Re: The envelope problem, and a possible solution
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You asked for something that makes common sense. How much common sense does your statement make?
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Remember, I've said from the beginning that there is no common sense answer.
At this point, I think we should just agree that your common sense is broader than mine. You can accept probabilities that change when you look at them, as a Bayesian does, and also mathematical formulae that are different depending on whether X is a number or a variable, as a Frequentist does.
I'd rather reject both and live with having no rigorous theory of probability that can also answer useful questions. Many people agree with me, many others choose the less distasteful (to them) of the two alternatives above. But you are rare in being willing to embrace both. For you, the envelope problem is no problem at all.
That probably sounds sarcastic, and maybe I meant it that way a little, but I admit I have no argument against it. You might well be right, I just hope you aren't.
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