Where Do Probabilities Come from?

Your “subjective” probability is not something fetched out of the sky on a whim; it is what your actual judgment should be, in view of your information to date and of your sense of other people's information, even if you do not regard it as a judgment that everyone must share on pain of being wrong in one sense or another.

But of course you are not always clear about what your judgment is, or should be. The most important questions in the theory of probability concern ways and means of constructing reasonably satisfactory probability assignments to fit your present state of mind. (Think: trying on shoes.) For this, there is no overarching algorithm. Here we examine two answers to these questions that were floated by Bruno de Finetti in the decade from (roughly) 1928 to 1938. The second of them, “Exchangeability”, postulates a definite sort of initial probabilistic state of mind, which is then updated by conditioning on statistical data. The first (“Minimalism”) is more primitive: The input probability assignment will have large gaps, and the output will not arise via conditioning.

Probabilities from Statistics: Minimalism

Statistical data are a prime determinant of subjective probabilities; that is the truth in frequentism. But that truth must be understood in the light of certain features of judgmental probabilizing.