We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Traditionally, epistemologists have distinguished between epistemic and pragmatic goals. In so doing, they presume that much of game theory is irrelevant to epistemic enterprises. I will show that this is a mistake. Even if we restrict attention to purely epistemic motivations, members of epistemic groups will face a multitude of strategic choices. I illustrate several contexts where individuals who are concerned solely with the discovery of truth will nonetheless face difficult game theoretic problems. Examples of purely epistemic coordination problems and (...) social dilemmas will be presented. These show that there is a far deeper connection between economics and epistemology than previous appreciated. (shrink)

Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.

Lewis’ analysis of modality faces a problem in that it appears to confer unintended truth values to certain modal claims about the pluriverse: e.g. ‘It is possible that there are many worlds’ is false when we expect truth. This is the problem of advanced modalizing. Divers presents a principled solution to this problem by treating modal modifiers as semantically redundant in some such cases. However, this semantic move does not deal adequately with advanced de re modal claims. Here, we motivate (...) and detail a comprehensive semantics for advanced modalizing de dicto and de re. The generalized semantic feature of the initial solution is not redundancy but absence from counterpart-theoretic translations of world-constrictions. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed (...) by practicing experimentalists. (shrink)

Epistemic decision theory aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule. This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that no (...) satisfactory justification has been given. I then investigate one possible response to my argument and show the problems with this response. The conclusion is that there is a further need for justifying the requirement that a scoring rule should be strictly proper for precise credences. For scoring rules in the context of imprecise credences, an impossibility result has been established in the literature purporting to show that no strictly proper, continuous and real-valued scoring rule exists. However, a precise statement of the impossibility result requires precise definitions both of strict propriety and of continuity in the context of imprecise credences. Moreover, the result implies that we need to drop one of the three properties - strict propriety, continuity or being real-valued - to have a scoring rule for applying EpDT to imprecise credences. So, firstly, I offer definitions of strict propriety and of continuity and clarify the impossibility result. Then, I investigate what will happen if we drop one of the three properties. I argue that we should drop the property of being real-valued and I offer the general forms of two kinds of strictly proper, continuous and lexicographic scoring rules for imprecise credences. (shrink)

Darrell P. Rowbottom reviews the book "In defense of objective Bayesianism" by Jon Williamson.

Bayesians defend norms of ideal rationality such as probabilism, which they claim should be approximated by non-ideal thinkers. Yet, it is not often discussed exactly in what sense it is beneficial for an agent’s credence function to approximate probabilistic coherence. Some existing research indicates that approximating coherence leads to improvements in accuracy, whereas other research suggests that it decreases Dutch book vulnerability. Yet, the existing results don’t settle whether there is a way of approximating coherence that delivers both benefits at (...) once. We show that there is. (shrink)

Many philosophers hold that the probability axioms constitute norms of rationality governing degrees of belief. This view, known as subjective Bayesianism, has been widely criticized for being too idealized. It is claimed that the norms on degrees of belief postulated by subjective Bayesianism cannot be followed by human agents, and hence have no normative force for beings like us. This problem is especially pressing since the standard framework of subjective Bayesianism only allows us to distinguish between two kinds of credence (...) functions—coherent ones that obey the probability axioms perfectly, and incoherent ones that don’t. An attractive response to this problem is to extend the framework of subjective Bayesianism in such a way that we can measure differences between incoherent credence functions. This lets us explain how the Bayesian ideals can be approximated by humans. I argue that we should look for a measure that captures what I call the ‘overall degree of incoherence’ of a credence function. I then examine various incoherence measures that have been proposed in the literature, and evaluate whether they are suitable for measuring overall incoherence. The competitors are a qualitative measure that relies on finding coherent subsets of incoherent credence functions, a class of quantitative measures that measure incoherence in terms of normalized Dutch book loss, and a class of distance measures that determine the distance to the closest coherent credence function. I argue that one particular Dutch book measure and a corresponding distance measure are particularly well suited for capturing the overall degree of incoherence of a credence function. (shrink)