tldr: TIL that someone has ever given a not-(obviously-to-me-)crazy explanation for hyperbolic discounting.
Today I asked ChatGPT, Claude, and Gemini the following question that I’ve had for quite a while:
> I’ve heard that one common quantitative explanation for phenomena like addiction and procrastination is hyperbolic, as opposed to exponential, discounting. Are there clean stories for *why* humans and other animals might end up factored such that they do hyperbolic discounting? It seems like a very potentially “clean” theory, i.e. we value events inversely proportionally to how far away in time they are, but at the same time I don’t know why it might convey an evolutionary advantage compared to exponential discounting (which has a relatively simple explanation like, “on the scale of a year or so, you have a roughly constant probability of e.g. dying or becoming infertile on any given day; so value that’s further in the future should be discounted exponentially based on that probability”)
All three LLMs pointed me to work by Peter Sozou[1] arguing that if you don’t know the hazard rate, but instead have uncertainty about it that you update over time, hyperbolic-looking discounting can fall out from there.
A quick search reveals that Sozou has been mentioned on LW once before, in a comment[2] pointing at a blog post by Jason Collins explaining the idea[3].
Interesting! Of course, a bayesian explanation also predicts rationally changing behavior as you gain more info about good discount rates. Doubtful that people are so neat. I think an evolutionary explanation of our discount rate will have to sound more like “here are the ways the brain can easily represent time, and here are the different jobs that thoughts have to do that all get overloaded into salience+valence, and so here’s why the thing our brain does is clever and evolutionarily stable even though on some of the jobs it does worse than the theoretical maximum.”
I would be really interested in someone doing an obvious study here, like, “the first time you give Alice a set of choices to elicit a discount schedule, how is that schedule different from the 100th time you give her the same set of choices in the same setting? i.e. does she update to have a tighter implied distribution over hazard rates?” (maybe someone has done this study; if anyone knows about it I’d love a link)
I don’t think I have quite the same sense that the story will have to be in terms like those you’re describing; it seems totally plausible to me that there is a very general / simple / Bayes-compatible story underlying this, since hyperbolic (or at least non-exponential) discounting seems extremely widespread, and neural architecture appears to me to be highly adaptable.
I’ve always seen this idea attributed to Martin Weitzman, and he cites thesepapers as making a similar point. Seems like an interesting case of simultaneous discovery: four papers making the same sort of point all appearing between 1996 and 1999.
How confident are we that hyperbolic time discounting is even real? I think you can explain these results with zero time discounting.
Normal Person: hey I have some money I don’t need right now
Completely Legit Businessperson #1: I advise you to invest that. You can invest it in A for 5% annual returns, or if you are willing to have just slightly less liquidity, in B for 10% annual returns.
Normal Person: I guess B.
Completely Legit Businessperson #2: Hey, do I have some investment opportunities for you?
Normal Person: Yes?
Completely Legit Businessperson #2: And so you know you can trust me, the first $100 in the account is free!
Normal Person: Cool.
Completely Legit Businessperson #2: These accounts have an amazingly high return. In just one week our AI trading strategy will double—
This isn’t even necessarily a risk thing, like would be analogous to the claim. If the reward is small, it also raises the question of friction costs. Taking the prize now has no ongoing cost. Taking it at a later date has a sizable upfront cost and a small ongoing cost.
arguing that if you don’t know the hazard rate, but instead have uncertainty about it that you update over time, hyperbolic-looking discounting can fall out from there
tldr: TIL that someone has ever given a not-(obviously-to-me-)crazy explanation for hyperbolic discounting.
Today I asked ChatGPT, Claude, and Gemini the following question that I’ve had for quite a while:
> I’ve heard that one common quantitative explanation for phenomena like addiction and procrastination is hyperbolic, as opposed to exponential, discounting. Are there clean stories for *why* humans and other animals might end up factored such that they do hyperbolic discounting? It seems like a very potentially “clean” theory, i.e. we value events inversely proportionally to how far away in time they are, but at the same time I don’t know why it might convey an evolutionary advantage compared to exponential discounting (which has a relatively simple explanation like, “on the scale of a year or so, you have a roughly constant probability of e.g. dying or becoming infertile on any given day; so value that’s further in the future should be discounted exponentially based on that probability”)
All three LLMs pointed me to work by Peter Sozou[1] arguing that if you don’t know the hazard rate, but instead have uncertainty about it that you update over time, hyperbolic-looking discounting can fall out from there.
A quick search reveals that Sozou has been mentioned on LW once before, in a comment[2] pointing at a blog post by Jason Collins explaining the idea[3].
https://pmc.ncbi.nlm.nih.gov/articles/PMC1689473/pdf/T9KA20YDP8PB1QP4_265_2015.pdf
https://www.lesswrong.com/posts/d5q6vKrLopC36zttS/rationalists-don-t-care-about-the-future#bX9y45aqWTWKDZQLe
https://www.jasoncollins.blog/posts/evolution-and-irrationality
Interesting! Of course, a bayesian explanation also predicts rationally changing behavior as you gain more info about good discount rates. Doubtful that people are so neat. I think an evolutionary explanation of our discount rate will have to sound more like “here are the ways the brain can easily represent time, and here are the different jobs that thoughts have to do that all get overloaded into salience+valence, and so here’s why the thing our brain does is clever and evolutionarily stable even though on some of the jobs it does worse than the theoretical maximum.”
I would be really interested in someone doing an obvious study here, like, “the first time you give Alice a set of choices to elicit a discount schedule, how is that schedule different from the 100th time you give her the same set of choices in the same setting? i.e. does she update to have a tighter implied distribution over hazard rates?” (maybe someone has done this study; if anyone knows about it I’d love a link)
I don’t think I have quite the same sense that the story will have to be in terms like those you’re describing; it seems totally plausible to me that there is a very general / simple / Bayes-compatible story underlying this, since hyperbolic (or at least non-exponential) discounting seems extremely widespread, and neural architecture appears to me to be highly adaptable.
I’ve always seen this idea attributed to Martin Weitzman, and he cites these papers as making a similar point. Seems like an interesting case of simultaneous discovery: four papers making the same sort of point all appearing between 1996 and 1999.
Here’s another justification for hyperbolic discounting, drawing on the idea that you’re less psychologically connected to your future selves.
I thought this was the existing standard explanation. Is this not well-known by old school LessWrongers?
How confident are we that hyperbolic time discounting is even real? I think you can explain these results with zero time discounting.
Normal Person: hey I have some money I don’t need right now
Completely Legit Businessperson #1: I advise you to invest that. You can invest it in A for 5% annual returns, or if you are willing to have just slightly less liquidity, in B for 10% annual returns.
Normal Person: I guess B.
Completely Legit Businessperson #2: Hey, do I have some investment opportunities for you?
Normal Person: Yes?
Completely Legit Businessperson #2: And so you know you can trust me, the first $100 in the account is free!
Normal Person: Cool.
Completely Legit Businessperson #2: These accounts have an amazingly high return. In just one week our AI trading strategy will double—
Normal Person: Yeah no thanks I’ll take the $100.
This isn’t even necessarily a risk thing, like would be analogous to the claim. If the reward is small, it also raises the question of friction costs. Taking the prize now has no ongoing cost. Taking it at a later date has a sizable upfront cost and a small ongoing cost.
This seems relevant to X-risk discussions.