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:
“I’ve never been a fan of the notion that we should (normatively) have a discount rate in our pure preferences—as opposed to a pseudo-discount rate arising from monetary inflation, or from opportunity costs of other investments, or from various probabilistic catastrophes that destroy resources or consumers.”
(Also, I don’t see how that example is ‘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.
More broadly it assumes no model error. Whatever decision model you are using you need to be 100% certain of it to justify exponential discounting.
Nassim Taleb points out that quite a few alleged biases are actually quite rational when taking into account model error and he includes a derivation of why the hyperbolic discounting formula is actually valid in many situations.
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.
Good point.
More generally as per the wikipedia article http://en.wikipedia.org/wiki/Hyperbolic_discounting#Criticism exponential discounting is only correct if you are equally certain of the payoffs at all the different times.
More broadly it assumes no model error. Whatever decision model you are using you need to be 100% certain of it to justify exponential discounting.
Nassim Taleb points out that quite a few alleged biases are actually quite rational when taking into account model error and he includes a derivation of why the hyperbolic discounting formula is actually valid in many situations.
Silent Risk Section 4.6 Psychological pseudo-biases under second layer of uncertainty. Draft at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2392310