Lots of efforts have been paid for interpreting the concept of probability by another familiar concept such as ignorance, degree of a partial logical entailment, degree of belief, frequency, and propensity. In this paper the subjective theory is addressed. According to this theory, probability is interpreted as coherent degree of belief of a particular individual. This interpretation is achieved through following the two-step replacements: (1) Degree of belief is interpreted as fair betting quotient; (2) Fair betting quotient is interpreted as probability. The first replacement is based on the claim that in a bet (decision-making in an uncertain situation) a bettor's degree of belief whether an event will occur can be measured by a real number which she gives through her judgement on the fairness of the bet. The second replacement is based on the fact that when a bettor makes bets on events, in order to be guaranteed not to lose whatever happens (in order to be coherent) she should assign her betting quotients in accordance with the probability axioms, and vice versa. It is the so-called Dutch Book Theorem that guarantees this fact mathematically. The purpose of this paper is to clarify and confirm the contents of the subjective theory in terms of betting systems along the following approach (Ramsey (1931), de Finetti (1937), Howson  Urbach (1993), Gillies (2000), etc.).

研究ノート