August 11, 2008

The Hidden Zero Effect


$5 today or $10 in a year.

Picking $5 is called temporal discounting-- you pick a sooner-but-smaller outcome simply because it is sooner.

But it's more than a preference based on how soon you get paid.  If the question is changed:

$5 in 7 years, or $10 in 8 years

Then you can feel the pull to choose the $10-- even though the $5 is still one year earlier than the $10.  So it's not simply people prefer sooner over later.  It's also how far away the payoffs are.  How soon is sooner?  At some point in the future, your choices flip.

In fact, this is predictable (reliably so in animals)-- and follows a hyperbolic function:

discounting function.jpg

Imagine there is a smaller-sooner reward at time T3, and a larger- later one at a time T4.  At a very distant, early time T1, you prefer the solid line (the larger-later reward), because they are both far enough away that the time delay seems insignificant.

But if you choose at a close time T2, the choice has flipped and you prefer the smaller reward, because it seems sooner.  The closer "soon" is, the more you're willing to settle.  Hyperbolically.


Why does this happen?

It's behaviorism.  The effect of rewards are temporally dependent.  Try it on your kid.

How this phenomenon is described is important, and it is frequently backwards.  You don't prefer sooner choices that are smaller, but if they are both far enough away you'll choose the larger choice; you choose the larger choice all the time except if the choice is asked of you close to payoff.

If you intuitively know your future is long, and real, you don't succumb to it as much.  But if the future is an abstraction, then you begin to discount your choices.

The future is real only if you are real, i.e. your identity is fixed.  If your identity is in flux-- whether from personality disorder, bipolar, being a teenager, going through a divorce-- if there are different "yous" all the time, you cannot make decisions based on the future.  If "you" aren't going to be the same in the future, how can you make decisions about it?

In other words, temporal discounting is not exactly an error; it is an accurate reading of the likelihood of change of one's identity.


So how do you resist this?

One way is to make explicit the hidden zero:

Choose $5 today and $0 in a year, or $10 in a year and $0 today.

That hidden zero seems obvious, and it is obvious cognitively, but not instinctively.  These habits and "errors" are hard wired in us because they are protective-- eat while you can, jackals are coming.

But they don't help when you're opting into a 401(k): "Choose $13,000 today and $0 at retirement, or $0 today and $13,000 at retirement."

When you make the hidden zero explicit, people choose differently-- less impulsively:

hidden zero.jpg

Whether it's real or hypothetical money, people choose sooner-but-smaller less often when they are told about the $0.

When dealing with impulsive people, or people whose identity is in flux, it is important to make explicit all parts of a choice, because time has little meaning.


But what caught my attention about this is the difference between real and hypothetical money.  Why does making it real money significantly reduce the number of sooner-but-smaller choices, whether or not the zero is explicit?  If anything, seeing the money on the table might drive them to choose the sooner (but smaller) choice-- the instinct becomes real ("eat now.")

The experiment was to ask subjects 15 questions of the form "$X today, or $Y in a month."  But a second group of people, the "Real Money" group, were told that one of these hypothetical choices would randomly be used to pay them real money at the end of the questionnaire.

Do you see the problem?  The subject isn't making a choice between a sooner payoff vs. a later payoff, but between sooner payoffs vs. all the other sooner payoffs, and later payoffs vs. all the other later payoffs.

Immediate rewards ranged from $2 to $8, delayed rewards ranged from $5.40 to $8.70, and delays ranged from 7 to 140 days.
In effect, this stops becoming a temporal discounting problem and becomes a game theory problem.  He's maximizing the sooner payoffs, the later payoffs, and then also temporally discounting.  E.g.,

$6 now, or $12 in a month----- he chooses $6. 
$8 now vs. $10 in four days---- he chooses $10.

But now he's told one of these choices, randomly, will be paid to him.  So instead he picks:

$6 now vs. $12 in a month--- he chooses $12
$8 now vs. $10 in four days-- he chooses $10

Because in the first pair, he would have been paid either $6 now or $10 in four days.   "No way, I'm not risking losing $10 in four days just to get $6 now.  In order to risk losing $10 in four days, I need a bigger payment down the road.  The only choice available to me is $12, so I'll take it."  Get it?

Aggregate 15 such choices and it's no surprise people pick larger-later payoffs more often.  The real way to do this would be to offer the people real money for every single choice they made, but that didn't happen here.

Unfortunately, it doesn't happen in real life, either.  Most of the time, people make decisions based on hypothetical scenarios, with a faint expectation that perhaps one of these decisions will result in an actual payoff.   When people with identity issues are presented with a series of binary choices, we expect them to consider them independently, and we often marvel at how bad their choices seem to be.  But they may be taking a series of binary choices and inappropriately pooling them to maximize an overall outcome.

That's why we get frustrated with their choices.  We can't understand why they made that choice because the reason has to do with an entirely different decision that should be unrelated but to them is linked. 

And so it becomes important to restate things into independent, binary choices.  Certainly life choices are affected by other life choices, but for those floundering in their own identities, things need to become more concrete, not less.


I choose the $5 today, beca... (Below threshold)

August 11, 2008 8:09 PM | Posted by Anonymous: | Reply

I choose the $5 today, because $5 more isn't worth the mental effort of remembering and collecting the money a year later.

Vote up Vote down Report this comment Score: 4 (10 votes cast)
Wait, I'm confused. Are you... (Below threshold)

August 12, 2008 5:11 AM | Posted by Anonymous: | Reply

Wait, I'm confused. Are you saying that people don't know "themselves" so they'll choose biggest pay, or is it their situation or is it their reaction to that they don't know.

If it's the situation than could you set up a game type situation to have the person test out their emotion/reaction to better understand themselves?

If it's themselves, do you get them to define themselves, through writing or talk?

If it's their reaction do you get them to practice reacting the way they want?

uhh did I just say a bunch of the same thing? I think I did...
Anyways here's the main question (I guess) What sort of exercises would you do to make things more concrete?

I imagine that when you only have two chioces, both option displeasurable, it tends to put pressure on people resulting in a bad reation (angery, fear, confusion)...

Vote up Vote down Report this comment Score: 0 (2 votes cast)
The function is not hyperbo... (Below threshold)

August 12, 2008 6:03 AM | Posted by Janne Sinkkonen: | Reply

The function is not hyperbolic but exponential (look for compound interest and discounting on an economy context).

You have an interesting point about changing identity and discounting. Potential death is, of course, also a change in identity and may be the original evolutionary reason for discounting. Also meditation, its effects on perceived identity and long-term thinking come to mind.

Also a related thought is differential discounting between positive and negative outcomes. Negative outcomes tend to lead to identity shifts and catastrophes. Therefore when you are planning and see alternative future scenarios, it makes sense to discount the negative more than the positive. This applies to resources used for planning, too. This leads to optimism.

Vote up Vote down Report this comment Score: 1 (1 votes cast)
So... what does it say abou... (Below threshold)

August 12, 2008 8:47 AM | Posted by fragola: | Reply

So... what does it say about me that I assumed from the excerpt that the question was asking me to pay, and not be given money?

I actually already know the answer to this -- since it goes well with one of your site's focuses, I'll explain: I've had dreams recently where I have to unfairly "pay twice over", and together with my therapist, we interpreted that this was exactly what my narcissist (as in diagnosed NPD) mother did to me all my life. My unconscious expectation until now has always been "I'm going to pay for this..." even when I do well. My mother was an amazing master at giving precise instructions, then denying she'd given them, and then adding that if she had given instructions, they certainly weren't what I remembered of them, and in any case I was supposed to just know (except that in her eyes, what I "knew" was always wrong). In other words, I spent my entire childhood getting punished for things I'd done right, in addition to things I did wrong. When I'd done them right, I would defend myself, which would only infuriate my mother all the more: "pay twice over".

(Just imagine poor me's reaction when on occasion, like everyone, I honestly misremember instructions at work as an adult. I used to freak out and think my world would end -- which from my childhood perception, was what happened with my mother. Hell hath no fury like a narcissistic mother on a power spree with a defenseless child. At least I'm safe and healing now. ...Or so I thought until I chose "pay five dollars now, obviously" then clicked through and was dumbstruck! More work to do... :) )

Vote up Vote down Report this comment Score: 5 (5 votes cast)
Dan Ariely has written a ne... (Below threshold)

August 12, 2008 8:39 PM | Posted by Jack Coupal: | Reply

Dan Ariely has written a new book, Predictably Irrational, which has a subtitle of: The Hidden Forces That Shape our Decisions.

His third chapter is entitled, The Cost of Zero Cost, which covers all of the above really well.

Vote up Vote down Report this comment Score: 1 (1 votes cast)
Actually, it's neither h... (Below threshold)

August 12, 2008 11:48 PM | Posted, in reply to fragola's comment, by Alone: | Reply

Actually, it's neither hyperbolic nor exponential-- it is quasi-hyperbolic.

The essence of temporal discounting is that there is a discount rate that decreases the further in the future the choices are. So a choice in the distant future is discounted less than one in the present. That's the key.

In simple terms, for periods of time t, the discount rate is 1/t, which is a hyperbola. Hence, temporal discounting is hyperbolic discounting.

In fact, it's not exactly 1/t. The function is more specifically (1+at)^(-b/a), as a=b ---> infinity. More simply, discounted value=(undiscounted value)/[1+xt]

That's the model that actually fits the observed data with animals. Again, the key is that the discount rate itself changes over time. People judging today do not appreciate how impulsive they will be the closer to the choice they get-- and then the choices flip.

If, however, you assume a constant discount rate over time-- things get discounted by the same "amount" no matter when-- then that would be an exponential function. (discounted value=(undiscounted value)exp(t)) But think about it for a moment, and you can intuit that things are discounted at a constant rate.

Again, when you plot the data points derived from animal experiments, the curve that best fits the data is the hyperbolic one, above.

Vote up Vote down Report this comment Score: 1 (1 votes cast)
I'm saying that people (... (Below threshold)

August 12, 2008 11:59 PM | Posted, in reply to Anonymous's comment, by Alone: | Reply

I'm saying that people (with identity issues) only know themselves in the present and the near term, so they could not possibly predict how they will choose in the distant future.

The "exercises", as you put it, are really to try to stabilize the identity, not the choice. For example, in a 401(k) decision (to open, or not to open), two methods to improve the likelihood of opening such an account would be a) identify a constant in their identity that they will accept as constant-- for example, make real that they will be alive at 65. "How old is your Dad? He's alive. Do you think you'll be dead when your kid graduates from college? What are you going to do with no money? (etc.)" b) reverse the decision, not whether to open a 401(k), but whether to NOT open a 401(k). In other words, make the default that a 401(k) will be opened, and then the decision gets discounted favorably (e.g. laziness.)

Vote up Vote down Report this comment Score: 1 (1 votes cast)
Thanks for the clarificatio... (Below threshold)

August 13, 2008 1:29 PM | Posted, in reply to Alone's comment, by Anonymous: | Reply

Thanks for the clarification - the hyperbolic form of observed discounting was news to me.

Constant rate discounting, leading to exp(-kt), is rational under the simple model of "memorylessly decaying utility", for example due to constant probability of death.

1/t discounting would be a nice ground for theoretical speculation, although it may of course be just an empirical coincidence. For example, on logarithmic time scale 1/t discounting becomes constant discounting.

Vote up Vote down Report this comment Score: 0 (0 votes cast)
i think you are overselling... (Below threshold)

August 13, 2008 10:51 PM | Posted by misanthropope: | Reply

i think you are overselling your data by a lot. i would take 5 now instead of 10 in a year, but 10 in 8 years instead of 5 in seven. but i would do it on a rational consideration of my best interest.

"now" versus a year there is a tremendous increase in the likelihood of the payoff actually materializing [granting that this is a verbal offer and not presented in a contract]. 7 vs 8 years, the likelihood consideration is pretty much a wash, and we are down to pure time-value-of-money calculations.

Vote up Vote down Report this comment Score: 0 (2 votes cast)
Great post. Very informativ... (Below threshold)

August 15, 2008 2:11 PM | Posted by Stop Smoking: | Reply

Great post. Very informative, too bad more sites weren't as good as this one!

Vote up Vote down Report this comment Score: 0 (0 votes cast)
Could the difference betwee... (Below threshold)

August 16, 2008 5:43 AM | Posted by Jon: | Reply

Could the difference between real and hypothetical money be partialy explained if you consider the reward not to be the actual recieving of cash, but the moment when you recieve the commitment of cash. Then the payoff for the real cash happens at the same time regardless, and so the only difference is how much money the commitment is for. Or maybe there's in innate impusle to try and 'win' the game, by securing the most money. When you play for hypotheticals for act only for your benefit, with real money you are also trying to maximise this opportunity and don't want to feel like you missed the chance to get more money out of the 'opponent'.

Vote up Vote down Report this comment Score: 0 (0 votes cast)
continuing the hyperboli... (Below threshold)

August 18, 2008 2:27 PM | Posted, in reply to Anonymous's comment, by Alone: | Reply

continuing the hyperbolic vs. exponential discussion: actually, both are hypothetical models that could conceivably explain behavior. But for some reason, when actual data (with animals) is plotted, the curve that comes out is hyperbolic. But it isn't at all obvious why that and not an exponential function should be the case, only that it is the case. Weird. The interesting thing or me, of course, is int he realm of identity-- if one's behavior relative to a reward and the time away from that reward is predictable, how much choice did you have-- and is it actually measuring the choice, or the degree of constancy in one's identity? In other words, if you found some other experiment that measured changeability of identity (e.g.likelihood of being divorced x present age x time in the future) does that also follow a hyperbolic function? If so, is personality disorder a hyperbolic function? etc, etc.

Vote up Vote down Report this comment Score: 1 (1 votes cast)
I'd take the five dollars b... (Below threshold)

August 20, 2008 9:16 PM | Posted by Anonymous: | Reply

I'd take the five dollars because I know I need money right now, my financial situation in a year is unknown right now, I have no idea if I'll be as poor as I am right now or even if I'll still live in the USA.

Vote up Vote down Report this comment Score: 3 (3 votes cast)
You have to take into accou... (Below threshold)

August 24, 2008 12:09 AM | Posted by Chase: | Reply

You have to take into account not only the time span from now to option A, and from now to option B, but also the difference between option A and B

$5 now, or a $1 million in 10 years, I'll go with option B.
$5 now, or $10 in 10 years, I'll go with option A.

$5 now, or $10 next week, I'd probably take the $10.
$5 now, or $6 next week, I'd take the $5.

So, even if you put the hidden $0 back in, its still a variable that has to be accounted for.

Another variable is need. You use the example of "eat now". If by not taking the $5 now, you put yourself in a position where you won't be able to take the $10 later, then no matter how small the time span span between the two events and no matter how large the difference between the two amounts, the logical choice is take the $5 now.


Another thing that would be interesting to see is how the choices are effected by adding uncertainty to the occurrence of Event B. I can give you $5 today, but if you wait a year, I MIGHT be able to give you $1 million dollars. I'd wait, the sacrifice of $5 is worth the chance at $1 million. But, I can give you $5 today, or I MIGHT be able to give you $10 tomorrow. I'd take the $5. If there is a chance I will end up getting nothing if I wait, then I wouldn't risk that $5. Its like the person that goes to their boss and threatens to quit if they don't get a raise. You are giving up your current salary in hopes of getting a higher salary tomorrow, but you are risking having NO salary tomorrow.

Vote up Vote down Report this comment Score: 2 (2 votes cast)
Someone could use the $5 to... (Below threshold)

September 1, 2008 8:58 AM | Posted by lyrical: | Reply

Someone could use the $5 today as a resource to make $20 by next year. I thought you were all about the capitalism? :-)

Vote up Vote down Report this comment Score: 2 (2 votes cast)
Remarkable article. It depe... (Below threshold)

November 10, 2008 2:30 PM | Posted by Answer My Health Question: | Reply

Remarkable article. It depends on the your perspective of what is the higher value of money for you with regards to the time element.

Vote up Vote down Report this comment Score: 0 (0 votes cast)
I say it depends on who's o... (Below threshold)

February 10, 2009 4:41 AM | Posted by Sreve: | Reply

I say it depends on who's offering the deal:
a) My bank offers $5 cash when I'm already at the counter or $10 automatically added after a year, and I take the $10.00. I need do nothing, I trust the bank and I take the 100% interest.
Make that $500 now or $1000 in a year and I'm even more certain to take it.
2) Some dude on a university campus with a clipboard says he's from the Psychology faculty doing a test. He offers me the same deal. He's got $5 in his hand? I take it.
He's got $500? I grab it with glee.
Moral: Donate more to psychology research. The poor bastards are stuck with the $5 test system.

Vote up Vote down Report this comment Score: 5 (5 votes cast)
Thanks for sharing that, my... (Below threshold)

March 22, 2012 10:42 AM | Posted, in reply to fragola's comment, by Anonymous: | Reply

Thanks for sharing that, my mom did stuff like that too.

Vote up Vote down Report this comment Score: 2 (2 votes cast)
. . . which is actually whe... (Below threshold)

January 3, 2015 4:20 PM | Posted, in reply to Anonymous's comment, by Anonymous: | Reply

. . . which is actually where the study fails.

If you said, "A thousand dollars now, or $2,000 at the end of the year," I bet that most would choose the two thousand at the end of the year.
If you say, "$5,000 now or $10,000 in a year," I am even MORE certain they would choose the $10,000 in a year. The higher the numbers, the more likely it is that they'll choose to wait.

Twenty-thousand now, or fifty-thousand a year from now? Two years from now? People will wait.

Vote up Vote down Report this comment Score: 1 (1 votes cast)