gwern comments on Against Discount Rates - Less Wrong
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Obviously there's another sort of discounting that does make sense. If you offer me a choice of a dollar now or $1.10 in a year, I am almost certain you will make good on the dollar now if I accept it, whereas there are many reasons why you might fail to make good on the $1.10. This sort of discounting is rationally hyperbolic, and so doesn't lead to the paradoxes of magnitude over time that you highlight here.
Yes, that discounting makes sense, but it's explicitly not what Eliezer is talking about. His very first sentence:
(Also, I don't see how that example is 'hyperbolic'.)
Agree. Not hyperbolic.
Assuming, in Paul Crowley's example, that there is a constant rate of failure (conditional on not having already failed), this yields well-behaved exponential discounting, which is relatively paradox-free.