4.2 Problems of the Dual Self
4.2.3 When to Clean?: Sophistication Mitigates
Let us first consider how the timing of doing tedious work differs between naı¨ve and sophisticated decision-makers. For instance, let us say that today is December 29th and that you need to plan to spend 1 day of the 3 days before New Year’s Eve on cleaning. The amount of work is the same regardless of when you clean, but since you will become busier later, the displeasure or disutility you will feelat the time of cleaning will be smaller if you clean earlier. However, if you were to clean later, the level of displeasure is evaluated at a discount because the displeasure occurs with more delay. In short, this is a question of when to clean, under the trade-off where later cleaning is more onerous but the effort is discounted and therefore perceived as smaller.
To simplify the story, suppose that the toil of cleaning in the future is discounted by half, whether it is done tomorrow or the day after tomorrow. In other words, when evaluated as of today, although one unit of disutility for tomorrow is evalu- ated equally as the one for the day after tomorrow, both are discounted by half (0.5) compared to one unit of disutility for today. Note here that the nature of hyperbolic discounting (present bias)—wherein a higher discount rate is applied to a more immediate choice—is incorporated to the present setting in a simple way.1This is because, whereas there is no discounting when converting disutility for the day after tomorrow in the units of disutility for tomorrow, there is discounting at a higher rate (50 %) when converting disutility for tomorrow in the units of the disutility for today.
Figure4.1illustrates this scenario in graph form. Since the vertical axis mea- sures the disutility felt at each point in time, a higher bar represents larger disutility (toil). It shows that the toil of cleaning on the 29th is the smallest (A29) and the largest on the 31st (C31). How those toils are evaluated at each point in time is shown by two dotted lines, I and II. Dotted line I indicates that the toil of cleaning on the 30th (B30) is discounted by half (A30) when evaluated on the previous day, on the 29th. Dotted line II indicates that the toil of cleaning on the 31st (C31) is discounted in a similar manner by half on earlier dates, on the 29th and 30th (A31 and B31, respectively).
In the illustrated example, a naı¨ve person would think as of today (the 29th) that it is best to clean tomorrow, on the 30th, because the toil on A30 will be smaller than that on A29 and A31. Needless to say, the toil of cleaning on the 30th is larger on the day of cleaning; however, in discounting and rating the toil as of today, he or she thinks that it will be smaller for tomorrow (A30) than for today (A29). That person would of course think about the option of cleaning 2 days later, on the 31st;
however, because for hyperbolic discounters, discounting tomorrow (the 30th)
1More formally, the discussion here is based on the assumption of quasi-hyperbolic discounting (βδτ), discussed in Chap.3, by setting parameterβ, which relates to present bias, to 0.5 and the long-term discount rate (δ) to 1.
will not differ greatly from discounting the day after tomorrow (the 31st), the person will determine that as of today (the 29th), cleaning on the 31st (A31), which poses the largest toil on the day of the cleaning, will be the most onerous option. Thus, on the 29th, having decided to clean tomorrow (the 30th), he or she will spend his or her time on something else—probably something more fun.
Now, dawn breaks and today is the 30th. Although delegated to clean by yesterday’s self, the self on the 30th has the freedom as an executor to determine whether or not to carry out the cleaning as planned. The person would clean today, as expected by the self of yesterday, if he or she follows exponential discounting as a bank clerk would. However, in this case, under the influence of hyperbolic discounting, the person begins to think that the displeasure associated with cleaning on the 31st (B31) is not as onerous as that of cleaning today, on the 30th (B30), because the subjective discount rate suddenly rises. This thinking occurs despite the fact that the person determined on the previous day that the toil of cleaning would be smaller on the 30th (A30) than on the 31st (A31). As a result, the naı¨ve self of the 30th will naturally skip cleaning and delegate it to the self of the 31st. Ultimately, the naı¨ve person will end up cleaning on New Year’s Eve, the busiest day, while feeling great toil (C31).
Such behavior is self-destructive. It is undesirable from two perspectives. First, cleaning on the 31st was supposed to be less desirable than cleaning on the 29th, even as of the 29th.
Second, cleaning on the 31st considerably differs from the rational choice under exponential discounting. In the current setting, exponential discounters would Fig. 4.1 When to clean? Note:Dotted line Iindicates how the disutility (toil) of cleaning on the 30th is rated on the 29th.Dotted line IIindicates how the disutility (toil) of cleaning on the 31st is rated on the 29th and 30th, respectively. Naı¨ve people would clean on the 31st, while sophisticated people would finish cleaning on the 29th
evaluate the future disutility without discounting it by half.2Therefore, cleaning on the 29th—when the toil on the day of cleaning is the smallest—is the rational choice under exponential discounting; the naı¨ve choice of cleaning on the 31st is largely an act of procrastination, relative to that choice.
Another method for determining the desirability of the choice is to consider the choice one would have made on the 28th, the day before the first day of the cleaning period. Because the future toil is rated by systematically discounting it by half under the current setting, the self on the 28th would compare the toils of cleaning on the 29th, 30th, and 31st (A29, A30, and A31) by discounting them equally by half.
As a result, what he or she would choose is the 29th, as expected—the same choice under exponential discounting. The fact that the naı¨ve behavior is largely procras- tinated compared to the desirable behavior remains true.
In short, naı¨ve people tend to fall into the situation in which they end up cleaning on the day with the largest toil, even though they try to consider the whole future and act with the intention of minimizing the toil. This paradoxical situation can be seen in the process of choosing A30 and then B31 in Fig. 4.1by pursuing the options with the least amount of toil but ending up with C31. One of the reasons for such self-destructive decision-making lies in the fact that the decision-maker is unable to anticipate the change in his or her own impatience in the future, because he or she does not realize the precise implication of hyperbolic discounting.
A sophisticated decision-maker who is aware of the influence of hyperbolic discounting would make a choice so as to not procrastinate 1 day after another. As we saw above, once he or she delegates the tedious work to the self of the following day, that self will probably delegate the cleaning to the self of the day after that, and, ultimately, he or she will have no choice but to clean on busy New Year’s Eve.
The sophisticated person’s choice would be to put in some effort now and finish cleaning, without postponing it to the 30th.
As of the 29th, a consideration of when the decision maker can clean in order to minimize the toil would naturally make he or she prefer the 30th, when the toil is the smallest (A30). However, the sophisticated self on the 29th knows that if he or she were to do so, the self on the 30th will pass the baton to the self on the 31st.
Consequently, what the sophisticated self on the 29th must decide becomes
“whether to clean today (the 29th) or postpone it to the 31st” rather than “on which day of the 3 to clean.” Therefore, as shown by A29 and A31 in Fig.4.1, the sophisticated person’s choice would be to finish cleaning today rather than postpone it until later, as long as the toil of cleaning on the 29th is evaluated as being smaller than that of doing it on the 31st.
As explained, procrastination in cleaning is mitigated by taking into account in decision-making that the future self will suddenly become more impatient. People
2Under exponential discounting, the discount rate would be the same at any given point in time.
Because it is assumed that the discount rate for converting the value for the day after tomorrow to the value for tomorrow is 0 under the current setting, the rate used to discount the value for tomorrow to the value for today under exponential discounting must also be 0.
often find that the toil of finishing cleaning early is ultimately much smaller than the large toil of making a naı¨ve choice to work against time to clean on the deadline (New Year’s Eve). We can say that this is the benefit of being sophisticated.
The notion that being sophisticated bears the benefit of mitigating procrastina- tion generally holds true for certain problems such as on which calendar day to perform tedious work that will incur an immediate cost, as in the case of cleaning.
Of course, in many cases, the work produces some benefit; however, as Ted O’Donoghue and Matthew Rabin (1999) showed, the bottom line is basically the same if the benefit is realized only later. When to do the vacation homework, when to start a diet, when to renew the driver’s license, when to eat what you do not like—regardless of what decision-making is involved, a person who is overconfident about his or her future self will procrastinate, and the person who is appropriately pessimistic about the self can somewhat mitigate negative effects.