4.3.1 Self-Restraining Smart Choice to See the Grand-Prize Winning Movie
The above discussions about cleaning and movies are about very limited decision- making processes that pertain to one-time or one-shot actions. To consider broader problems such as savings and obesity, it is necessary to think about more general decision problems, such as choosing the timing of frequently made actions performed within a certain time period. Even in such a case, the conclusion that hyperbolic discounting works in the direction of choosing an “easy option” basi- cally applies if decision-makers are naı¨ve and thus do not anticipate the incompe- tency of their future selves. Therefore, in the case of a naı¨ve person, hyperbolic discounting will result in the preproperation of consumption (overspending, undersaving, etc.) and the procrastination of abstinence (nicotine dependency, obesity, etc.)
Things are more complicated when a decision-maker is sophisticated. When deciding multiple timings, for example, “when to go seeXnumber of movies in a year” and “when to do X times of cleaning,” paradoxical situations like “the preproperation of a fun activity is mitigated in the end” and “the procrastination of tedious work is further exacerbated” can take place.
Let us consider this by taking the movie problem as an example. The setting is the same as before: the third-place, second-place, and grand-prize winning movies will be screened in that order over 3 weekends. In this case, however, consider the case of seeing two movies with two tickets. Referencing Fig.4.3again, think about which movies a person should see. If there is no discounting, it is best to go see the movies shown on the second and third weeks. The same is true under exponential discounting.
The story would be simple, if the decision maker were a naı¨ve decision-maker.
Although he or she chooses A3 (i.e., the grand-prize winning movie) and A1 (i.e., the third-place movie)—the two movies with high utility as of the first week—once
the second week comes, you end up changing the plan from the prior week and go to the second-place movie because the utility value of the second-place movie screened on that day will exceed the (discounted) utility value of the grand-prize winning movie due to hyperbolic discounting. Ultimately, as summarized in Table4.1, the naı¨ve choice is to see the movies in the first and second weeks.
In contrast, a sophisticated decision-maker who foresees the future self changing his or her mind knows already, as of the first week, that he or she will never be able to see the combination of movies in the first and third weeks; the decision maker knows that he or she will not be able to wait for the grand-prize winning movie once the second week comes. Therefore, the choices he or she is left with are either to see the movies in the first and second weeks—as if a naı¨ve decision-maker—or see the movies in the second and third weeks. Since the second week is common to both choices, the choice is ultimately between the first week’s movie and the third week’s movie. In the end, seeing the movies in the second and third weeks would be the sophisticated choice.
As summarized in Table4.1, the sophisticated choice is the same as the choice made under exponential discounting. Compared to the naı¨ve choice, you can see that the acceleration of the schedule is mitigated in the sense that the person is seeing a movie in the third week rather than in the first week. This is in contrast to the previous movie problem of choosing only one movie to see, where sophistica- tion always worked in the direction that exacerbated the preproperation of a schedule to eat an unripe apple.
How should we interpret these results? Making a pessimistic choice by antici- pating the indulgent future self is the same as in the case of deciding the timing for one action. The point is whether or not a pessimistic prediction about the future self will increase the net cost of choosing an easy option today (in this example, the option to see the movie early). When it increases, the sophistication leads to a more abstentious choice; when it decreases, the sophistication leads to a more indulgent behavior.
In this movie problem, let us consider the cost of going to see the first week’s movie, as perceived in the first week. In the case of a naı¨ve person, since he or she has already decided to see the grand-prize winning movie in the third week, the cost of seeing the first week’s movie is A2, which is the lost benefit—the opportunity cost (or lost profit)—incurred by not being able to see the second week’s movie. In Table 4.1 When to see two movies
Week 1 Week 2 Week 3
Movie
Third-place movie
Second-place movie
Grand-prize winning movie
Exponential discounter (optimal choice) ○ ○
Hyperbolic discounter Naı¨ve ○ ○
Sophisticated ○ ○
Note: Unlike the case of seeing one movie, the acceleration of schedule is mitigated by sophis- ticated decision-making
contrast, in the case of a sophisticated decision-maker, the opportunity cost of seeing the first week’s movie could be as high as the already high A3 (i.e., not being able to see the third week’s movie), because he or she foresees winding up seeing the second week’s movie anyway. In other words, being correctly pessimis- tic about the future self increases the cost of seeing the first week’s movie by the difference between A3 and A2. This is why the preproperation of schedule is mitigated in the case of sophisticated decision-makers.
In short, if a decision-maker knows that he or she will wind up seeing the movie in the second week, he or she will resist seeing the movie in the first week because seeing the second-week movie would lead to a large loss: not being able to see the grand-prize winning movie in the final week. The same can also be restated as follows: by not seeing the first week’s movie, the person is guaranteeing that he or she will be able to see the grand-prize winner in the third week. Restricting the behavior of the future self through the present choice is called “self-locking” or
“precommitment.” In this case, the choice of not seeing the first week’s movie acts as a precommitment device for the purpose of seeing the grand-prize winning movie. That is to say, choosing to see the first week’s movie requires the opportu- nity cost of giving up such a precommitment device, resulting in an extra cost of A3 minus A2.
4.3.2 Excessive Abstinence and Indulgence Due to Sophisticated Decisions
The discussion herein has become somewhat complicated. In general, choices and behavior that cannot intuitively be attributed to hyperbolic discounting could occur whenever people make choices by taking into account the weak willpower of the future self. To reiterate, whether correctly incorporating the future self will rein- force the choice to be more abstinent or indulgent and extravagant depends on whether pessimism toward the future self will increase or reduce the cost of choosing an easy option today. Depending on it, it is possible that abstinence will be overly tightened or indulgence will end up being promoted.
For example, suppose that it is best to enjoy alcohol by limiting the amount of consumption per day to a certain level. In this scenario, a sophisticated person who is aware of the weak future self may take into account the future self, who will become out-of-control once he or she starts drinking, and hence choose not to start drinking. This type of abstinence might seem desirable at first glance; however, this choice of not starting to drink is overly abstinent because exponential people who lack self-control problems would choose to enjoy drinking at a desirable level without any inconsistency. Although this behavior is hard to imagine from the perspective of hyperbolic discounting, which overestimates the immediate benefit, from the perspective of sophisticated people, having a drink now is an act that will
cost dearly in the long run, and the excessive abstinence of not drinking is actually a choice under hyperbolic discounting.
Conversely, there are cases in which people resign themselves to a lifelong drinking habit by recognizing their own weak willpower. In such cases, a drinking habit may wind up being reinforced by a sophisticated choice, because the cost of having one drink actually becomes lower for them than it is for naı¨ve people who do not recognize their own weak willpower. The sophisticated people make an even weaker choice because they take into consideration the weak-willed future self. As it is colloquially said, “there is no arguing with a crying child or city hall”; you cannot fight against a crying child that is the weak-willed future self, so to speak.
When the present self cannot improve the weak-willed future self, no matter how he or she controls the situation, the cost of choosing an easy option will itself be lowered for today’s self, and the easy option winds up being reinforced.
The mechanism behind such expectations-based behavior can explain well phenomena that cannot be explained by simple exponential discounting or the naı¨ve choice model: overly strict choices and easy choices that are made by taking the future self into consideration.
Sophisticated children who take into account the weak-willed future self can endure rigorous but well-balanced study plans because they perceive the cost of not studying now to be that much larger. On the other hand, a child who has, for some reason, resigned himself or herself to unfortunate circumstances would be at a higher risk of quitting rehabilitation and becoming a repeat offender.
People who do not want to become obese attempt to go on a decisive diet by taking into account their own self-control problems and avoiding procrastination.
However, those who consider future obesity unavoidable due to heredity or the environment would perceive the cost of overeating to be small compared to that seen among other people.
While some people refuse to turn on the TV or computer—knowing that they will not be able to stop watching TV or surfing the Internet—those who cannot work without the Internet would knowingly allow their daily lives to become dependent on the Internet.
Similarly, while there are honest husbands who would not get involved in an extramarital relationship from the beginning—knowing that it would eventually become a hopeless mess—there are lovers who reinforce their relationship after having realized the difficulty inherent in breaking it off. Such circumstances have been the subjects of songs and stories since time immemorial.
Excessive abstinence seems to be counterintuitive to hyperbolic discounting, and excessive indulgence and extravagance seem to contradict the assumption of sophisticated choice. However, it is not a strange phenomenon in any way from the perspective of strategic reciprocity between the present and future selves—reci- procity created when the present self takes the future self into consideration. As described below, this type of situation can also occur with saving behavior.
4.3.3 Does Sophisticated Decision-Making Increase or Reduce One ’ s Savings?
In general, a sophisticated choice that takes into account the future self can mitigate or exacerbate the negative effect of undersaving that occurs under a naı¨ve choice;
which will take place depends on two effects of incorporating the future self.
One is the effect of taking a pessimistic view of the future self. That is, it becomes more desirable to spend now than to save because the weak-willed future self will not continue to grow the savings and spend them wisely, even if the present self were to save now. This works toward lowering the incentive for the present self to save money. In the problem of choosing when to see one movie, it corresponds to the scenario where the tendency to accelerate the schedule is exacerbated by taking into account the future self.
On the other hand, when the decision maker acknowledges that his or her weak- willed future self will not save sufficiently, he or she can anticipate that future consumption levels will be lowered. As a result, from the perspective of a consumer’s interest in maintaining consumption levels over time—also known in economics as the motivation to smooth consumption—it becomes necessary to accept the fact that there will be overspending in the future and save extra money in the present. This will work toward increasing the incentive to save.
Ultimately, whether sophistication will mitigate or reinforce undersaving caused by hyperbolic discounting is determined based on the relative magnitudes of the first negative effect due to pessimism and the second positive effect due to the motivation for smoothing. Roughly speaking, the above discussion can be applied to the general problem of the intertemporal allocation of gratification because how much money to save is part of the problem of how to allocate the gratification from consumption over a certain period of time. However, please note that the second effect (namely, abstinence caused by the motivation to smooth consumption) takes place only when one considers how much moneythe future self will save, that is, how much moneythe future self’s future self will spend for consumption. In relation to the earlier movie program (Fig.4.3), this abstinence effect is observed only in the choices of multiple movies within a given period and not in the choices of seeing a single movie. Recall that, in the decision-making problem of seeing one movie (see Sect. 4.2.5), the sophisticated choice always exacerbates the acceleration of sched- ule caused by hyperbolic discounting—just as one “eats an even less ripe apple.”
This is because the effort to promote abstinence does not work.
Here, I have discussed how savings could increase or decrease whenever the weak-willed future self is taken into consideration. However, this is strictly in comparison to the savings of naı¨ve people, who cannot correctly anticipate their own future selves. In the case of a naı¨ve choice, the decision-maker always falls into undersaving because his or her savings plan is perpetually scrapped over time. The discussion in this subsection is about how the situation changes when the preference reversal in the future is taken into consideration. Therefore, although the negative effect of hyperbolic discounting is reduced when it mitigates undersaving, this does
not mean that one can generally make a more efficient choice compared to that made without hyperbolic discounting. It literally mitigates only the negative effect of hyperbolic discounting; the consequences of inherent self-control problems will probably remain somewhat typically in the form of inefficient undersaving.