I think that this isn’t a problem about rational choice given a certain utility function, but about what your utility function should be in the first place, and there’s no “correct” answer to that question.
No one can tell you whether you should prefer to be tortured horribly, then given amnesia, then given $1 trillion, or whether you should prefer to be slapped and then given $100.01. Decide which one you would prefer, and how much, and then we can talk about constructing a utility function that accurately reflects your preferences.
Once you’ve figured out your preferences and assigned consistent utilities, then we can do the sort of mathematical reasoning you are trying to do. For example, maybe you decide that hell+amnesia+riches has a utility of −100 and that slaps+money has a utility of +1, for example by deciding that you’d accept at most a 1% chance of hell+amnesia+riches in exchange for slaps+money. Then we can immediately use this to, say, calculate what other bets you should and shouldn’t take with regard to these options.
But we can’t tell you which one you should prefer: you have to decide that yourself. You’re allowed to prefer hell+amnesia+riches if you want!
I think that this isn’t a problem about rational choice given a certain utility function, but about what your utility function should be in the first place, and there’s no “correct” answer to that question.
No one can tell you whether you should prefer to be tortured horribly, then given amnesia, then given $1 trillion, or whether you should prefer to be slapped and then given $100.01. Decide which one you would prefer, and how much, and then we can talk about constructing a utility function that accurately reflects your preferences.
Once you’ve figured out your preferences and assigned consistent utilities, then we can do the sort of mathematical reasoning you are trying to do. For example, maybe you decide that hell+amnesia+riches has a utility of −100 and that slaps+money has a utility of +1, for example by deciding that you’d accept at most a 1% chance of hell+amnesia+riches in exchange for slaps+money. Then we can immediately use this to, say, calculate what other bets you should and shouldn’t take with regard to these options.
But we can’t tell you which one you should prefer: you have to decide that yourself. You’re allowed to prefer hell+amnesia+riches if you want!