Dutch Book Arguments (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy # Dutch Book Arguments First published Wed Jun 15, 2011; substantive revision Sat May 14, 2022 The Dutch Book argument (DBA) for probabilism (namely the view that an agent’s degrees of belief should satisfy the axioms of probability) traces to Ramsey’s work in “Truth and Probability”. He mentioned only in passing that an agent who violates the probability axioms would be vulnerable to having a book made against him and this has led to considerable debate and confusion both about exactly what Ramsey intended to show and about if, and how, a cogent version of the argument can be given. The basic idea behind the argument has also been applied in defense of a variety of principles, some of which place additional constraints on an agent’s current beliefs, with others, such as Conditionalization, purporting to govern how degrees of belief should evolve over time. ## 1. The Basic Dutch Book Argument for Probabilism ### 1.1 The Probability Axioms and the Dutch Book Theorem The conclusion of the basic DBA is that the degrees of belief, or credences, that an agent attaches to the members of

Bayesian Epistemology > Supplementary Documents (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy #### Supplement to Bayesian Epistemology ## Supplementary Documents - A. Unsharp Credences and Dutch Books - B. Comparative Probability and Conditional Credence - C. The Indifference Principle: The Jeffreys-Jaynes Approach - D. The Principle of Maximum Entropy - E. Objective Bayesianism and Impermissive Bayesianism - F. Shimony’s Qualification of Conditionalization - G. Jeffrey Conditionalization: A General Formulation - H. Proof of the Result about the Red Jelly Bean --- ### A. Unsharp Credences and Dutch Books Walley (1991: sec. 2.2 and 2.3) develops a betting account of credences that permits one to have a variety of attitudes toward bets or the lack of thereof, which does not force a credence to be as sharp as a real number. On this view, a credence can be unsharp in this way: it can be bounded by one or another interval of real numbers without being equal to any particular real number or interval—even the tightest bound on a credence can be an incomplete description of that credence. The result is a version of Probabili

# Objective Bayesianism and the Maximum Entropy Principle Entropy. Published: 2013-09-04. 30 citations. ## Authors - Jürgen Landes (University of Kent): h-index 17; 890 citations - Jon Williamson (University of Kent): h-index 34; 5,125 citations; corresponding author ## Topics - Epistemology, Ethics, and Metaphysics - Statistical Mechanics and Entropy - Bayesian Modeling and Causal Inference ## Funding - Arts and Humanities Research Council --- # entropy ## Abstract Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising wor