Time and Effort Discounting

by Scott Alexander4 min read7th Jul 201132 comments


Utility Functions

Related to: Akrasia, hyperbolic discounting, and picoeconomics

If you're tired of studies where you inevitably get deceived, electric shocked, or tricked into developing a sexual attraction to penny jars, you might want to sign up for Brian Wansink's next experiment. He provided secretaries with a month of unlimited free candy at their workplace. The only catch was that half of them got the candy in a bowl on their desk, and half got it in a bowl six feet away. The deskers ate five candies/day more than the six-footers, which the scientists calculated would correspond to a weight gain of over 10 pounds more per year1.

Beware trivial inconveniences (or, in this case, if you don't want to gain weight, beware the lack of them!) Small modifications to the difficulty of obtaining a reward can make big differences in whether the corresponding behavior gets executed.


The best studied example of this is time discounting. When offered two choices, where A will lead to a small reward now and B will lead to a big reward later, people will sometimes choose smaller-sooner rather than larger-later depending on the length of the delay and the size of the difference. For example, in one study, people preferred $250 today to $300 in a year; it took a promise of at least $350 to convince them to wait.

Time discounting was later found to be "hyperbolic", meaning that the discount amount between two fixed points decreases the further you move those two points into the future. For example, you might prefer $80 today to $100 one week from now, but it's unlikely you would prefer $80 in one hundred weeks to $100 in one hundred one weeks. Yet this is offering essentially the same choice: wait an extra week for an extra $20. So it's not enough to say that the discount rate is a constant 20% per week - the discount rate changes depending on what interval of time we're talking about. If you graph experimentally obtained human discount rates on a curve, they form a hyperbola.

Hyperbolic discounting creates the unpleasant experience of "preference reversals", in which people can suddenly change their mind on a preference as they move along the hyperbola. For example, if I ask you today whether you would prefer $250 in 2019 or $300 in 2020 (a choice between small reward in 8 years or large reward in 9), you might say the $300 in 2020; if I ask you in 2019 (when it's a choice between small reward now and large reward in 1 year), you might say no, give me the $250 now. In summary, people prefer larger-later rewards most of the time EXCEPT for a brief period right before they can get the smaller-sooner reward.

George Ainslie ties this to akrasia and addiction: call the enjoyment of a cigarette in five minutes the smaller-sooner reward, and the enjoyment of not having cancer in thirty years the larger-later reward. You'll prefer to abstain right up until the point where there's a cigarette in front of you and you think "I should smoke this", at which point you will do so.

Discounting can happen on any scale from seconds to decades, and it has previously been mentioned that the second or sub-second level may have disproportionate effects on our actions. Eliezer concentrated on the difficult of changing tasks, but I would add that any task which allows continuous delivery of small amounts of reinforcement with near zero delay can become incredibly addictive even if it isn't all that fun (this is why I usually read all the way through online joke lists, or stay on Reddit for hours). This is also why the XKCD solution to internet addiction - an extension that makes you wait 30 seconds before loading addictive sites - is so useful.


Effort discounting is time discounting's lesser-known cousin. It's not obvious that it's an independent entity; it's hard to disentangle from time discounting (most efforts usually take time) and from garden-variety balancing benefits against costs (most efforts are also slightly costly). There have really been only one or two good studies on it and they don't do much more than say it probably exists and has its own signal in the nucleus accumbens.

Nevertheless, I expect that effort discounting, like time discounting, will be found to be hyperbolic. Many of these trivial inconveniences involve not just time but effort: the secretaries had to actually stand up and walk six feet to get the candy. If a tiny amount of effort held the same power as a tiny amount of time, it would go even further toward explaining garden-variety procrastination.


Hyperbolic discounting stretches our intuitive notion of "preference" to the breaking point.

Traditionally, discount rates are viewed as just another preference: not only do I prefer to have money, but I prefer to have it now. But hyperbolic discounting shows that we have no single discount rate: instead, we have different preferences for discount rates at different future times.

It gets worse. Time discount rates seem to be different for losses and gains, and different for large amounts vs. small amounts (I gave the example of $250 now being worth $350 in a year, but the same study found that $3000 now is only worth $4000 in a year, and $15 now is worth a whopping $60 in a year). You can even get people to exhibit negative discount rates in certain situations: offer people $10 now, $20 in a month, $30 in two months, and $40 in three months, and they'll prefer it to $40 now, $30 in a month, and so on - maybe because it's nice to think things are only going to get better?

Are there utility functions that can account for this sort of behavior? Of course: you can do a lot of things just by adding enough terms to an equation. But what is the "preference" that the math is describing? When I say I like having money, that seems clear enough: preferring $20 to $15 is not a separate preference than preferring $406 to $405.

But when we discuss time discounting, most of the preferences cited are specific: that I would prefer $100 now to $150 later. Generalizing these preferences, when it's possible at all, takes several complicated equations. Do I really want to discount gains more than losses, if I've never consciously thought about it and I don't consciously endorse it? Sure, there might be such things as unconscious preferences, but saying that the unconscious just loves following these strange equations, in the same way that it loves food or sex or status, seems about as contrived as saying that our robot just really likes switching from blue-minimization to yellow-minimization every time we put a lens on its sensor.

It makes more sense to consider time and effort discounting as describing reward functions and not utility functions. The brain estimates the value of reward in neural currency using these equations (or a neural network that these equations approximate) and then people execute whatever behavior has been assigned the highest reward.


1: Also cited in the same Nutrition Action article: if the candy was in a clear bowl, participants ate on average two/day more than if the candy was in an opaque bowl.