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  1. Ernest W. Adams (1964). On Rational Betting Systems. Archiv für Mathematische Logik Und Grundlagenforschung 6:7-29.
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  2. Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra (2008). De Finetti's No-Dutch-Book Criterion for Gödel Logic. Studia Logica 90 (1):25 - 41.
    We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
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  3. Paul Anand, Prasanta Pattanaik & Clemens Puppe (eds.) (2008). The Oxford Handbook of Rational and Social Choice. Oxford University Press.
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  4. Brad Armendt (2010). Stakes and Beliefs. Philosophical Studies 147 (1):71 - 87.
    The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief as stake-invariant (...)
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  5. Brad Armendt (1993). Dutch Books, Additivity, and Utility Theory. Philosophical Topics 21 (1):1-20.
    One guide to an argument's significance is the number and variety of refutations it attracts. By this measure, the Dutch book argument has considerable importance.2 Of course this measure alone is not a sure guide to locating arguments deserving of our attention—if a decisive refutation has really been given, we are better off pursuing other topics. But the presence of many and varied counterarguments at least suggests that either the refutations are controversial, or that their target admits of more than (...)
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  6. Brad Armendt (1980). Is There a Dutch Book Argument for Probability Kinematics? Philosophy of Science 47 (4):583-588.
    Dutch Book arguments have been presented for static belief systems and for belief change by conditionalization. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a Dutch Book.
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  7. Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  8. Frank Arntzenius, Adam Elga & John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251 - 283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  9. Patricia Baillie (1973). Confirmation and the Dutch Book Argument. British Journal for the Philosophy of Science 24 (4):393-397.
  10. Paul Bartha (2004). Countable Additivity and the de Finetti Lottery. British Journal for the Philosophy of Science 55 (2):301-321.
    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 (...)
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  11. Luc Bovens, Four Brides for Twelve Brothers - How to Dutch Book a Group of Fully Rational Players.
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  12. Darren Bradley & Hannes Leitgeb (2006). When Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments. Analysis 66 (290):119–127.
    If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. (...)
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  13. Seamus Bradley (2012). Dutch Book Arguments and Imprecise Probabilities. In Dennis Dieks, Stephan Hartmann, Michael Stoeltzner & Marcel Weber (eds.), Probabilities, Laws and Structures. Springer.
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  14. John Cantwell (2002). The Pragmatic Stance. Croatian Journal of Philosophy 2 (3):319-336.
    The view that decision methods can only be justified by appeal to pragmatic considerations is defended. Pragmatic considerations are viewed as providing the underlying subject matter (“semantics”) of decision theories. It is argued that other approaches (e.g. justifying principles by appeal to obviousness, common usage, etc.) fail to provide grounds for a normative decision theory.It is argued that preferences that can lead to pragmatically adverse outcomes in a relevantly similar possible decision situation are pragmatically unsound, even if the decision situation (...)
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  15. Shoutir Kishore Chatterjee (2003). Statistical Thought: A Perspective and History. OUP Oxford.
    In this unique monograph, based on years of extensive work, Chatterjee presents the historical evolution of statistical thought from the perspective of various approaches to statistical induction. Developments in statistical concepts and theories are discussed alongside philosophical ideas on the ways we learn from experience. -/- Suitable for researchers, lecturers and students in statistics and the history of science this book is aimed at those who have had some exposure to statistical theory. It is also useful to logicians and philosophers (...)
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  16. David Christensen (2007). Epistemic Self-Respect. Proceedings of the Aristotelian Society 107 (1pt3):319-337.
  17. David Christensen (2001). Preference-Based Arguments for Probabilism. Philosophy of Science 68 (3):356-376.
    Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each case (...)
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  18. David Christensen (1996). Dutch-Book Arguments Depragmatized: Epistemic Consistency for Partial Believers. Journal of Philosophy 93 (9):450-479.
    The most immediately appealing model for formal constraints on degrees of belief is provided by probability theory, which tells us, for instance, that the probability of P can never be greater than that of (P v Q). But while this model has much intuitive appeal, many have been concerned to provide arguments showing that ideally rational degrees of belief would conform to the calculus of probabilities. The arguments most frequently used to make this claim plausible are the so-called "Dutch Book" (...)
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  19. David Christensen (1991). Clever Bookies and Coherent Beliefs. Philosophical Review 100 (2):229-247.
  20. David Phiroze Christensen (2004). Putting Logic in its Place: Formal Constraints on Rational Belief. Oxford University Press.
    What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.
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  21. A. I. Dale (1976). Probability Logic and F. Philosophy of Science 43 (2):254 - 265.
    In order that a degree-of-belief function be coherent it is necessary and sufficient that it satisfy the axioms of probability theory. This theorem relies heavily for its proof on the two-valued sentential calculus, which emerges as a limiting case of a continuous scale of truth-values. In this "continuum of certainty" a theorem analogous to that instanced above is proved.
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  22. Barbara Davidson & Robert Pargetter (1985). In Defence of the Dutch Book Argument. Canadian Journal of Philosophy 15 (3):405 - 423.
  23. Bruno de Finetti (1981). The Role of 'Dutch Books' and of 'Proper Scoring Rules'. British Journal for the Philosophy of Science 32 (1):55-56.
  24. Bruno de Finetti (1981). The Role of 'Dutch Books' and of 'Proper Scoring Rules'. British Journal for the Philosophy of Science 32 (1):55-56.
  25. Bruno de Finetti (1970). Theory of Probability. New York: John Wiley.
  26. Bruno de Finetti (1937). La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Annales de l'Institut Henri Poincaré 17:1-68.
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  27. Richard Dietz (2010). On Generalizing Kolmogorov. Notre Dame Journal of Formal Logic 51 (3):323-335.
    In his "From classical to constructive probability," Weatherson offers a generalization of Kolmogorov's axioms of classical probability that is neutral regarding the logic for the object-language. Weatherson's generalized notion of probability can hardly be regarded as adequate, as the example of supervaluationist logic shows. At least, if we model credences as betting rates, the Dutch-Book argument strategy does not support Weatherson's notion of supervaluationist probability, but various alternatives. Depending on whether supervaluationist bets are specified as (a) conditional bets (Cantwell), (b) (...)
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  28. Frank Doring (2000). Conditional Probability and Dutch Books. Philosophy of Science 67 (3):391 - 409.
    There is no set Δ of probability axioms that meets the following three desiderata: (1) Δ is vindicated by a Dutch book theorem; (2) Δ does not imply regularity (and thus allows, among other things, updating by conditionalization); (3) Δ constrains the conditional probability q(·,z) even when the unconditional probability p(z) (=q(z,T)) equals 0. This has significant consequences for Bayesian epistemology, some of which are discussed.
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  29. Frank Döring (2000). Conditional Probability and Dutch Books. Philosophy of Science 67 (3):391-409.
    There is no set Δ of probability axioms that meets the following three desiderata: (1) Δ is vindicated by a Dutch book theorem; (2) Δ does not imply regularity (and thus allows, among other things, updating by conditionalization); (3) Δ constrains the conditional probability q(·,z) even when the unconditional probability p(z) (=q(z,T)) equals 0. This has significant consequences for Bayesian epistemology, some of which are discussed.
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  30. Igor Douven (1999). Inference to the Best Explanation Made Coherent. Philosophy of Science 66 (Supplement):S424-S435.
    Van Fraassen (1989) argues that Inference to the Best Explanation is incoherent in the sense that adopting it as a rule for belief change will make one susceptible to a dynamic Dutch book. The present paper argues against this. A strategy is described that allows us to infer to the best explanation free of charge.
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  31. Kai Draper & Joel Pust (2008). Diachronic Dutch Books and Sleeping Beauty. Synthese 164 (2):281 - 287.
    Hitchcock advances a diachronic Dutch Book argument (DDB) for a 1/3 answer to the Sleeping Beauty problem. Bradley and Leitgeb argue that Hitchcock’s DDB argument fails. We demonstrate the following: (a) Bradley and Leitgeb’s criticism of Hitchcock is unconvincing; (b) nonetheless, there are serious reasons to worry about the success of Hitchcock’s argument; (c) however, it is possible to construct a new DDB for 1/3 about which such worries cannot be raised.
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  32. Patryk Dziurosz-Serafinowicz (2009). Subiektywne prawdopodobieństwo i problem przeliczalnej addytywności. Filozofia Nauki 1.
    The aim of this paper is to present and analyse Bruno de Finetti's view that the axiom of countable additivity of the probability calculus cannot be justified in terms of the subjective interpretation of probability. After presenting the core of the subjective theory of probability and the main de Finetti's argument against the axiom of countable additivity (the so called de Finetti's infinite lottery) I argue against de Finetti's view. In particular, I claim that de Finetti does not prove the (...)
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  33. Patryk Dziurosz-Serafinowicz (2009). Subjective Probability and the Problem of Countable Additivity. Filozofia Nauki 1.
    The aim of this paper is to present and analyse Bruno de Finetti's view that the axiom of countable additivity of the probability calculus cannot be justified in terms of the subjective interpretation of probability. After presenting the core of the subjective theory of probability and the main de Finetti's argument against the axiom of countable additivity (the so called de Finetti's infinite lottery) I argue against de Finetti's view. In particular, I claim that de Finetti does not prove the (...)
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  34. Kenny Easwaran (2014). Regularity and Hyperreal Credences. Philosophical Review 123 (1):1-41.
    Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...)
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  35. Adam Elga (2010). Subjective Probabilities Should Be Sharp. Philosophers' Imprint 10 (05).
    Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.
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  36. Donald Gillies (1991). Intersubjective Probability and Confirmation Theory. British Journal for the Philosophy of Science 42 (4):513-533.
    This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of (...)
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  37. Clark Glymour (1980). Theory and Evidence. Princeton University Press.
  38. D. Goldstick (2000). Three Epistemic Senses of Probability. Philosophical Studies 101 (1):59-76.
  39. A. Hajek (2008). Arguments for-or Against-Probabilism? British Journal for the Philosophy of Science 59 (4):793-819.
    Four important arguments for probabilism--the Dutch Book, representation theorem, calibration, and gradational accuracy arguments--have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...)
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  40. Alan Hajek (2008). Dutch Book Arguments. In Paul Anand, Prasanta Pattanaik & Clemens Puppe (eds.), The Oxford Handbook of Rational and Social Choice. Oxford University Press.
    in The Oxford Handbook of Corporate Social Responsibility, ed. Paul Anand, Prasanta Pattanaik, and Clemens Puppe, forthcoming 2007.
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  41. Alan Hajek (2005). Scotching Dutch Books? Philosophical Perspectives 19 (1):139-151.
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  42. Alan Hájek (2005). Scotching Dutch Books? Philosophical Perspectives 19 (1):139–151.
    The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...)
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  43. James Hawthorne & Michael Silberstein (1995). For Whom the Bell Arguments Toll. Synthese 102 (1):99-138.
    We will formulate two Bell arguments. Together they show that if the probabilities given by quantum mechanics are approximately correct, then the properties exhibited by certain physical systems must be nontrivially dependent on thetypes of measurements performedand eithernonlocally connected orholistically related to distant events. Although a number of related arguments have appeared since John Bell's original paper (1964), they tend to be either highly technical or to lack full generality. The following arguments depend on the weakest of premises, and the (...)
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  44. Brian Hedden (2013). Incoherence Without Exploitability. Noûs 47 (3):482-495.
  45. Klaus Heilig (1978). Carnap and de Finetti on Bets and the Probability of Singular Events: The Dutch Book Argument Reconsidered. British Journal for the Philosophy of Science 29 (4):325-346.
  46. Colin Howson (2008). De Finetti, Countable Additivity, Consistency and Coherence. British Journal for the Philosophy of Science 59 (1):1-23.
    Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...)
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  47. Colin Howson (2012). Modelling Uncertain Inference. Synthese 186 (2):475-492.
    Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical interpretation of the formalism, one which, it is argued, is both more natural and also avoids other, widely-made (...)
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  48. Colin Howson (2007). Logic with Numbers. Synthese 156 (3):491-512.
    Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...)
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  49. Colin Howson (1989). Subjective Probabilities and Betting Quotients. Synthese 81 (1):1 - 8.
    This paper addresses the problem of why the conditions under which standard proofs of the Dutch Book argument proceed should ever be met. In particular, the condition that there should be odds at which you would be willing to bet indifferently for or against are hardly plausible in practice, and relaxing it and applying Dutch book considerations gives only the theory of upper and lower probabilities. It is argued that there are nevertheless admittedly rather idealised circumstances in which the classic (...)
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  50. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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