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Yvain comments on Time and Effort Discounting - Less Wrong
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Do any of the studies on hyperbolic discounting attempt to show that it is not just a consequence of combining uncertainty with something like a standard exponential discounting function? That's always seemed the most plausible explanation of hyperbolic discounting to me and it meshes with what seems to be going on when I introspect on these kinds of choices.
Most of the discussions of hyperbolic discounting I see don't even consider how increasing uncertainty for more distant rewards should factor into preferences. Ignoring uncertainty seems like it would be a sub-optimal strategy for agents making decisions in the real world.
I think exponential discounting already assumes uncertainty. You need uncertainty to discount at all - if things are going to stay the same, might as well wait until later. And it doesn't intuitively lead to hyperbolic discounts - if there's a 1% chance you'll die each week, then waiting from now until next week should make you discount the same amount as waiting from ten weeks from now until eleven.
But there is a way to use uncertainty to get from exponential to hyperbolic discounting. You get exponential if you're worried about yourself dying/being unable to use the reward/etc. But if you add in the chance of the reward going away, based on a prior where you don't know anything about how likely that is, you might get hyperbolic discounting. If you don't eat an animal you've killed in the next ten minutes, then it might get stolen by hyenas. But common-sensibly, if it goes a year without being stolen by hyenas or going bad or anything, there's not much chance of hyenas suddenly coming along in the next ten minutes after that.
This doesn't explain many of the effect described in the post, such as the choice of 10-20-30-40 over 40-30-20-10 and the fact that people's preferences can reverse like you explained, though the latter may just be because evolution found a simpler solution rather than a more accurate one.
I'm not sure you need uncertainty to discount at all - in finance exponential discounting comes from interest rates which are predicated on an assumption of somewhat stable economic growth rather than deriving from uncertainty.
As you point out, hyperbolic discounting can come from combining exponential discounting with an uncertain hazard rate. It seems many of the studies on hyperbolic discounting assume they are measuring a utility function directly when they may in fact be measuring the combination of a utility function with reasonable assumptions about the uncertainty of claiming a reward. It's not clear to me that they have actually shown that humans have time inconsistent preferences rather than just establishing that people don't separate the utility they attach to a reward from their expectation of actually receiving it in their responses to these kinds of studies.
What the best-known paper on this says is:
It goes on to say: