I thought we had agreed that the historical behaviour of coins was “compatible with subjectivism”:
Jaynes’ perspective on the historical behaviour of biased coins would make no mention of probability—unless he was talking about the history of the expectations of some observer with partial information about the situation.
An observer with one set of partial information might have predicted a coin would come up heads 50% of the time. An observer with another set of partial information might have predicted a coin would come up heads 60% of the time. That the predictions of these observers differs illustrates the subjective element of probability estimates.
However, it is their (partial) ignorance of the state of the world that leads to such assessments. With complete information (and a big computer) an observer would know which way the coin would land—and would find probabilities irrelevant. The probabilities arise from ignorance and lack of computing power—properties of observers, not properties of the observed.
I thought we had agreed that the historical behaviour of coins was “compatible with subjectivism”:
An observer with one set of partial information might have predicted a coin would come up heads 50% of the time. An observer with another set of partial information might have predicted a coin would come up heads 60% of the time. That the predictions of these observers differs illustrates the subjective element of probability estimates.
However, it is their (partial) ignorance of the state of the world that leads to such assessments. With complete information (and a big computer) an observer would know which way the coin would land—and would find probabilities irrelevant. The probabilities arise from ignorance and lack of computing power—properties of observers, not properties of the observed.