Someone had just asked a malformed version of an old probability puzzle [...] someone said to me, “Well, what you just gave is the Bayesian answer, but in orthodox statistics the answer is 1⁄3.” [..] That was when I discovered that I was of the type called ‘Bayesian’.
I think a more reasonable conclusion is: yes indeed it is malformed, and the person I am speaking to is evidently not competent enough to notice how this necessarily affects the answer and invalidates the familiar answer, and so they may not be a reliable guide to probability and in particular to what is or is not “orthodox” or “bayesian.” What I think you ought to have discovered was not that you were Bayesian, but that you had not blundered, whereas the person you were speaking to had blundered.
I think a more reasonable conclusion is: yes indeed it is malformed, and the person I am speaking to is evidently not competent enough to notice how this necessarily affects the answer and invalidates the familiar answer, and so they may not be a reliable guide to probability and in particular to what is or is not “orthodox” or “bayesian.” What I think you ought to have discovered was not that you were Bayesian, but that you had not blundered, whereas the person you were speaking to had blundered.