The insufficiency of the Dutch Book argument

Darrell Patrick ROWBOTTOM

doi:10.1007/s11225-007-9077-2

The insufficiency of the Dutch Book argument

Darrell Patrick ROWBOTTOM

Research output: Journal Publications › Journal Article (refereed) › peer-review

9 Citations (Scopus)

Abstract

It is a common view that the axioms of probability can be derived from the following assumptions: (a) probabilities reflect (rational) degrees of belief, (b) degrees of belief can be measured as betting quotients; and (c) a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that (b) and (c) are incorrect. In particular, I show how a rational agent might assign a ‘probability’ of zero to an event which she is sure will occur.

Original language	English
Pages (from-to)	65-71
Number of pages	7
Journal	Studia Logica
Volume	87
Issue number	1
DOIs	https://doi.org/10.1007/s11225-007-9077-2
Publication status	Published - 1 Oct 2007
Externally published	Yes

Bibliographical note

The same paper is presented at the 2006 Joint Session of the Aristotelian Society and the Mind Association, University of Southampton, Southampton, United Kingdom, July 2006.

Keywords

Dutch Book
coherence
degree of belief
probabolistic theories of rationality
subjective interpretation of probability

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10.1007/s11225-007-9077-2

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abstract = "It is a common view that the axioms of probability can be derived from the following assumptions: (a) probabilities reflect (rational) degrees of belief, (b) degrees of belief can be measured as betting quotients; and (c) a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that (b) and (c) are incorrect. In particular, I show how a rational agent might assign a {\textquoteleft}probability{\textquoteright} of zero to an event which she is sure will occur.",

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AB - It is a common view that the axioms of probability can be derived from the following assumptions: (a) probabilities reflect (rational) degrees of belief, (b) degrees of belief can be measured as betting quotients; and (c) a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that (b) and (c) are incorrect. In particular, I show how a rational agent might assign a ‘probability’ of zero to an event which she is sure will occur.

KW - Dutch Book

KW - coherence

KW - degree of belief

KW - probabolistic theories of rationality

KW - subjective interpretation of probability

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VL - 87

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EP - 71

JO - Studia Logica

JF - Studia Logica

IS - 1

ER -

The insufficiency of the Dutch Book argument

Abstract

Bibliographical note

Keywords

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