Hyperbolic Discounting, Willpower

Theories of addiction have traditionally not analyzed very carefully the basic problems of choice that addicted people are faced with. Addicts are conceived as consumption robots, helpless victims of their environment or their vices. Under these circumstances, addiction is not much more than a label, a ghost in the machine, called upon to explain norm-violating, self-destructive consumption behavior. Unfortunately, the proof of addiction is the very same behavior, and the explanation therefore becomes circular. A proper understanding of addiction requires a theory of how people conceive their world, how they evaluate different options, and how they make their choices. Among other things, we need to understand the role of ambivalence and inconsistencies in their deliberations. In this chapter, I discuss and compare two attempts in this direction. 

In standard rational choice theory, actors are assumed to have consistent preferences and to act according to their own better judgment. In particular, rational actors are assumed to be dynamically consistent planners If actors prefer an early, small reward A to a later, bigger reward at a certain point in time, they will do so at all times. Hence, rational actors do not suffer from weakness of the will, and they never give in to temptations that they later regret. Addictions are often mentioned as an example of behavior that violates rationality Many addicts seem to act contrary to their own better judgment, as they claim that they would like to stop their self-destructive consumption behavior, but still they continue consuming the substance they are addicted to. 

The two latter difficulties can be resolved by relaxing the assumption of stable preferences and full information about future mental states. In fact, if we allow actors future orientation (that is, their discount function) to fluctuate over time, actors may move in and out of the high consumption mode (Skog 1997). However, according to George Ainslie (1992), the basic assumption of dynamic consistency in Becker and Murphy s theory is at variance with the empirical evidence. Ainslie claims that people 

Note For ease of comparison, a mirror image of the negative consequence is also shown broken lines). 

George Ainslie s theory of addiction (Ainslie 1999) is centered on this dynamic inconsistency and its consequences. The temporary preference shift induced by hyperbolic discounting gives rise to regrets. As 

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The aim of this chapter is, therefore, to analyze from an Ainsliean point of view a consumption good with the same properties that Becker and Murphy analyze, in order to see how a hyperbolic discounter with willpower will tend to act. 1 continue as follows In the next section, I discuss Ainslie s full theory of discounting, that is, hyperbolic discounting plus willpower. In the following section, 1 outline Becker and Murphy s consumption problem and analyze the Ainsliean discounter s choice in this type of situation. In the next section, the inconsistencies in the Ainsliean discounter s plans are analyzed, and in the last section I make a comparison between the two theories of addiction. 

Ainslie s theory of discounting can be conceived as a two-tier theory, consisting of hard-wired hyperbolic discount curves and a cognitive element, namely willpower, in the form of personal rules. 

In fact, in can be demonstrated that, with hyperbolic discounting, any temptation may in principle be resisted, provided that enough future events are taken into consideration (for a proof, see the appendix to this chapter). Hence, even if the instantaneous value of A is very much bigger than the discounted value of B, the temptation can be resisted if actors have formed a belief to the effect that their current choice is a precedent for numerous and very remote future events. In principle, willpower and personal rules could therefore solve all consumption problems of this type. The actual outcome would depend on actors cognitive horizon, as measured by N. Ainslie does not offer a systematic theory of intraindividual and interindividual variations in the parameter N. I will not try to develop such a theory either. I instead focus on the consequences of variations in N. 

We now consider hyperbolic discounters with willpower and personal rules to see how they will behave when they are faced with the same choice problem. Given their consumption history, we let the actors evaluate the two alternative consumption careers consuming little now and in the future and consuming much now and in the future. Actors have a fixed time horizon N, so they will consider the present and the next (N-1) consecutive consumption events. The welfare levels associated with the different options are assumed to be the ones given in figure 5.2. We assume that the time intervals between consumption events are one time unit. We start by considering consumers immediately before the first choice has to be made, that is, at t=0. 

In effect, hyperbolic discounters with only a little amount of willpower (N < 11) will not be able to quit their addiction, and if they have been abstaining for a while, they will quickly relapse to addiction. Hence, unless they are able to cultivate their willpower, they will continue their self-destructive lifestyle. These people are consonant addicts (Skog 1999) They are unable to quit and really do not wish to quit, as they consider life without the addictive substance to be even worse than life as a heavy consumer. 

Consequently, when faced with a consumption choice of the same type as Becker and Murphy s rational consumer, hyperbolic discounters with willpower will act in a similar way. In particular, the asymmetry between stopping and starting, which is the defining characteristic of Becker and Murphy s rational addict, is reproduced in the hyperbolic case. 

This is not true for hyperbolic discounters. Generally, they cannot be expected to come up with the same conclusion at all times. Although hyperbolic discounters with willpower and personal rules are less dynamically inconsistent than discounters without personal rules, they are not entirely consistent, and we cannot expect that their evaluation in advance is identical to their evaluation at the time of choice. In the preceding section we calculated their evaluations at the time of choice. Now we analyze their evaluations some time in advance. 

This implies that dissonant addicts with hyperbolic discounting plus willpower may go to bed with the firm intention of not drinking tomorrow nevertheless, they will end up drinking again the next day. Even consonant addicts may occasionally experience doubts as to whether they really wish to go on with their heavy-consumption lifestyle. Thus, the distinction between consonant and dissonant addicts is not as clear-cut within the Ainsliean framework as within the dynamically consistent framework of the rational consumer. 

This function, which includes the cognitive element of willpower, represents Ainslie s complete discount function. It discounts the future less than the original hyperbolic function (Skog 1997) and is also less deeply bowed. 

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