The Self — The Choice, Plate vii

The person who sets the alarm at night knows something about the person who will silence it in the morning. He puts it beyond reach, asks another to wake him, arranges a consequence for sleeping through. Both decisions belong to him: the determination to rise and the determination, when rising becomes immediate, to remain in bed. The difficulty begins when the evening’s plan already allows for the morning’s tiredness, and the morning brings no news that explains the reversal. The same future occasion has been judged differently as it approaches. Schelling describes this conflict through the image of alternating selves, each capable of wanting something that another version of the person will resist. The image need imply no separate personalities. It puts a question to the single chooser of the earlier plates: which of his choices shall be taken to reveal what serves him?¹

1. Thomas Schelling, Ethics, Law, and the Exercise of Self-Command, Tanner Lectures delivered in 1982, opening discussion following the Ahab example. He distinguishes conflicting preferences across occasions from ordinary changes of appetite within an integrated plan. The opening develops his alarm-clock illustration; it is not an experimental observation.

Impatience by itself need not divide the chooser. Someone who consistently discounts each additional period by the same proportion can prefer a smaller benefit sooner while remaining faithful to every comparison between future dates. With the outcomes, information and underlying tastes held fixed, the passage of a period removes a common discount factor from both alternatives; their order survives. A reversal requires something more. In Laibson’s model, the present receives a special weight against everything still to come. Benefits one and two periods away can be compared patiently, because both stand beyond the present’s boundary. When the nearer benefit reaches that boundary, its position changes. This is a particular account of time-inconsistency, not a diagnosis to be inferred whenever someone spends rather than saves. A person short of food or cash may have compelling reasons to place a high value on what arrives today.²

2. David Laibson, Golden Eggs and Hyperbolic Discounting (1997), §II, pp. 449–451. The quasi-hyperbolic weights are 1, βδ, βδ², …, with an extra present–future gap when β < 1. Exponential discounting is the case β = 1. Consistency here concerns the same outcomes under unchanged information and tastes.

An invented example makes the reversal exact. At date zero, the chooser considers ten units of satisfaction at date one against twelve at date two. Suppose each period carries a factor of nine tenths, while every benefit still in the future is also multiplied by one half. The ten is then worth four and a half; the twelve, four and eighty-six hundredths. He plans to wait for twelve. At date one, the ten is available immediately and receives its full weight, while the twelve remains ahead and is worth only five and four tenths. He now takes ten. Nothing has happened to the rewards, their certainty or the interval between them. The earlier reward has crossed into the present. These are stipulated units of satisfaction, not sums of money or an estimate of anybody’s patience; the example isolates what the model assumes.³

3. Authored calculation using Laibson’s discount form, not his calibration. At date zero: 0.5 × 0.9 × 10 = 4.5 and 0.5 × 0.9² × 12 = 4.86. At date one: 10 > 0.5 × 0.9 × 12 = 5.4. Removing the extra half-weight gives 9 < 9.72 initially and 10 < 10.8 later: no reversal.

⁂

A chooser who anticipates the reversal has a reason to bind his later choice. He can arrange that the ten will be unavailable when it becomes tempting, so that the twelve survives to be received. This is the logic of the mast in the earlier Impatience: the constraint does work precisely because a later desire would otherwise undo the plan. Laibson gives the mechanism an economic form through an illiquid asset whose proceeds take a period to become available. Money placed there cannot all be spent at once by the next self. The protection is incomplete, and the later self makes plans of his own. The model therefore treats the person as a succession of strategic decision-makers, each anticipating how the others will act. It can explain why somebody chooses a narrower future menu without assuming that he has forgotten the value of having options.

The value of commitment depends on what the restriction protects and what it prevents. An inaccessible balance can preserve a planned saving and also be unavailable when a need arises that the plan did not foresee. Laibson’s welfare analysis expressly leaves room for such a qualification: the gain from access and the loss of commitment depend on the model’s parameters, while emergencies omitted from its deterministic setting can make liquidity more valuable. Even within the model, greater access need not make the current self worse off. Nor does choosing an illiquid asset establish that self-command was its purpose; returns, security and other features may matter. The relevant comparison is between specified arrangements, with their costs and escape routes, evaluated from a specified standpoint. A willingness to impose a restriction is evidence of one self’s preference for it. The benefits to the person across time remain to be argued.⁴

4. Laibson (1997), §II, pp. 447–451, and §IV.F, pp. 465–468. His illiquid asset has a one-period delay; welfare in §IV.F is evaluated from the current self’s perspective. The analysis identifies parameter-dependent gains and losses from greater liquidity and explicitly notes the omitted value of meeting emergencies.

Calling the earlier self farsighted does not by itself establish his authority. He may indeed have considered a larger part of the life; he may also have made an ill-judged promise that the later person has good reason to escape. Schelling presses on the observer’s tendency to take the side of the planner, the person awake at a desk writing about the person who wants to sleep. A later expression of gratitude can support that judgment, but it cannot supply a universal rule for every conflict. Both preferences can belong authentically to the person, and their incompatibility leaves an evaluative question. One can give weight to deliberate commitments, repeated endorsement or consequences across a longer horizon. Each supplies a reason to examine. None is secretly contained in the bare fact that a choice occurred, or in the mathematical prediction that a reversal will occur.⁵

5. Schelling, Self-Command, the discussions of the observer’s allegiance, the individual as a collectivity and the authenticity of alternating selves. These units examine the grounds for taking sides in conflicts among successive preferences, including the possibility that both selves are authentic. They do not establish an automatic priority for the earlier plan.

Whose choice counts therefore depends on what the count is meant to decide. To predict the next action, the preference of the person who then controls it matters. To assess a life, or justify a device that binds its future, the assessment must say why that moment’s preference should govern the others. The morning does not win merely by arriving last, and the night does not win merely by having planned. Their disagreement exposes a missing premise in the equation between choosing and being served: a person’s welfare needs a standard capable of addressing conflict within the person. Commitment can help him live by such a standard; it cannot choose the standard for him. The next plate’s menu is accordingly more complicated than a list of opportunities. Some of its entries may be promises about which opportunities a later self will be allowed to have.