As Wei Dai and Roko have observed, that depends on why you’re asking in the first place. Probability estimates should pay rent in correct decisions. If you’re making a bet that will pay off once at the end of the experiment, you should count the fraction of branches. If you’re making a bet that will pay off once per wake-up call, you should count the fraction of wake-up calls.
That’s the wrong way to look at it. A certain bet may be the “correct” action to perform, or even a certain ritual of cognition may pay its rent, but it won’t be about the concept of probability. Circumstances may make it preferable to do or say anything, but that won’t influence the meaning of fixed concepts. You can’t argue that 2+2 is in fact 5 on the grounds that saying that saves puppies. You may say that 2+2 is 5, or think that “probability of Tuesday” is 1⁄3 or 1⁄4 in order to win, but that won’t make it so, it will merely make you win.
Subjective probability is not a well-defined concept in the general case. Fractions are well-defined, but only after you’ve decided where you are getting the numerator and denominator from.
As Wei Dai and Roko have observed, that depends on why you’re asking in the first place. Probability estimates should pay rent in correct decisions. If you’re making a bet that will pay off once at the end of the experiment, you should count the fraction of branches. If you’re making a bet that will pay off once per wake-up call, you should count the fraction of wake-up calls.
That’s the wrong way to look at it. A certain bet may be the “correct” action to perform, or even a certain ritual of cognition may pay its rent, but it won’t be about the concept of probability. Circumstances may make it preferable to do or say anything, but that won’t influence the meaning of fixed concepts. You can’t argue that 2+2 is in fact 5 on the grounds that saying that saves puppies. You may say that 2+2 is 5, or think that “probability of Tuesday” is 1⁄3 or 1⁄4 in order to win, but that won’t make it so, it will merely make you win.
Subjective probability is not a well-defined concept in the general case. Fractions are well-defined, but only after you’ve decided where you are getting the numerator and denominator from.
That fractions are well-defined doesn’t make them probabilities.