History of the Term Dutch Book

by Peter P. Wakker

1. Introduction

The origin of the term Dutch book is unknown to me, unfortunately. I spent quite some time trying to find out. In the modern literature, the term is mostly used in an informal sense, describing principles for dynamic decision situations. Such works are usually informal, leaving assumptions implicit and the domain of choice not defined formally. Sometimes choice options are added and deleted as the decision tree enroles in ways that essentially change the strategic situation (criticized by Machina, 1989, under the term “hidden nodes”). Here is what I found on the history.

Someone told me around 1987 that the term Dutch book had been invented when Dutch insurance companies for ships in the 19th century would organize and combine insurances in such a way as to make money whatever contingency occurred. When I later asked the person for references or evidence otherwise he did not know.

The English language has several negative expressions using the term Dutch, such as Dutch uncle, Dutch treat, etc. This terminology seems to date from the 17th century, when Holland and England had powerful and rivalry fleets. The term Dutch book is in line with this tradition.

I heard it say that Dutch book is a common term in horse racing and possibly it was taken from there. Lehman, R. (1955) writes that the term is known among professional bettors. I never investigated this possibility but it seems to be a plausible origin, in agreement with the linguistic tradition just mentioned. In horse racing, “making a book” means setting the betting odds and the “bookmaker” is the person doing it. See for instance the opening sentence in
Cain, Michael, David Law, & Dennis V. Lindley (2000), “The Construction of a Simple Book,” Journal of Risk and Uncertainty 20, 119-140.
The paper doesn't give further references to specific literature on horse racing. The terms do not entail that the bookmaker will always make a profit no matter what happens, as they do in decision theory. Maybe the adjective Dutch is used to add that meaning?

The earliest written explanation of the concept that I am aware of is in works by de Finetti, but Ramsey has a mysterious use of the term, without explanation, as if well-known in those days. See the next section.

2. References on Dutch Books


Ramsey, Frank P. (1931), “Truth and Probability.” InThe Foundations of Mathematics and other Logical Essays,” 156-198, Routledge and Kegan Paul, London. Reprinted in Henry E. Kyburg Jr. & Howard E. Smokler (1964, Eds.), Studies in Subjective Probability, 61-92, Wiley, New York. (2nd edition 1980, Krieger, New York.)

Ramsey mentions the book argument three times. The first mention is on p. 172, l.-7, it is in his Section 3, the 13th paragraph there. The context is elicitation of subjective probabilities through betting odds. Ramsey mentions the desire to make a book as a reason why betting odds might not work. Probably he is thinking of gaming effects.

The second mention is more remarkable, and is on p. 182. It is near the end of Section 3, end of first paragraph after the completion of the formal work. Ramsey again writes that book can be made against people who do not satisfy the laws of probability. The reversed implication, that no book can be made against people who do satisfy the laws of probability, is stated in the third mention which is most clear and which already describes de Finetti's idea.

The third mention is on p. 183. It says:

Having any definite degree of belief implies a certain measure of consistency, namely willingness to bet on a given proposition at the same odds for any stake, the stakes being measured in terms of ultimate values. Having degrees of belief obeying the laws of probability implies a further measure of consistency, namely such a consistency between the odds acceptable on different propositions as shall prevent a book being made against you.

de Finetti

The exact mathematical content of de Finettiys ideas is not easily distilled from his writings. A mathematical statement of the book making theorem (as I interpret it) is given at p. 161, Theorem A2.1, in

Wakker, Peter P. (1989), “Additive Representations of Preferences, A New Foundation of Decision Analysis.” Kluwer Academic Publishers, Dordrecht.

References to de Finettiys works are:

de Finetti, Bruno (1931), “Sul Significato Soggettivo della Probabilità,” Fundamenta Mathematicae 17, 298-329. Translated into English as “On the Subjective Meaning of Probability,” in Paola Monari and Daniela Cocchi (Eds., 1993) “Probabilitá e Induzione,” Clueb, Bologna, 291-321.

de Finetti, Bruno (1937), “La Prévision: Ses Lois Logiques, ses Sources Subjectives,” Annales de lyInstitut Henri Poincaré 7, 1-68. Translated into English by Henry E. Kyburg Jr., “Foresight: Its Logical Laws, its Subjective Sources.” In Henry E. Kyburg Jr. & Howard E. Smokler (1964, Eds.), Studies in Subjective Probability, Wiley, New York, 53-118; 2nd edition 1980, Krieger, New York.
%pp. 93-158 in first edition?

de Finetti, Bruno (1972), “Probability, Induction and Statistics.” Wiley, New York.

de Finetti, Bruno (1974), “Theory of Probability.” Vol.I. Wiley, New York.

Other references

Bunn, Derek W. (1984), “Applied Decision Analysis.” McGraw-Hill book Company, New York.

% Refers to Dutch auctions as possible origin. Also to gangster Dutch Schulz, killed in 1935, who apparently referred to similar combinations of betting. So then “Dutch” would be a first name not related to the country in particular.
Coleman, Andrew W. (2001), “Dutch Book.” From: A Dictionary of Psychology. Link.

a % first with money pump argument; ascribe idea to Norman Dalkey;
Davidson, Donald, J.C.C. McKinsey, & Patrick Suppes (1955), “Outlines of a Formal Theory of Value, I,” Philosophy of Science 22, 140-160.

% Discusses several closely related terms.
Humphreys, Paul (updated October 6, 2008 and maybe later): “Notes on the Origin of the Term `Dutch Book'.” Link.

% Refers to horse racing for the term Dutch book;
Lehman, R. (1955), “On Confirmation and Rational Betting,” Journal of Symbolic Logic 20, 251-262.

Resnik, Michael (1987), “Choices: An Introduction to Decision Theory.” University of Minnesota Press, Minneapolis, Minnesota.

Schick, Fredrick (1986), “Dutch Bookies and Money Pumps,” Journal of Philosophy 83, 112-119.

Last update: July 1, 2011