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Kaj_Sotala comments on Is Rationality Maximization of Expected Value? - Less Wrong
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Assigning a non-repeating event the probability P means that, for a well-calibrated agent, if you assign 100 different things this probability then 100 * P of them will actually occur. I believe this is a standard interpretation of Bayesian probability, and it puts things in terms of frequencies of actual event outcomes.
ETA: Alternatively, one may think of Bayesian probability as the answer to the question "if I believed this statement, then in which fraction P of all plausible worlds in which I ended up with this information would I be correct"?
I have to disagree with this interpretation. The whole point is that the frequency interpretation of probability can be a specific case of the Bayesian (probability = belief) interpretation, but not vice versa.
If I say I belief in the existence of aliens with 0.2 belief i think its non-intuitive and unrealistic that what im really saying is, "i think aliens exist in 20% of all plausible worlds". Apart from the difficulty in clearly defining 'plausible' the point of Bayesianism is that this simply represents my state of knowledge/belief.
I find Bayesian probability to be meaningless unless you connect it to a pseudo-frequentist interpretation somehow. Sure, you can say "Bayesian probability measures my subjective belief in something", but in that case, what does having a 20% subjective belief in something actually mean, and how's it different from having an 80% subjective belief? You need some scheme of translating it from a meaningless number to an expectation, and all such translations (e.g. in terms of betting behavior) always end up being pseudo-frequentist somehow.
The traditional way of defining the degree of a belief held by some agent is by finding what the agent thinks is a fair wager on the proposition. Is that pseudo-frequentist in a way I'm not seeing?