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DSherron comments on The Ultimate Sleeping Beauty Problem - Less Wrong
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She responds "I'm sorry, but while I am a highly skilled mathematician, I'm actually from an alternate universe which is identical to yours except that in mine 'subjective probability' is the name of a particularly delicious ice cream flavor. Please precisely define what you mean by 'subjective probability', preferably by describing in detail a payoff structure such that my winnings will be maximized by selecting the correct answer to your query."
I agree with that response to the sleeping beauty problem, and the way you set up the payoff structure will probably make this problem equivalent to the St. Petersburg Paradox.
It's like the St. Petersburg game except you gain money on even n and lose money on odd n.
That's right. What I said above was just stupid. Oops. It is not equivalent at all. I think the two problems are two instances of the same "paradox" though.
This is unlike the St Petersburg paradox because it involves amnesia, so assigning probabilities arguably forces you to decide on some SIA/SSA-like quandary. But I do agree that making this into a decision problem is the key.