Crossposted from my personal blog: https://mechanisticmind.com/hyperbolic-discounting-and-pascals-mugging/

TL;DR

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Hyperbolic discounting, shown in 🟥, is an imperfect approximation for exponential discounting, shown in 🟦. It's commonly pointed out that this causes humans to overvalue nearterm rewards, but it's less commonly appreciated that this causes us to overvalue distant rewards as well. There's a lot of evidence that humans use hyperbolic discounting, and it helps explain why humans pursue unrealistic longterm goals.

What is Hyperbolic Discounting?

If you search the words “hyperbolic discounting”, Google tells you that it is “a psychological bias where people to prioritize immediate rewards and satisfaction over future rewards”. In fact, this is only half right. Hyperbolic discounting also causes people to overvalue distant rewards in addition to overvaluing near-term rewards.

Temporal discounting is basically a way of thinking about how to answer questions like this one:

Would you rather have $100 today, or $120 one year from now?

This is relatively easy to think about in monetary terms, and you probably know that the answer to this question has to do with interest rates, and the idea that taking $120 one year from now is equal to a 20% annual return, which is better than the 4-10% you might expect in the stock market, and also better than the 4.88% rate you can currently get for a 1-year treasury bond.

This model of calculating the interest rate is known as exponential discounting, and it’s basically represented by this equation:

$value at time t = \frac{a}{d^{t}}$

This says that if something would be worth $a$ at time $t=0$, such as a $100 bill now, then its value drops off exponentially the more you need to wait for it.

So it turns out that humans and other animals don’t appear to be using this equation to estimate the value of future rewards. Instead, they use something called hyperbolic discounting, which can be represented by this equation:

$value at time t = \frac{1}{1 + d t}$

This says that as a reward gets more distant, it’s value falls off according to an inverse.

How we Know

Scientists did experiments with undergraduates and $100 bills. Realistically, grant funding is hard to come by, so most of them used $10 bills, and researchers from lesser-known universities presumably had to get by with $1 bills and some change.

They also did experiments with monkeys and juice. Monke...