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Manfred comments on Pascal's Mugging for bounded utility functions - Less Wrong
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I agree for the typical implementation of discounting - though if someone just had a utility function that got non-exponentially smaller as the numbers on the calendar got bigger, you could see some different behavior.
Hm, you're right. For nonexponential discounting, future!you discounts differently than you want it to if it resets its utility, but not if it doesn't.