Hyperbolic Discounting
I have always been fascinated with the study of how people make decisions. Its a complicated process that involves as much ‘gut instinct’ as rational evaluation, and is rife with systematic errors in judgement. For a long list of common mistakes, check out Wikipedia’s list of cognitive biases, particularly the decision-making section. The majority of them are things that most people are probably aware of, like picking a option just because other people picked it. However, a couple of them are a bit surprising, especially the one I want to talk about today: the phenomenon of hyperbolic discounting.
The core question is how people penalize various options for having a ‘delayed payoff’. Would you rather have $30 now and $50 in five years? Implicit in the decision-making process is that later payoffs aren’t worth as much. You might need the money now more than later, or there’s a risk you won’t get the money later, due to death/bankrupcty of the source/etc. The drop in value of a payoff due to the delay involved is called the ‘delay discount’.
How might one rationally evaluate this discount? Well, virtually every reason you can name for de-valuing later payoffs is due to some source of roughly constant risk. Therefore, the value of an object should decay exponentially with time, at a rate determined by the amount of risk. However, this is not what people usually do! Studies have shown that people discount delayed payoffs hyperbolically; that is, roughly proportional to the inverse of the delay. Specifically, a payoff of value 
This has two main consequences. The first is that we tend to over-prefer options with more immediate payouts, which should be no surprise to anyone who has interacted with humans before. The second is that we tend to over-value the further of two distant options, which is a bit weird. For instance, many people might choose $1200 in forty years over $1000 in thirty years, even though inflation alone would make the two roughly equal.
So why does this happen? It should be noted that animals do this as well as people, so it seems pretty hard-wired. I don’t think a good answer is known at this point, but I can think of a few curious options.
One is that people have a skewed perception of future time, and that in their minds ‘in thirty years’ and ‘in forty years’ aren’t as far apart as ‘now’ and ‘in ten years’. I think something like a logarithmic measure on actual time might give the hyperbolic discounting model. Can anyone think of a different kind of experiment that would test how people value future lengths of time?
A second possibility is that we just don’t viscerally understand the exponential function. It is certainly true that most people lack a good qualitative understanding of it (just ask an undergrad with a graphing calculator how many times 
Now, I just need to figure out how to use this to swindle people…
February 25, 2008 at 4:55 pm
You could definitely use it to swindle people somehow — the problem is that it’ll take a long time to make money with such a scheme, because you’re taking advantage of the skewed way in which people see long times. So this is not a get-rich-quick scheme.
And what do undergrads say about e^x and 10x^2, anyway? I’ve never asked.
February 25, 2008 at 6:17 pm
Isabel: I’m pretty sure the “with a graphing calculator” comes into it. That is, they plug them into the calculator, see the exponential cut across through the parabola — crossing twice — and never stop to think that the exponential eventually rises faster than the quadratic — thus crossing again, far above the part of the graph near the origin.
February 25, 2008 at 8:11 pm
Now, I just need to figure out how to use this to swindle people…
That’s easy; start a credit card company.
February 26, 2008 at 1:09 am
That is pretty funny, Greg. You’d think anyone who took 2 years of high school algebra would immediately correlate changes in money with exponential growth/decay just like interest or inflation since that the exponential function is hammered into their brains for weeks while they do interest computations. Then again I’ve seen enough scratch tickets in convenience stores to realize typical people aren’t doing any computations when dealing with money.
February 26, 2008 at 11:37 am
Yeah, I think this is gonna be too much work to make money off of; all the ways of capitalizing on immediate gratification are pretty well-exploited, and all the long term ways of swindling people take too long.
The
versus 
thing was actually on my GRE math subject test (or maybe a practice test I took? its hard to remember), with a picture kindly provided. It would seem that I have a fondness for ways of tricking people mathematically, since I remembered it from then.
February 26, 2008 at 4:32 pm
Here’s a a good scam (if you own a store): advertise some product at an after-rebate price. Assume some percentage of people will make a purchase based on that price that they wouldn’t have made otherwise.
When those customers realize that they won’t actually get the rebate for 6 to 8 weeks, the value of the rebate will shrink. Probably for many people it will drop below the minimum value threshold required to make filling out a form and walking to the mailbox worth their time.
the “No Payments For 90 Days!” trick is similar, but it relies on cost discounting over time. I don’t know whether that’s also hyperbolic.
of course describing your prices as “So low, manufacturers have hired men to kill us!!!” could also be described as hyperbolic discounting, but that’s something different…
February 26, 2008 at 5:13 pm
Argh, I hate hidden rebates. Though, I think this is a function of my difficulty in executing basic tasks, like filling out a form, mailing a letter and depositing a check, rather than discounting the future payoff.
March 3, 2008 at 8:35 pm
If someone was interested into continuing to study this, they might consider replacing monetary value with something of constant worth, like snacks. Greg, for example, might consider five jelly beans now substantially more important then six jelly beans tomorrow if not just for the fact that a single jelly bean would fail to make a detectable difference in the levels of enjoyment. However, were I to offer him ten jelly beans any amount of time down the line in place of his immediate five, he would be more likely to scratch his chin and consider where he will be at that point in the future (for studies have shown his love of jelly beans does not diminish over time).
If the above is true, then I believe the initial base of gratification has a much larger role in people’s thought process, and the time frame has less to do with the equation than what multiples of the original offered (if that makes any sense). To relate to the above example, were I to offer Greg three jelly beans today or four tomorrow, the value of the single jelly bean in question is greater as it represents a larger portion of the immediate offer. Likewise, were I to offer three beans now, or nine after a wait, the amount of time he would wait is not even relative as three times as many jelly beans is worth any wait.
Maybe I’ll conduct some research at my dorm with candies.