Dutch Book

A Dutch book is a gambling term for a set of odds and bets that guarantees a profit, regardless of the outcome of the gamble. At the very least, one who practices self-consistent reasoning should not be susceptible to having a Dutch book made against them. If an individual is not susceptible to a Dutch book, their previsions are said to be coherent. A set of betting quotients is coherent if (Ramsey (1926), de Finetti (1937), Shimony (1955)) and only if (Kemeny (1955), Lehman (1955)) they satisfy the axioms of probability.

The Dutch book argument assumes that people are risk neutral, there is no "game theory", exact odds are required, the hypothesis they are betting on can be falsified and verified, that they are forced to bet and the bet is settled within a reasonable time frame.

Bibliography

DAVIDSON, B. and R. PARGETTER, In Defence of the Dutch Book Argument, Canadian Journal of Philosophy, 1985. [Cited by 1]
de FINETTI, B., La prévision: ses lois logiques, ses sources subjectives, Annales de l'Intstitute Henri Poincaré, 1937, Vol.7 pp.1-68. [Cited by 255]
de FINETTI, B., Sul significato soggetivo della probabilità, Fundamenta Mathematicae, 1931, Vol.17, pp.298-329. [Cited by 6]
H�JEK, Alan, Scotching Dutch Books?
KEMENY, J.G., Fair bets and inductive probabilities, Journal of Symbolic Logic, 1955, Vol.20, pp.1-28. [Cited by 23]
KENNEDY, Ralph and Charles CHIHARA, The Dutch book argument: Its logical flaws, its subjective sources [Cited by 6]
PARIS, J. B., A note on the Dutch Book method, 2002.
RAMSEY, F.P., The foundations of mathematics and other logical essays, London, 1931.
SHIMONY, A., Coherence and the axioms of confirmation, Journal of Symbolic Logic, 1955, Vol.20, pp.263-273. [Cited by 17]