Dutch Book Arguments

by

Susan Vineberg

• LAST REVIEWED: 07 September 2022
• LAST MODIFIED: 31 March 2016
• DOI: 10.1093/obo/9780195396577-0301

Introduction

Dutch Book arguments have been invoked to defend various probabilistic norms of rationality. The idea originates with Ramsey, who observed that an agent whose degrees of belief (or credences) fail to satisfy the basic axioms of probability would be vulnerable to a sure betting loss (i.e., a Dutch Book). Here probabilities are understood as functions that attach values to sentences (or propositions), with the basic axioms requiring: (1) For each A, 0 ≤ pr (A) [non-negativity] (2) if A is a tautology, pr (A) = 1 [normalization] (sometimes this is strengthened to require that all logical or necessary truths are assigned the maximum value), and (3) if A and B are mutually exclusive, pr (A or B) = pr (A) + pr (B) [finite additivity]. Intuitively, credences that are associated with sure losses are rationally defective. But there has been considerable discussion over how to fill in the details of the argument, which Ramsey sketched, and over its overall cogency in defending the probability axioms as a constraint on rational degrees of belief (probabilism). Beyond defending the probability axioms as a constraint on rational credences, Dutch Book arguments have also been given to defend a variety of other norms including conditionalization principles that purport to govern belief change over time. The first few sections of this article focus on works that consider the premises and structure of the basic Dutch Book argument, its interpretation, and its connection with decision theory. The remaining sections are devoted to extensions of the basic Dutch Book argument for the probability axioms to arguments for additional constraints on rational credences.

General Overviews

There are a number of survey articles on Bayesianism and Bayesian epistemology that include a brief discussion of Dutch Book arguments, including Easwaran 2013 and Talbott 2015, as well as some devoted exclusively to Dutch Book arguments, such as Hájek 2008 and Vineberg 2011 that provide more thorough coverage, including some of the nuances of their interpretation along with criticism.

• Easwaran, Kenny. “Bayesianism.” In Oxford Bibliographies. 2013.

  Provides a brief but useful introduction to Bayesianism. Dutch Book arguments, accuracy arguments for probabilism, decision theory, conditionals, Bayesian philosophy of science and Bayesian epistemology are among the main topics.

• Hájek, Alan. “Dutch Book Arguments.” In Oxford Handbook of Rational and Social Choice. Edited by Paul Anand, Prasanta Pattanaik, and Clemens Puppe, 173–195. Oxford: Oxford University Press, 2008.

  A well-written introduction covering Dutch Book arguments for the probability axioms and various other norms. The treatment includes just the minimum technical detail needed to clearly present the relevant points about (and criticisms of) the arguments.

• Talbott, William. “Bayesian Epistemology.” In Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2015.

  Presents the fundamentals of Bayesian epistemology, including a short section on Dutch Book arguments.

• Vineberg, Susan. “Dutch Book Arguments.” In Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2011.

  Gives broad coverage of Dutch Book arguments for the probability axioms, conditionalization, and other norms. Provides the basic mechanics of these arguments and discusses their interpretation in considerable detail.