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.
Bibliographical noteThe 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.
- Dutch Book
- degree of belief
- probabolistic theories of rationality
- subjective interpretation of probability