Discounting and the ethic of denial

It is not always best to delay gratification.

Posted Jul 31, 2010

Now or later?
Now or later?

The curbing of impulses to which we are led by forethought averts physical disaster at the cost of worry, and general lack of joy. [. . .] In this respect, therefore, I am not convinced that there has been any progress at all.

~ Bertrand Russell (1950; Unpopular Essays: Ideas that helped mankind)

Stretching his hand up to reach the stars, too often man forgets the flowers at his feet.
~ Jeremy Bentham

We often have to choose between something nice that we can have right away and something better that we'd need to wait for. Other choices involve something we desire but know that we'll have to pay a price in money or pain later. Do we choose to have it anyway? Consider some concrete examples: Would you take $80 now or rather wait a week to receive $100? Would you date the imperfect 8 tonight or rather wait for a perfect 10 -- assuming that you can't have both? Would you smoke a pack of cigarettes today, when it tastes oh-so-good, and accept significant health risks three decades later?

Conventional social norms ask you to desist and wait, and many scientists agree. Economists complain that we are not saving enough for retirement (while simultaneously complaining about "low consumer confidence" [i.e., spending], but that's another story). Evolutionary psychologists want you (especially the women) to hold out for the fittest mate and certain conservatives want you to, well, conserve yourself as much as inhumanly possible. Public health pundits counsel against smoking, thereby revealing their implicit preference that it is better for you to die of Alzheimer's instead of heart disease.

It is easy to see why the imperative to wait does not work as a hard rule. If you had a choice between $80 today and $81 (in today's dollars) thirty years from now, it would be silly to wait. Which brings us to discounting. It is critical to know just how much of its appeal a reward loses with the passage of time. With a little probing, we can find your point of indifference. Let's say we find that you don't care if you get $80 now or $100 in a week. This means that your discount rate is 20%.

So far so good. No one can argue with your discount rate. It is yours. It is a preference like other preferences. Those who tell you to wait a week for $90 when you prefer not to, only reveal their own preferences for what they want you to do. When the choice is yours, those who object are meddling with your freedom.

The persuasive force of those who want you to wait becomes stronger when they can show that your discount rate is too high. But how can they do that? Why should a discount rate of 20% be too high? What is the "correct" discount rate? The dirty little secret is that there is no way to brand any particular discount rate as too high (or too low). What can be done is to ask whether the rate remains stable over an extended period of time. If it doesn't, preference reversals can emerge. Preference reversals are irrational, which means you messed up, which means you should accept counseling.

Consider a discount rate that is stable at 20% per week. You take $80 now over $90 in a week, and you also take $80 ten weeks later over $90 another week after that. No reversal here. In contrast, suppose your discount rate starts out high and then falls off as time marches on. If for example, your discount rate is 50% for the first week and 5% for the eleventh week, you will first prefer $80 over $90 because .5*$90=$45, and later prefer $90 over $80 because you value the $90 at $85.5. Now you're in trouble with the Church of Rational Choice.

Scores of studies with humans and other animals have shown that temporal discounting is hyperbolic, a term describing a certain type of mathematical curve that is first steeper and then flatter than an exponential curve. A conservative interpretation of hyperbolic discounting is simply to say that there are preference reversals. Rationality demands that such reversals be eliminated, but it gives no guidance on how to do it. In the example above, you could make your choices coherent by using the 50% rate at both times, which means that you would prefer the numerically smaller amount at both times. You could also use the 5% rate at both times, which means that you would prefer the numerically larger amount at both times. If moralists want you to always resist temptation, they have to find other arguments. Appeals to rationality won't help.

There is something weird about preference reversals in temporal discounting. I find it easy to imagine that our ancestors often had to choose between immediate benefits and somewhat delayed benefits, which were potentially larger but also potentially uncertain. I find it harder to imagine that the ancestral environment (or the present one for that matter) presented many choices between options that were both displaced far into the future, but one more so than the other.

That's why I think that choices displaced into the future are somewhat contrived. Perhaps they appear in studies on behavioral economics to cast doubt on preferences for immediate benefits. If indeed choices between options in the distant future and options in the distant future plus one week are not very common, not very important, and not very emotionally engaging, then it is perhaps these choices that should fall in line with present-time choices. You end up doing what you want to do in the here and now, and the demands of rationality are satisfied.

Look again at the numbers three paragraphs up. Assuming hyperbolic discounting, we saw that $80 > $45 in the near-future scenario but $80 < $85.5 in the remote scenario. Notice that we cannot fit a smooth curve through these numbers. By setting the small reward to $80 and the large reward to $90 in both choice problems, we imply that discounting occurs only within week 1 and within week 11. But must we not assume that discounting progresses relentlessly through time and thus must we not concede that by week 11, the $80 ($90) rewards have been greatly devalued? Why would we reset the later rewards to their initial values as if nothing had happened?

When discounting continues hyperbolically throughout the year, the difference between the subjective values becomes awfully small; too small perhaps to let one make much theoretical hay. Consider an example based on the simple numbers above. If we assume a discount rate of 50% for the first week and let it shrink by 20% each week, we end up with subjective values of $5.37 (down from $80) in week 11 and $5.71 (down from $90). If you then prefer a few subjective pennies more or less, who cares? Perhaps it is not only the shrinking values in the distant future that take the steam out of remote-future choices, but also the subjective shrinkage of the interval. The seven days that begin tomorrow appear to be a lot longer than the seven days starting at Christmas. I suspect that the preference reversal in the remote future is a mere device to unhinge the preference for the small but immediate reward in the here and now.

Society and its agents demand restraint. When appeals to rationality don't work very well, what else is left? A popular method is for society's agents to claim that they know better what your preferences should be, and you would agree if you only knew what was good for you. This is a challenge to your freedom. Parents use it all the time and their right to do so is enshrined in the law. Being able to dictate preferences is a very strong kind of power indeed, and I am not suggesting that it should never-ever be exercised. Yet, such an intervention should at least be grounded in evidence. Drawing on psychological science, one can point to correlations between the ability to delay gratification and overall success and adjustment to life. Alas, such evidence is contaminated. The test is not independent of the testers' motives. Of course, society rewards those who play by its rules, even if those rules involve the denial of basic self-interest.

Let me return to the choice between taking an immediate reward that comes with later pain and doing nothing. Desire and discounting favor taking the reward, whereas the outside view (society, the super-ego, fear) demands resistance. We are socialized to yield to the outside view, and the messages designed to reinforce our continued deference emphasize those later pains that are great indeed (lung cancer). But what about love? Will you forego a wonderful love relationship when you know that it must end after a few months? Desire and fear battle in your mind. But desire has discounting on its side. Thank God!

Postscript: The same argument can be made for almost anything worthwhile we do in life. If we only knew the pain that would ultimately come from what we enjoy now, we would never get up in the morning (love, build homes, have kids). We would not choose to live. Thankfully, we find ourselves in this life; we did not choose it. Or did we? According to one myth, souls resist being born because they foresee all the trouble. They have to be blinded to the future. Once born, we can go from one nice thing to the next, and let the chips fall where they may.