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Manfred comments on Pascal's Mugging for bounded utility functions - Less Wrong
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Say that living 50 more years without getting sick was 90 utilons, and the maximum score was 100. This means that there are only 10 utilons with which to describe the quality of your life between 50 years from now and the far future - being healthy 51 years from now is worth only 1/10 as being healthy now. So for each day you can use as you wish this year, you'd be willing to spend 10 days bedridden, or doing boring work, or in jail 50 years from now.
So in a word, procrastination. And because the utility function is actually shifting over time so that it stays 100-points-max, each point in time looks the same - there's no point where they'd stop procrastinating, once they started, unless the rate of work piling up changed.
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.