3.3 Inconsistent Choices
3.3.2 Patient Plan with Impatient Behavior
Under hyperbolic discounting and hence the resulting ambivalent predilection, people tend to behave in inconsistent ways. Hyperbolic discounters tend to behave impatiently for immediate gratification and at high discount rates even though they previously planned to behave patiently over that period at lower discount rates. Let us look at Fig.3.2, where a respondent who had been scheduled to receive USD 10 in 3 months will accept a 1-week delay with USD 0.91 interest; that person, however, would not wait the same length of delay for the same amount of money that he or she had been scheduled to receive today unless compensated by USD 1.01 or more. Similarly, a person can make a perfect plan to start a diet in 1 month.
However, as that 1 month passes, that person would find the diet too strict to carry out and would not be able to resist changing the plan to a much easier one.
The phenomenon is similar to what we experience in comparing height between a short and distant tree and a taller and more distant building. Figure3.6aillustrates this. When one looks at them in the distance, the tall building naturally looks taller than the tree. When looking at them from a closer distance, however, the tree looks taller than the building. The same can be seen in temporal evaluations in the case of
hyperbolic discounting, if the close short tree and the distant tall building are interpreted as an imminent small gratification and a longer delayed larger gratifi- cation, respectively.
Figure3.6billustrates the inconsistent evaluation under hyperbolic discounting, where the horizontal and vertical axes represent time and the current subjective value, respectively. RewardRSrepresents a short-run gratification (e.g., eating a sweet) that is obtained at an early point in time,ts; meanwhile,RLis a greater long- run gratification (e.g., good health) that is realized with a longer delay at timetL. The two discounted-value curves indicate how highly the two rewardsRSandRLare evaluated at each point in time. Due to the effect of discounting, the curves are Fig. 3.6 Time-inconsistent choices under hyperbolic discounting. (a) Sooner gratifications look more tempting. (b) Preference reversal
upward sloping; the rewards are more highly evaluated as the due dates draw closer.
The long-run reward is larger but more delayed than the short-run one. By taking the tradeoff into account, the decision-maker chooses the more preferable ofRSand RLat each point in time. As time passes from the initial point in time 0, the decision- maker moves rightward along the horizontal axis, and the present values of “cake”
and “health” go up along the discounted-value curves. While the time interval to—
and hence the delay of—reward realization is sufficiently long, the gratificationRL
of “health” is evaluated more highly than the gratificationRSof “cake.” However, after time t*, at which the two curves cross, the “cake” becomes preferable to
“health.” After all, the decision-maker would eat cake at the sacrifice of the greater long-run benefit of health, even though he or she planned to pursue the long-run gratification of health until timet*. That is, the preferences reverse over time. This phenomenon is called “preference reversal.”
With preference reversal, initially scheduled behavioral plans become inconsis- tent as time passes. Even when people make a wonderful but challenging plan to diet, they often give up on it as time passes and revise it to an easier one that accommodates more immediate but smaller gratifications. Similar examples include scrapping a smoking moderation plan before or on the way to carrying out the plan, binge shopping by postponing a great savings plan for retirement, changing a study plan in favor of various leisure activities, and so on. In short, preference reversal occurs whenever one is faced with a conflict between a plan to pursue a great and long-delayed gratification and the temptation of a more imme- diate but smaller gratification.
Note, however, that in the conflict between health (i.e., a great and long-delayed gratification) and cake (i.e., a sooner but smaller gratification), choosing “cake”
may not in itself be problematic. Some people make eating such a priority that they would rather die than go on a diet. Some other people would prefer developing cancer to quitting smoking. They just follow their own preferences. Insofar as their decision-making is rational, their choices may not be problematic. The true problem with hyperbolic discounting does not lie in the fact that hyperbolic discounters prefer an immediate but smaller gratification to a larger but delayed gratification;
rather, the problem lies in that they reverse their previous choice of a great long-run gratification in favor of a sooner but smaller gratification as time passes, and they are exposed to the temptation of an imminent gratification. Such inconsistency that occurs over time is called “time inconsistency.” Hyperbolic discounting leads us to make time-inconsistent, self-destructive decisions.
In standard economics, the problem of time-inconsistent decisions and resulting self-destructive behavior has been left unexamined because exponential discounting has been presupposed the culprit. In the case of exponential discounting, a person who prefers “health” to “cake” at one point in time consis- tently evaluates “health” more highly than “cake” before and after that time (see Fig.3.7a). Thus, inasmuch as external environments do not change, one will never change a plan to pursue “health” in favor of “cake” just before carrying it out. The same is true of those who prefer “cake” to “health” at a point in time (see Fig.3.7b).
The preference order, wherein “cake” is preferred to “health,” will remain
consistent over time. Hence, the plan to eat “cake,” scheduled at a point in time, will certainly be carried out as planned. This consistency property under exponential discounting corresponds to the fact that if one were to deposit a larger amount of money into accountAthan into another accountBat a point in time, the sum of the principal and interest will be definitely larger in accountAthan inBbefore and after that time so long as the interest rates are the same.
Fig. 3.7 Time-consistent choices under exponential discounting. (a) “Health” is consistently chosen. (b) “Cake” is consistently chosen