by Richard Robb
Choosing across Time Involves a Contradiction
Is planning for the future, deciding when to do what, similar to selecting a consumer good? That is, do we mentally line up all available options and pick the one that’s best? In the case of a consumption plan—this much for today, this much for next week, next month, next year—that would mean picking the pattern that provides the best combination of current well-being and anticipated future well-being. Most economists would say, yes, that’s what we do, and many non-economists would probably agree.
Let’s consider the problem abstractly. To apply rational choice to planning as we did to renting an apartment, we must (1) pick the path that balances our desire to enjoy ourselves now and provide enjoyment for the future, and (2) willingly stay on that path as time passes. The trouble is, (1) and (2) can’t coexist because our future selves will care about their futures with an intensity comparable to our direct concern about the future from today’s point of view. Nearly any way we define the problem, we’ll arrive at a contradiction. Assuming people enjoy both consuming and anticipating their future well-being, they will want to change their former plans when the imagined future turns into the present. This is not a statement about “weakness of the will” or human psychology; all conscious beings, even those living on distant planets, are subject to the same mathematics and therefore experience the immediate present in a different way than the imagined future. My aim is not to replace the old calculus with a new one but rather to show that no calculus is going to work.
Although a mathematical proof is necessary to make this argument with precision, it’s possible to follow the logic without the math. To see why there can be no stable plan for consuming over time, we will consider two cases. In the first, people look ahead two or more time periods. These periods can be expressed in any units—days, weeks, months, or years. If people are free to change their minds and derive well-being from thinking about how their future selves will obtain pleasure from thinking about their futures, they will not stick with any single plan. In the second case, people look ahead only one period. Here, it’s possible to arrive at a model that accords with rational choice and leads to a consistent plan over time, but only by performing bizarre and implausible mental feats.
Both cases operate under the most stripped-down set of assumptions—perfect certainty and one type of consumption. If rational choice can’t be made to fit in even these simple conditions, think how confused it would become if more realism were introduced to the model with factors like technological progress, social change, or uncertainty about lifespan, health, income, and interest rates.
We conclude from all this that purposeful choice simply does not apply to planning over time if people are able to reevaluate. This doesn’t make them irrational, and moreover, it’s not even problematic. Some things just can’t be crammed into the purposeful choice framework. We can’t choose what we prefer among available plans because “prefer” loses its meaning when options refer to different paths in the future.
Looking Ahead More than One Period
According to purposeful choice, everything is commensurable. That is, everything can be translated into a common currency (for instance, money, hours worked), then compared and evaluated. The price of leisure, at this high level of abstraction, is the agent’s wage—he “purchases” an hour of leisure by working one hour less. He frames each situation as an optimization problem, then finds the solution that maximizes utility subject to constraints. Since everything has a price, we’re justified in aggregating all the inputs into utility and calling that aggregate “consumption,” the more the better.
Suppose a person assumes that he will stick to whatever plan he sets, then tries to figure out how to maximize well-being at each point in time, considering the satisfaction he will enjoy from consuming in each period plus satisfaction from anticipating the future. This problem, from today’s point of view, should have a solution—some array of consumption should look best. But as long as the person looks more than one period into the future, he will want to deviate from the plan he set out previously.1 The assumption that he’ll stick with the plan cannot hold. Moreover, as a rational actor, he must have known all along that he wouldn’t voluntarily stick to the plan, so his assumption was spurious, and it wasn’t much of a plan in the first place.
To be a bit more precise, consider someone who derives pleasure on Monday both from consuming and from anticipating his well-being on Tuesday, Wednesday, and beyond. On Monday, he maps out a consumption plan. From the vantage point of Monday, he anticipates his consumption on Tuesday and Wednesday and can also anticipate the pleasure he will feel on Tuesday from anticipating Wednesday. Consumption planned for Wednesday will make him feel more secure on both of the first two days of the week.
Now imagine that a day passes and Tuesday becomes the present. The appeal of Wednesday’s consumption must erode relative to Tuesday’s. Intuitively, Wednesday’s consumption becomes less desirable because the person can only anticipate it once, while Tuesday’s consumption becomes more desirable than it appeared on Monday. Why? On Tuesday, even though he loses the benefit of anticipating Tuesday’s consumption, he gets to consume it. On the margin, that actual consumption must be at least as satisfying as anticipation was back on Monday. Otherwise there’s no hope of a stable solution—he’d perpetually tease himself by anticipating a binge of consumption that he’d flip forward as soon as the time came to partake. As a result of these fluctuating valuations, when Tuesday arrives, the person shifts some of the consumption planned for Wednesday to Tuesday.
As long as today’s plan looks more than one period into the future, we find ourselves with a contradiction. No plan that appears optimal in the present will look optimal once the future becomes the present. Simply put, we cannot choose what feels best in each period, including the positive or negative pleasures of anticipating the future, without getting tied up in a knot.2
Looking Ahead One Period Only
If people looked ahead only one period, it would be possible to find a solution that is consistent with rational choice, although the underlying assumptions are unappealing. To see why, suppose well-being at any one time depends on the satisfaction a person experiences from consumption in the present plus the well-being she expects in the next period, divided by a factor of 1 + ρ. In this case, ρ is a psychological constant that represents the trade-off between satisfaction today and satisfaction tomorrow. If we care less about the future than the present, whether the future involves a reward or a punishment, then we underweight the future and ρ is a positive number. By contrast, if we innately cared more about the future, then ρ would be negative but larger than −1.
To achieve a result that is consistent over time, the individual must do three things in the present, which we’ll say is Monday. She must hold in her mind the way she expects to feel on Tuesday, Wednesday, and beyond; she must imagine how her consumption flow will appear from the perspective of Tuesday, since her concern for Wednesday operates exclusively through her concern for Tuesday; and she must choose what she prefers after carefully purging from her mind any direct concern for Wednesday. That is, Wednesday’s consumption enters into her plan only because she cares about Tuesday’s iteration of herself and knows that Tuesday’s iteration will care about Wednesday’s.3
If these mental acrobatics seem like a strange account of how we plan for the future, consider further that the three requirements must be applied to one and only one time scale. If a plan holds for units expressed in days, it does not hold for months. That is, Monday’s self cares about Tuesday’s self, but not directly about Wednesday’s self except to the extent that she knows Wednesday’s welfare will be an input into Tuesday’s. In this case, however, January, February, and March will obey no such relationship.4
One More Way Out … Maybe
Let’s say you’re desperate to find a way to understand time in terms of rational choice. There’s one more approach you can take, but you’re goi
ng to have to make two assumptions and, on close inspection, you’re not going to like them.
First, when you think about the future, you must think only about consumption and not how you’ll feel about the arrangement that prevails at different points in time. For this model to work, even if the consumption plan you set in April leaves you to starve in June, you must ignore the distress you’ll feel about it in May. It’s a peculiar assumption, especially since you’re already displaying concern about the future by postponing consumption.
Second, you must assume that everyone in the world shares the same innate taste for trading off present satisfaction for future satisfaction, and that this taste happens to be described by one particular mathematical formula. This is another peculiar assumption because there’s no reason to think that human nature coincides with the one formula that’s compatible with rational choice.5
An economist trying to apply rational choice to planning has got a problem. She can go in one of three directions to construct a time-consistent model from first principles: (1) assume individuals have only one shot to plan their lives (the moment the economist is observing them), a perfect ability to bind themselves to that plan, and a desire to compel their future selves to do things those future selves might not wish to do; (2) assume individuals can look only one period ahead and that there is a single natural time scale for planning; or (3) assume individuals care about only present and future consumption and not how they will feel in the future, and that they coincidentally discount satisfaction from future consumption according to the one formula that works mathematically.
When their models fail to describe actual behavior, economists resort to blaming the cognitive bias known as “hyperbolic discounting.”6 This so-called bias leads to preferences that are “time-inconsistent,” meaning we can’t set a plan and then stick to it. But are “time-inconsistent” preferences really preferences at all? Preferences hinge on the ability to rank options, but we can’t rank options here. In fact, we can’t even choose, in any meaningful sense, a path, since we can’t commit our future selves to staying on it. Rather than a consequence of cognitive bias, “time-inconsistent preferences” is an oxymoron.
The realization that people cannot exhibit true preferences over the timing of their consumption is no cause for a crisis in our understanding of the human condition. A lack of such preferences won’t get me into trouble. The analog to time-inconsistent preferences in more static choices would be “intransitive preferences.” These are genuinely bad. Suppose I prefer strawberry ice cream to chocolate, given a choice between the two, and simultaneously prefer chocolate to vanilla and vanilla to strawberry. I could then fall victim to the famous “money pump”: a wise guy could give me chocolate for free, charge me to switch to strawberry (which I prefer), charge me again to switch to vanilla (which I prefer to strawberry), then charge me to switch to chocolate. If those were truly my preferences, he’d continue like that until he’d pumped out all my money. Yet holding “time-inconsistent preferences,” that is, wanting out of the plan the enforcement demon and I agreed to, causes no corresponding bad thing to happen. That’s because enforcement demons don’t exist.
Is the entire argument that there can be no time-consistent plan really just a fancy way of saying that life is a journey—a sentiment so tired it appears on greeting cards? Perhaps, but no greeting card explains why life should be conceived of as a journey rather than a sequence of destinations over which we have well-defined preferences.
Fooling Ourselves
As we’ve just discussed, intertemporal planning cannot be made to fit into rational choice. The fact that we change our minds may seem natural and self-evident to those who take life as it comes, as if playing a game. Others (like me) may find this more difficult to see. It can be especially difficult since rational choice gives us license to wait until after we act to ferret out our motives. If my wife asks why I failed to stop at the store on my way home, I can list reasons why it made sense to shop later. She might then ask, “Did you actually think through those reasons at the time?” But that’s not a serious challenge to my belief that I paid attention to her request. For my story to hold water and for me to feel truthful in the telling, I don’t need to claim or believe that the explanation came up to my consciousness.
Lately, I’ve been studying Japanese a little bit each day, a project that makes no sense. I was never that good at it when I heard it all day working at a Japanese bank and have little talent for foreign languages in general. I have no need for it in my life—if I’m lucky, I’ll get to go to Japan on business once a year, and everyone I meet there speaks English. Plenty of interesting subjects would be easier to learn and more relevant to my life.
Yet, if probed, I could rattle off reasons why this is a sound idea. For instance, it’s efficient to spend a relatively small amount of time to preserve what little Japanese I still know before it all slips away, it’s good for mental agility, and so on. (I wouldn’t say I find the studying pleasant because I experience it as a chore.) Rational choice theory doesn’t require that actors be aware of how their behavior optimizes, so long as it does. Perhaps my slow, casual study of Japanese really is rational, but I suspect it’s not. It feels more like a small challenge I’ve undertaken for its own sake.
Attributing motives to our own actions comes naturally. Psychological studies have demonstrated that people cook up explanations when none are readily available. One well-known experiment was conducted on a “split-brain” patient whose corpus callosum, the bundle of fibers connecting the right cerebral hemisphere to the left, had been severed to control epilepsy. A card with “Walk” written on it was shown to the patient in such a way that only the right cerebral hemisphere received the instruction. He began walking. When the researcher asked the subject why he was walking, the answer could only come from the left side of his brain, the seat of language. Since the left hemisphere was unable to communicate with the right, the left did not know that he was following a written instruction. The subject replied: “I wanted to get a Coke.” The researcher was convinced that the subject genuinely believed his explanation.7
This process may be observable even at the neurochemical level. Neuroscientist Benjamin Libet detected a specific electrical stimulus he called “readiness potential” that fires in the human brain as much as 350 to 400 milliseconds before subjects become conscious of their intent to act.8 While the interpretation of this study is controversial, it suggests that decisions may be initiated unconsciously from what Thomas Nagel calls the “blind spot … that hides something we cannot take into account in acting, because it is what acts.”9
This finding wouldn’t have surprised Schopenhauer, who wrote that “men are only apparently drawn from in front; really they are pushed from behind.”10 I wouldn’t go so far as to argue that this is always the case or to stake out the extreme position that reason is strictly a slave to passion and that we’re forever deluding ourselves about our motives. Often, reason and passion work together, just as rational choice assumes. But at other times, it only feels that way.
Discounting and Double Counting
Before moving on to an alternative, for-itself account of action over time, let’s look at a quick example that illustrates how reflexively treating choice over time like any other choice can lead to confusion.
Eating gave pleasure to humans before they understood anything about nutrition. Now we value both the pleasure of eating and nutrition. These benefits can be added together. When deciding what to eat, we weigh the combined benefits against the expense and various health concerns. Let’s say I’m serving myself chili from a large kettle and can take as much as I want for free. If I don’t like chili but I’m hungry, I’ll eat a little. If I’m not hungry but like the taste, I’ll again eat a little. If I’m hungry and love chili, I’ll eat more than in either of the previous cases. It’s straightforward—we live to eat and eat to live.
But it’s not so straightforward with a similar choice invo
lving time in a puzzle posed by the philosopher Robert Nozick, who posits an evolutionary basis for discounting the future. In his analysis, if primitive humans had a 2 percent chance of dying each year, those who unconsciously discounted by about 2 percent per year when saving for the future (in their way) could have enjoyed a survival advantage. They would then have passed this present-mindedness on to their descendants, endowing modern humans with the same tendency to discount the future.11 (Never mind whether any of this sociobiology is true. We’re interested in the theoretical problem that arises from misclassifying the present-versus-future trade-off as purposeful choice.) Since we pick present-oriented paths, such as 101 units today and 99 tomorrow rather than 100 units each day, it may appear that we desire to discount the future.
Thanks to language and actuarial tables, we can now consciously reflect on the future in ways our ancestors could not. If there’s a 98 percent chance we’ll be around next year, we should discount expected consumption by 2 percent, holding everything else equal. (Assume for the sake of this puzzle that modern humans care only about consumption that occurs in their own lifetime and do not save money to bequeath to descendants or charity.) Yet we were already discounting by 2 percent because of our inherited cognitive apparatus. It feels wrong to combine the innate “desire” to discount (analogous to the pleasure of eating) with survival calculations (analogous to the nutritional value of food) and discount the future by 4 percent. One could argue that going with 2 percent instead maximizes expected consumption given survival probabilities and simultaneously satisfies our desire to discount. But is it right to double count 2 percent discounting, allowing it to satisfy two different “motives” at once?
