Willpower

When I was so sick that I was crawling, there wasn t anyone to help me. Mold was growing in my dirty dishes from sitting in the sink so long. I was desperate to find a way to gather back some health, and my willpower from running sustained me as I went from doctor to doctor. 

Are abstentions correctly seen as precedents Does p have a rational foundation It seems clear that if we do not believe p, we will as a matter of fact drink at six o clock on all days, even if we have a stable preference for never drink > always drink through time and believe that we will drink tomorrow if we drink today. This follows from the payoff structure. Without a belief in p, we will implement the strategy always drink, although we have a stable preference for never drink > always drink. We can see our drinking as giving in to temptation but being able to act upon the stable preference never drink > always drink as having willpower. 

Addicts are not people without willpower or people driven to act with out making choices. The clinical picture is of people who too often make choices that, in the long term, reduce their long-term utility and their total well being and, in addition, often burden both their families and society. These choices are suboptimal to long-term utility and, therefore, in the meaning of rational choice theory, irrational. The core problem is one of impeded rationality, of insufficient choice capacity to integrate present and future consideration in a sufficiently consistent pattern. 

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. 

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. 

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. 

People with willpower at an intermediate level (11 < N < 31) will ordinarily not be able to get out of their spree with the aid of sheer willpower. When they are in the high-consumption mode, the way out is too troublesome. However, if someone or something has helped them to stop consuming excessively for a while, they would not immediately relapse. In the sober mode, life feels better without the addictive drug or with only normal, moderate amounts. 

These people with intermediate willpower are dissonant addicts. When they are in the high-consumption mode, they prefer continued high consumption, but still they know that life would have been better (according to their own utility calculus) if they had been in the low-consumption mode. They can honestly say that they would not relapse if they somehow managed to get out of the high-consumption mode. 

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. 

Consider people with willpower N = 10. One time unit before they have to make the choice (at f = 1), they evaluate the two consumption alternatives as follows If they have consumed little in the past, consuming little on the imminent event is valued at 161.6, while consuming much on the imminent event is valued at 156,4 therefore, they will opt for little. If they have consumed much in the past, consuming little in the imminent event is valued at 141.6, while consuming much in the imminent event is valued at 141.4, so even in this case they will opt for little. 

It is easily verified that, for people with willpower N -10, the same ordering applies at time distances greater than one time unit. Hence, well in advance of the actual choice, these people will plan to go for the low-consumption alternative in the future. 

At the time the actual choice has to be made (at t = 0), actors with willpower N = 10 will prefer to consume much, whatever their consumption history has been (see table 5.1). Therefore, at this stage, even people with a low-consumption history will have changed their mind, as they now value future low consumption at 234.3 and future high consumption at 235.0. 

Figure 5.3 Preference Structures for People with Different Horizons (Willpower) at Different Times Before the Time of Choke...

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. 

We observe that the crossover, or instability, will occur for most consumers with a weak or moderate willpower. Only strong-willed indi-... 

The main difference between Becker and Murphy s standard rational choice theory and Ainslie s picoeconomic theory is dynamic consistency versus inconsistency. The congenital inconsistency that forms the starting in Ainslie s theory allows Ainsliean addicts to struggle to get out of their addiction, and relapse may be explained within the Ainsliean framework by erosion of personal rules and willpower. Hence, an addiction theory based on Ainslie s theory of motivation can handle the phenomena that are left unexplained by Becker and Murphy s theory of addiction. 

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