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 becomes one of value if it is delayed for time , where is a constant that determines roughly how ‘risky’ the delay is.
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 and intersect). However, it is unclear to me how much people are actually trying to model constant risk when making these decisions, versus just going with what their gut tells them. Though, gut instinct can manage a surprising amount of mathematical prowess, so who knows.
Now, I just need to figure out how to use this to swindle people…