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AlexMennen comments on Pascal's Mugging for bounded utility functions - Less Wrong
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That's a problem with any sort of discounting, but only counting future events in your utility function does not change that. It doesn't matter whether the next 50 can get you 90 out of 100 available future utils or .09 out of .1 available future utils (where the other 99.9 were determined in the past); your behavior will be the same.
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.