Chapter 4 of Donald Gillies’ Philosophical Theories of Probability (2000) deals with the subjective theory of probability, which was developed independently by Frank Ramsey (1903–1930) (1931) and Bruno de Finetti (1906–1985) (Gillies 2000: 50).
The subjective theory takes probability as a mathematical measure in the interval [0, 1] of a person’s degree of belief, but this belief is not necessarily rational not is the probability objective. Different people can hold different subjective beliefs about the probability of the same event.
Both Ramsey and de Finetti devised a method which uses betting to measure subjective belief (Gillies 2000: 54), and the related Ramsey-De Finetti theorem is the idea that a setting of betting quotients is only coherent if and only if they are able to satisfy the axioms of probability (Gillies 2000: 59). A person making a “coherent” bet ensures that a Dutch book cannot be made against him/her.
It is interesting that Ramsey and de Finetti disagreed about the existence of objective probabilities. As Gillies (2000: 69) points out, the fact that we can find real objective probabilities in the world was not denied by Ramsey, who admitted that probabilities are divided into objective and subjective classes. Other more extreme subjectivists like de Finetti insisted that all probabilities are ultimately subjective: indeed de Finetti held the view that objective probabilities are a type of illusion (Gillies 2000: 77).
Gillies (2000: 70–85) reviews the extreme subjectivist views of Finetti and finds them unacceptable: Gillies concludes that there seem to be real objective probabilities and a role for empirical statistics, using relative frequencies (Gillies 2000: 84).
Gillies, D. A. 2000. Philosophical Theories of Probability. Routledge, London.
Ramsey, Frank Plumpton. 1931. The Foundations of Mathematics: and Other Logical Essays (ed. by R.B. Braithwaite). Kegan Paul, London.