In light of this, I explore the conjecture that there are no requirements of formal coherence. I do so by trying to construct (...) a theory of error for the idea that there are such requirements. (shrink)

Critical race theorists and standpoint epistemologists argue that agents who are members of dominant social groups are often in a state of ignorance about the extent of their social dominance, where this ignorance is explained by these agents' membership in a socially dominant group (e.g., Mills 2007). To illustrate this claim bluntly, it is argued: 1) that many white men do not know the extent of their social dominance, 2) that they remain ignorant as to the extent of their dominant (...) social position even where this information is freely attainable, and 3) that this ignorance is due in part to the fact that they are white men. We argue that on Buchak's (2010, 2013) model of risk averse instrumental rationality, ignorance of one's privileges can be rational. This argument yields a new account of elite-group ignorance, why it may occur, and how it might be alleviated. (shrink)

This article considers the popular thesis that a more proportional relationship between a cause and its effect yields a more abstract causal explanation of that effect, which in turn produces a deeper explanation. This thesis is taken to have important implications for choosing the optimal granularity of explanation for a given explanandum. In this article, I argue that this thesis is not generally true of probabilistic causal relationships. In light of this finding, I propose a pragmatic, interest-relative measure of explanatory (...) depth. This measure uses a decision-theoretic model of information pricing to determine the optimal granularity of explanation for a given explanandum, agent, and decision problem. (shrink)

Why would decision makers adopt heuristics, priors, or in short “habits” that prevent them from optimally using pertinent information—even when such information is freely-available? One answer, Herbert Simon’s “procedural rationality” regards the question invalid: DMs do not, and in fact cannot, process information in an optimal fashion. For Simon, habits are the primitives, where humans are ready to replace them only when they no longer sustain a pregiven “satisficing” goal. An alternative answer, Daniel Kahneman’s “mental economy” regards the question valid: (...) DMs make decisions based on optimization. Kahneman understands optimization not differently from the standard economist’s “bounded rationality.” This might surprise some researchers given that the early Kahneman, along with Tversky, have uncovered biases that appear to suggest that choices depart greatly from rational choices. However, once we consider cognitive cost as part of the constraints, such biases turn out to be occasional failures of habits that are otherwise optimal on average. They are optimal as they save us the cognitive cost of case-by-case deliberation. While Kahneman’s bounded rationality situates him in the neoclassical economics camp, Simon’s procedural rationality echoes Bourdieu’s “habitus” camp. To abridge the fault line of the two camps, this paper proposes a “two problem areas hypothesis.” Along the neoclassical camp, habits satisfy wellbeing, what this paper calls “substantive satisfaction.” Along the Bourdieu camp, habits satisfy belonging, love, and bonding with one’s environment, what this paper calls “transcendental satisfaction.”. (shrink)

L. A. Paul’s Transformative Experience makes the claim that many important life decisions are epistemically and personally transformative in a way that does not allow us to assign subjective values to their outcomes. As a result, we cannot use normative decision theory to make such decisions rationally, or when we modify it to do so, decision theory leads us to choose in a way that is in tension with our authenticity. This paper examines Paul’s version of decision theory, and whether (...) this version in fact admits of the challenge she wants to raise. I focus on her psychological realist view of utilities and beliefs and her notion of rational, authentic preferences as informed by imaginative acquaintance. I argue that Paul fails to engage critically with traditional accounts of decision theory and, on closer inspection, it is not clear that her version of decision theory entails a tension between rational and authentic choice. More importantly, I argue that if her contribution is instead to bring to light the importance of authenticity alongside rational decision-making, the definition she provides of authenticity in fact undermines her argument. (shrink)

This paper reports an experimental comparison of attitudes toward time and toward money in experience-based decisions. Preferences were elicited under rank-dependent utility for prospects with two or three consequences expressed either in time or in monetary units. Probabilities were unknown but learned through sampling. More specifically, time and money were compared under two conditions. In a first experiment, both consequences and probabilities of prospects were unknown and learned through sequential sampling. In a second experiment, the possible consequences were revealed after (...) the sampling. A real incentive system was implemented for both time and money. The heterogeneity of preferences was assessed for time and for money through individual and mixed modeling estimations. We observe that the nature of consequences (time or money) modifies probability weighting in terms of elevation and sensitivity. Subjects exhibit more optimism and less sensitivity to probability changes when deciding about time than about money. Revealing the consequences impacts the shape of the utility function and leaves probability weighting unchanged. We also observe that the real incentives have no effect except for the reduction in decision errors. This effect is stronger for money than for time. (shrink)

I have applied a fairly general, learning theoretic perspective to some questions raised by Reichenbach's positions on induction and discovery. This is appropriate in an examination of the significance of Reichenbach's work, since the learning-theoretic perspective is to some degree part of Reichenbach's reliabilist legacy. I have argued that Reichenbach's positivism and his infatuation with probabilities are both irrelevant to his views on induction, which are principally grounded in the notion of limiting reliability. I have suggested that limiting reliability is (...) still a formidable basis for the formulation of methodological norms, particularly when reliability cannot possibly be had in the short run, so that refined judgments about evidential support must depend upon measure-theoretic choices having nothing to do in the short run with the truth of the hypothesis under investigation. To illustrate the generality of Reichenbach's program, I showed how it can be applied to methods that aim to solve arbitrary assessment and discovery problems in various senses. In this generalized Reichenbachian setting, we can characterize the intrinsic complexity of reliable inductive inference in terms of topological complexity. Finally, I let Reichenbach's theory of induction have the last say about hypothetico-deductive method. (shrink)

Les représentants de l'École autrichienne sont ici mis sous la même bannière pour autant seulement qu'ils ont été unanimes à revendiquer pour les postulats de l'économie pure, les «lois exactes» de la théorie économique, c'est-à-dire de la théorie marginale de l'utilité, un statut particulier en ce sens qu'ils tenaient pour impossible, voire absurde ou simplement inutile de soumettre les postulats en cause à des tests empiriques. L'apriorisme dont ils se réclament, fait à juste titre la marque de commerce de l'École (...) marginaliste autrichienne; Menger en a fourni les principes, von Mises la justification, et Rothbard s'est occupé de propager la doctrine de l'autre côté de l'Atlantique. (shrink)

This paper presents a procedure designed to aid physicians and patients in the process of making medical decisions, and illustrates its implementation to aid pregnant women, who decided to undergo prenatal diagnostic test choose a physician to administer it. The procedure is based on a medical decision-making model of Karni (J Risk Uncertain 39: 1–16, 2009). This model accommodates the possibility that the decision maker’s risk attitudes may vary with her state of health and incorporates other costs, such as pain (...) and inconvenience, associated with alternative treatments. The medical decision problem was chosen for its relative simplicity and the transparency it affords. (shrink)

Orthodox Probabilists hold that an inquirer ought to harbor a precise degree of confidence in each hypothesis about which she is concerned. Modest Probabilism is one of a family doctrines inspired by the thought that Orthodox Probabilists are thereby demanding that an inquirer effect a precision that is often unwarranted by her evidence. The purpose of this essay is (i) to explain the particular way in which Modest Probabilism answers to this thought, and (ii) to address an alleged counterexample to (...) Modest Probabilism meant to offer proof that Modest Probabilism is no better than its orthodox predecessor at avoiding unwarranted precision. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

Crucial to bayesian contributions to the philosophy of science has been a characteristic psychology, according to which investigators harbor degree of confidence assignments that (insofar as the agents are rational) obey the axioms of the probability calculus. The rub is that, if the evidence of introspection is to be trusted, this fruitful psychology is false: actual investigators harbor no such assignments. The orthodox bayesian response has been to argue that the evidence of introspection is not to be trusted here; it (...) is to investigators' dispositions--not to their felt convictions--that the psychology is meant to be (and succeeds in being) faithful. I argue that this response, in both its orthodox and convex-set bayesian forms, should be rejected--as should the regulative ideals that make the response seem so attractive. I offer a different variant of bayesianism, designed to give the evidence of introspection its due and thus realize (as I claim the other forms of bayesianism cannot) the prescriptive mission of the bayesian project. (shrink)

Incomplete preferences displaying ‘mildly sweetened’ structure are common, yet theoretically problematic. This paper examines the properties of the rankings induced by the set of all coherent completions of the mildly sweetened partial preference structure. Building on these properties, I propose an ensemble-based refinement of Hare’s prospectism criterion for rational choice when preferences are incomplete. Importantly, this ensemble-based refinement is immune to Peterson’s weak money pump argument. Hence, ensemble prospectism ensures outcome rationality. Furthermore, by recognizing the structural isomorphism between mildly sweetened (...) preference structures and Cover’s splitting rule in Blackwell’s Pick the Largest Number problem, ensemble prospectism can be shown to yield better-than-even odds of selecting the ex-post higher utility option—despite the absence of all-things-considered preferences ex ante. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model (...) for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment to make certain that, given the experimental outcome, the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model for the data but who (...) holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation (...) from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire. (shrink)

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not (...) decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory. (shrink)

It is widely assumed that a literal understanding of someone’s self-deception that p yields the following contradiction. Qua self-deceiver, she does not believe that p, yet – qua self-deceived – she does believe that p. I argue that this assumption is ill-founded. Literalism about self-deception – the view that self-deceivers literally self-deceive – is not committed to this contradiction. On the contrary, properly understood, literalism excludes it.

Risk is implicit in economic development. When does a course of economic development ethically balance risk and likely benefit? This paper examines the view of risk we find in Amartya Sen’s work on development. It shows that Sen’s capabilities approach leads to a more sensitive understanding of risk than traditional utility theory. Sen’s approach also supplies the basis of an argument for risk aversion in interventions that affect economic development. Sen’s approach describes development as aiming at freedom. The paper shows (...) how this claim can be made compatible with the social and relational basis of African communitarianism. (shrink)

We show that in infinite worlds the following three conditions are incompatible: The spatiotemporal ordering of individuals is morally irrelevant. All else being equal, the act of bringing about a good outcome with a high probability is better than the act of bringing about the same outcome with a low probability. One act is better than another only if there is a nonzero probability that it brings about a better outcome. The impossibility of combining these conditions shows that it is (...) more costly to endorse than has been previously acknowledged. (shrink)

Should social preferences conform to the principles of rationality we normally expect of individuals? Should they, for instance, conform to the consistency axioms of expected utility theory? This article considers one fragment of this question.

Whereas most commentators agree about the centrality of narratives in decision-making, the commentaries revealed little consensus about the nature of radical uncertainty. Here we consider thirteen objections to our views, including our characterization of the uncertain decision environment and associated cognitive, affective, and social processes. We conclude that under radical uncertainty, narratives rather than probabilities are the currency of thought.

Many decisions involve multiple stages of choices and events, and these decisions can be represented graphically as decision trees. Optimal decision strategies for decision trees are commonly determined by a backward induction analysis that demands adherence to three fundamental consistency principles: dynamic, consequential, and strategic. Previous research found that decision-makers tend to exhibit violations of dynamic and strategic consistency at rates significantly higher than choice inconsistency across various levels of potential reward. The current research extends these findings under new conditions; (...) specifically, it explores the extent to which these principles are violated as a function of the planning horizon length of the decision tree. Results from two experiments suggest that dynamic inconsistency increases as tree length increases; these results are explained within a dynamic approach–avoidance framework. (shrink)

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French philosopher’s (...) fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory. (shrink)

Conviction Narrative Theory (CNT) is a theory of choice underradical uncertainty– situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people usenarratives– structured representations of causal, temporal, analogical, and valence relationships – rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. According to CNT, (...) narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels “right” to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We identify 12 propositions to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, and communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences. (shrink)

In Chapter 12 of the General Theory, on “The State of Long-Term Expectation,” Keynes writes: “It would be foolish, in forming our expectations, to attach great weight to matters which are very uncertain”. In a footnote to this sentence, Keynes points out that by “very uncertain” he does not mean the same as “very improbable” and refers to the chapter on “The Weight of Arguments” in his earlier Treatise on Probability. The purpose of this article, in the first place, is (...) to provide an account of, and to sort out the relations between, Keynes's views on probability, uncertainty, and the weight of arguments. (shrink)

Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that (...) the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)

In this article we explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically (...) true: i.e. that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when Allais made his case against the neo-Bernoullians. (shrink)

In some situations, a decision is best represented by an incompletely analyzed act: conditionally on a given event A, the consequences of the decision on sub-events are perfectly known and uncertainty becomes probabilizable, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event ${\bar{A}}$ is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Resulting decision criteria aggregate partial evaluations consisting of (i) the conditional expected utility (...) associated with the analyzed part of the decision, and (ii) the best and worst consequences of its non-analyzed part. The representation theorem is consistent with a wide variety of decision criteria, which allows for expressing various degrees of knowledge on ( ${A, \bar{A}}$ ) and various types of attitude toward ambiguity and uncertainty. This diversity is taken into account by specific models already existing in the literature. We exploit this fact and propose some particular forms of our model incorporating these models as sub-models and moreover expressing various types of beliefs concerning the relative plausibility of the analyzed and the non-analyzed events ranging from probabilities to complete ignorance that include capacities. (shrink)

A question at the intersection of scientific modeling and public choice is how to deal with uncertainty about model predictions. This "high-level" uncertainty is necessarily value-laden, and thus must be treated as irreducibly subjective. Nevertheless, formal methods of uncertainty analysis should still be employed for the purpose of clarifying policy debates. I argue that such debates are best informed by models which integrate objective features with subjective ones. This integrated subjectivism is illustrated with a case study from the literature on (...) monetary policy. The paper concludes with some morals for the use of models in determining climate policy. (shrink)

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

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...) and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) ['P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained. The primary reason for this is that the weight of a piece of evidence varies (...) with the means by which it is provided, so knowledge of Y-ness does not have uniform impact on the probability of X. A better updating of the probability of X is provided by P(X|Y*), where Y* is not an outcome of the chance process being observed, but the sentence 'the outcome Y has been observed', an 'outcome' of the subsequent observation process. This alternative formula is widely endorsed in practice, but not well recognized in theory, where the oversight has generated some unsatisfactory consequences. (shrink)

In this paper I study dynamical models of rational deliberation within the context of Newcomb's problem. Such models have been used to argue against the soundness of the "tickle'" defense of evidential decision theory, which is based on the idea that sophisticated decision makers can break correlations between states and acts by introspecting their own beliefs and desires. If correct, this would show that evidential decision theory agrees with the recommendations of causal decision theory. I argue that an adequate understanding (...) of rational deliberation leads to deliberative processes for which this idea works. My proposal is modest, though. Evidential decision theory cannot always be reconciled with causal decision theory along the lines suggested here, but the agreement between the two theories is broader than previously thought. (shrink)

The concept of fitness is central to evolutionary biology. Models of evolutionary change typically use some quantity called “fitness” which measures an organism’s reproductive success. But what exactly does it mean that fitness is such a measure? In what follows, we look at the interplay between abstract evolutionary models and quantitative measures of fitness and develop a measurement-theoretic perspective on fitness in order to explore what makes certain measures of fitness significant.