Any decision problem still has the probability hidden (or not so hidden) in it—this trick works for sleeping beauty not because of a general property, but because the problems are swept under the rug even better than the probabilities.
Since it’s the same problem either way (at least if your solution to the decision problem is optimal), then this technique is not useful except as a way to clarify things for yourself, and it doesn’t always work.
Any decision problem still has the probability hidden (or not so hidden) in it—this trick works for sleeping beauty not because of a general property, but because the problems are swept under the rug even better than the probabilities.
Since it’s the same problem either way (at least if your solution to the decision problem is optimal), then this technique is not useful except as a way to clarify things for yourself, and it doesn’t always work.