Does the Rational Theory of Addiction Suffer Explanatory Impotence? Andy Reagan



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Does the Rational Theory of Addiction Suffer Explanatory Impotence?

Andy Reagan

a_reagan@charter.net

0.0 Introduction

In this essay I examine the Rational Theory of Addiction proposed by Becker and Murphy in 1988. Their theory is an extension of rational choice theory to explain and predict aspects of addiction. Becker and Murphy conceive of addiction as a process of deciding to use (or abstaining from use) based on a rationally well-informed decision that consumption (or non-consumption of) the drug will maximize benefit over costs.

In section 1, I outline the Rational Theory of Addiction (RTA hereafter). First I outline the conceptual structure of the theory and then illustrate the way these concepts map onto the mathematical formulae utilized by the theorist to calculate/predict various aspects of the addict. In section 2, I propose formal diagnostic conditions for understanding what an addict is according to RTA1. In section 3 I pose the explanatory problem for RTA: the theory is not able to differentiate in kind between an addict that wills their use to continue and an addict that wills their use to stop (yet continues despite their will, Frankfurt 1971). I show this by proposing a thought experiment with two addicts that have identical2 sets yet differ insofar as one has a will to use and the other has a will to not use. RTA must treat these addicts as the same kind of thing according to the formal diagnostic conditions. Yet these addicts are not the same kind of thing (they would be treated quite differently in therapy). This is a serious problem for RTA because the inability for differentiation in kind means that it would be poorly suited in any therapeutic context.

1.0 Overview of the Rational Theory of Addiction

The fundamental idea of RTA is that addicts make choices in pursuing and using their addictive good with forward-looking, optimal3 behavior (Becker and Murphy, 1988). RTA theorists maintain that addictive behavior can always be explained by appealing to the rationality of the agent. RTA holds that an addict’s choice to consume a particular ‘addictive good’ is based on a rationally well-informed decision that using the drug will maximize benefit relative to the future costs likely to incur.

How did RTA theorists (Becker and Murphy in particular) arrive at this theoretical commitment? Before Becker and Murphy’s (BM hereafter) model, the predominant models of addiction were chemical dependence models based on animal studies and focusing on past consumption as the primary causal factor. Past consumption reinforced future consumption through the plasticity of brute dopaminergic mechanisms (which were thought to be the reinforced ‘reward’ pathways).4,5 While reinforcement in drug use behavior in the sense that the animal model of chemical dependence elucidates is a necessary aspect of addiction, the scope of the conclusions found within the animal model of addiction is limited when applied to complex rational agents such as ourselves.

The impetus behind RTA was the idea that humans can be modeled as having conceptually quite complex reasons behind their behavior in using addictive goods that accounts for both future planning and a stable preference base (as well as reinforcement effects from past consumption). RTA maintains that addicts are not blindly operating based on brute dopaminergic mechanisms, but rather produce behavior as a result of complex reasoning processes. In this sense, RTA is a departure from the no responsibility views of the positive reinforcement chemical dependence theories (or of Berridge and Robinson’s Incentive Salience theory). BM’s theory is a full responsibility theory of addiction because the addict’s choices are made from a completely rational basis (there is no recognition of manipulation from irrational impulses or cravings).

Gruber and Köszegi write, “[I]ndividuals recognize the addictive nature of choices that they make, but may still make them because the gains from the activity exceed any costs through future addiction” (my emphasis, 2001, 1262). Rational is used within a very particular context here. The RTA theorists do not mean rational, i.e. reasonable. Rational is used to particularly connote a type of ‘means-end’ reasoning that our actions can be analyzed as if they are obeying the simple mathematical formulae used to model them (introduced later in this section). Despite the ‘common-sense view’ that the behavior of addicts seems at times irrational and inexplicable, the basis for explanation in RTA of the behavior an addict produces can be found in the same substrate that would explain a choice a person makes on where to go out to eat tonight or what to do with a couple of spare hours on a Saturday afternoon.

Remember West’s cursory definition of addiction that I am using throughout this thesis: ‘impaired control over reward-seeking (drug-taking) behavior from which harm ensues.’ The impairment of control according to RTA is in the knowledge base of the addict and not in the deliberative reasoning processes. They may not know certain critical facts about the drug they are consuming (for instance, that it causes cancer) or they may not weight these facts (if they do know them) with high enough priority (they may not be aware of the outcomes of having something like cancer). The important point here is to note that ‘impaired control’ is consistent with rational choice theory. The impaired control is not explained in the same way as Berridge and Robinson in chapter 3 (or the philosophers in chapter 4), but it is still nonetheless impaired control.



Reinforcement, utility, tolerance, stock, time preference, and wealth constraints are the basic constituents of the RTA concept of addiction. Understanding these basic concepts is necessary in order to understand the mathematical model of RTA that utilizes these concepts.

Reinforcement is the effect that consumption has on the future utility (usefulness) of the addictive good (positive reinforcement increases utility and negative reinforcement decreases utility).

The utility of an addictive good for an individual is contingent on a relation between past consumption and present consumption (the type of relation that economists call an adjacent complementarity6). This idea operates behind what BM calls the basic idea of RTA: that “current consumption of [the addictive good] increases future consumption of [the addictive good]” (1988, 681). If current consumption increases future utility, then it is understandable why the consumer pursues using the addictive good in the future.

Calculating utility is derived from the relation between past and present use. The relation of adjacent complementarity between past and present consumption defines a necessary condition on whether a good is addictive or not.7

Tolerance is the aspect of consumption of a particular addictive good in which an increase in present consumption results in a decrease in future utility (i.e. more units of the addictive good must be consumed to maintain the same level of utility (BM, 1988, 682).

The concepts of reinforcement and tolerance are integral to each other and are what provide the physiological ‘tension’ to an addiction (if future use is simultaneously less satisfying (tolerance) and more useful (reinforcement) then it is obvious why an addict would escalate their use). Reinforcement and tolerance do not develop together at a linear rate. Reinforcement might develop quicker than tolerance, or vice versa.8,9

The utility (u) of the addictive good for an individual at a specific time (t) equals a function of actual consumption at t (Ct) and the stock (put another way this is the strength of the addiction) that the individual has built up in the addictive good up to t (St). The relation of Ct to St is the complementarity I mentioned previously. The following formula illustrates this:

ut = u(Ct, St) (1)10

The stock an individual possesses in an addictive good is a function of reinforcement and tolerance effects relative to the individual’s psychology (some individuals may be more resistant to the reinforcing effects of a drug than others). The level of stock that an individual has built up in the addictive good is derived from taking into account the rate of depreciation of the addictive good ()11 subtracted from one, multiplied by the stock of the addictive good the individual possesses at a time, t-1, plus the actual consumption at t-1. This is expressed as follows:

St = (1 - ) St-1 + ct-1 (2)

Also critical to an understanding of addiction is the individual’s time preference. Time preference is an individual’s predilection toward favoring, for instance, current utility versus future utility. BM write:

Our analysis implies the common view that present-oriented individuals are potentially more addicted to harmful goods than future-oriented individuals [see formula 3 below for clarification -AR]. The reason for this is that an increase in past consumption leads to a smaller rise in full price when the future is more heavily discounted (1988, 682).


Finding the lifetime utility (U) of an addictive good for an individual at a certain time period (T) is just a matter of summing the utility across specific times across T adjusted by the individual’s time preference (). This is done by taking the sum of 1 plus , raised by the difference of T minus t+1, multiplied by the utility of the addictive good that the individual possesses at a certain time, t.

UT = (1 + )T - (t+1)(u(Ct, St)) (3)


If wealth was unrestricted, then individuals with time preferences biased toward the present would quickly escalate into using their addictive good to the exclusion of all other activities.12 In the real world, however, addicts face constraints on their use. Wealth is one of the primary constraints. An addict under the RTA model balances current use with the level of wealth they possess, relative to plans for future use. Wealth is the constraint that BM chose to quantify in order to model the ‘real-world’ constraints on the addict.13

In this section I have provided a basic understanding of the concept/theoretical structure of RTA as well as the mathematical formulae underpinning RTA.14 In the following section I draw out the normative implications that RTA is committed to based on the mathematical structure of the theory.



2.0 Diagnostic Conditions of ‘Addict’

In order to formalize the diagnostic conditions for the term ‘addict’ according to RTA, I propose conceptualizing the diagnostic conditions in terms of a multi-variable set. The variables are the same as the aspects analyzed in the mathematical formulae above.

{N, TP, U, W, X, S}

N: the name of the addict

TP: time preference

U: lifetime utility

W: wealth constraints

X: x constraints (where x is undesignated)15

S: stock

In order to provide the diagnostic conditions for a particular addict one would need to calculate the individual variables involved in the set above. These formal diagnostic conditions will be useful in section 4 where I discuss the primary explanatory problem in RTA. The diagnostic conditions I have proposed here are basically a way to formalize the extent of the aspects of an addict that RTA focuses on within their theory. With the formal diagnostic conditions in mind I am now ready to pose the primary explanatory problem in RTA.



3.0 The Primary Explanatory Problem in RTA

The main difficulty RTA faces is explaining the phenomenon of relapse. An addict is only able to relapses after they have decided they should quit using (and have quit). Imagine a person struggling with a heroin addiction for years, constantly battling the temptation to increase their regular dose, always chasing some fading image of a blissful high they remember from the early years of their habit. After enough help, either from friends or family or therapist, or even just a steeled reserve of their own mind, this person quits their habit. Days of sobriety turn into weeks and months of sobriety. The person begins to get their life and body in shape and recovered. They regain self-respect and respect from their peers and stabilize themselves financially. Enough time passes and the cravings to use again that once were so strong, so overwhelming, begin to subside. What was initially a strong phenomenological push to use is now just a rather calm conceptual ‘tickle’ to use (easily ignored).

There are three primary possibilities for the person in this situation. I will focus on the last two possibilities (as they are the possibilities that entail relapse). First, the person could continue to abstain from heroin (keeping their will in place) and not use the rest of their life, leading a normal life apart from a few rather bizarre memories of being on a lot of heroin laying numb somewhere in some room in some house and some vague memories of the pain of intermittent withdrawals.

Second, this person could decide to drop the will to not use and form a will to use again (despite the memories of pain and suffering that the drug brought, the person desires so strongly the sense of drug euphoria that it seems ‘worth it’). Here we have a relapse as a ‘willing addict’ that Harry Frankfurt discussed in 1971.

Third, and perhaps most tragically, the person could maintain their will to not use (maybe in the face of unexpected, mounting cravings) and despite their best efforts, a momentary lapse in judgment could result in their using again (and then of course the past habitual routine use begins once again). Here we have a relapse with Frankfurt’s ‘unwilling addict.’

What does RTA have to say about relapse? And, more importantly, what does RTA have to say about the two possibilities of relapse the addict faces? A reason can be formulated utilizing the RTA framework to explain why the addict relapsed in either case. This would be in the language of RTA and would have to do with the stock in the drug (heroin) that the individual possesses (i.e. how long ago they used, upregulation of opioid receptors in the individual’s brain, lack of endogenous opioids from past abuse, etc), the time preference of the individual, etc. RTA is fine here at giving a reason for both types of users.

The problem RTA faces is making a distinction between the two types of relapse (i.e. relapse by a ‘willing addict’ and relapse by an ‘unwilling addict’). Since there is no way to make a modification to the theoretical structure based on differences in volitional (willful) states of the organism, the RTA framework is only able to recognize these addicts on par as equivalents (on pain of assumption their past histories of consumption and their present behavior is isomorphic).

The problem, more succinctly, is that there are irrational aspects that contributed to the third possible user’s relapse that were not present in the second possible user’s relapse. The irrationality of impulsive cravings is a strong deterrent to careful and calculated reasoning. Sometimes, despite having a good reason to not use and having made up one’s mind to not use, the person will end up (tragically) using in the face of strong cravings. Quite simply, they cannot help themselves. It is not surprising RTA has difficulties explaining this possibility, because RTA also has commitments that the choices a drug user makes are done with full responsibility (so the concept of irrational forces of craving acting on them is difficult if not impossible to parse apart conceptually within the RTA framework).

Recall the formal set of diagnostic conditions for the term ‘addict’ proposed in section 2:

{N, TP, U, W, X, S}

N: the name of the addict

TP: time preference

U: lifetime utility

W: wealth constraints

X: x constraints (where x is undesignated)16

S: stock


These are the aspects that RTA analyzed an addict along. That is to say, these are the relevant aspects that differentiate one kind of addict from another. Any aspect falling outside of the set above is not relevant for analysis according to the theoretical structure of RTA.

Now let us return to our two possibilities for relapse. I represent these two possibilities with two individuals (call them Sam and Rebecca). Sam has a will to use during his relapse (i.e. his use is in accord with his will) and Rebecca has a will to not use during her relapse (i.e. her use is not in accord with her will). According to this quick thought experiment, assume that Sam and Rebecca have identical drug use history and also have identical time preferences and wealth/social constraints. Fill in the variables for Sam and Rebecca and you will produce sets that are nearly identical (they differ only in the ‘name’ variable which designates the individual).

But, clearly the two types of possible addicts highlighted above (the ‘willing addict’ and the ‘unwilling addict’) are not the same kind of thing (or should not be construed as the same kind of thing). In fact, it would be reckless and negligent to construe these two possibilities in the same way in a therapeutic/clinical (or legal) setting. The first type of addict would not be expected to show much remorse upon using (since her actions are ex hypothesi in accord with her will) – until perhaps later when she has realized ‘what she has gotten herself into’ so to speak. The second type of addict with a will to not use would be expected to show great remorse and regret for her actions (after relapsing back into heroin use). A therapist would want to be ready to deal with the onset of depression and learned helplessness in this individual. If RTA is unable to account for this distinction as it stands, then it is not a sufficient theory for explaining addictive behavior within a therapeutic context.

4.0 Conclusion

RTA is a useful theory of addiction if the desideratum of the theory is restricted to prediction of consumption of addictive goods on a societal level (i.e. not relative to a singular individual but based on group trends and probabilities). The theory runs into problems, however, when the framework and mathematical principles are applied to an individual in an attempt to explain what is going on in the individual’s mind, specifically during and after the phenomenon of relapse (which is an aspect of addiction that is of primary interest for any therapeutic context).

The RTA theorist can maintain that the challenge of explanatory impotence misses the point of the theory. The theory just is a theory of group prediction for the consumption of addictive goods. My contention with this counter-objection is that despite (perhaps) originally being intended as simply a theory of prediction, RTA is cited in the literature as providing a possible basis for analysis of welfare and as an explanatory construct of what is actually happening in the individual’s mind. In this respect, this essay has been an attempt to block any future attempts at extending the framework of RTA into a therapeutic context.


Works Cited

Ainslie, G. (1992). Picoeconomics: The Strategic Interaction of Successive Motivational States



Within the Person. Cambridge. Cambridge UP.

Becker, Gary and Murphy, Kevin (1988). “A Theory of Rational Addiction.” J Political



Economy, 96 (4): 675-700.

Becker, Gary, and Grossman, Michael, and Murphy, Kevin (1990). “An Empirical Analysis of

Cigarette Addiction.” NBER Working Paper #3322.

Berridge, Kent and Robinson (2000). The psychology and neurobiology of addiction: an

incentive–sensitization view.” Addiction (2000) 95 (Supplement 2), S91–S117.

Cook, Phillip and Tauchen, George (1982). “The Effect of Liquor Taxes on Heavy Drinking.



Bell Journal of Economics. 13: 379-390.

Fehr, Ernst and Zych, Peter (1998). “Do Addicts Behave Rationally?” Scandinavian J



Econ, 100 (3): 643-662.

Ferguson, Brian (2000). “Interpreting the Rational Addiction Model.” Health Econ, 9: 587-598.

Frankfurt, Harry (1971). “Freedom of the Will and the Concept of a Person.” J of Phil, 68 (1): 5-

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Graham, George (2008). The Disordered Mind. MS.

Gruber, Jonathon and Köszegi, Botond (2001). “Is Addiction “Rational”? Theory and Evidence.”



Quarterly J Econ, 116 (4): 1261-1303.

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Wallace, R. Jay (2006). Normativity and the Will. Clarendon P: Oxford.




1 By ‘diagnostic conditions’ here I mean what are the conditions according to the RTA theory that make a person an addict. I will propose in section 2 a set of variables that represents each individual addict. These variables are the aspects of analysis from the RTA theory.

2 Identical apart from the first variable which is the addict’s name.

3 Optimal according to the ‘epistemic boundary’ of the individual (i.e. the boundary according to what the individual knows). Optimality here might be construed along two dimensions. Dimension 1: relative to the individual’s belief/desire set. Dimension 2: relative to a theoretical individual possessing a normatively non-deviant belief/desire set. It is the former upon which optimality in the decision-making process for using addictive goods is based (i.e. on the individual). As a sidenote, the latter dimension, I take it, is the dimension upon which a RTA theorist would base a definition of the pathology to addiction (i.e. the pathology rests in deviating in a certain way which results in harm from the normative basis of the non-deviant belief/desire set).

4 For an updated theory of these dopaminergic pathways see Berridge and Robinson (2000) The activation of dopaminergic pathways no longer correlates with reward, but rather correlates to the ‘wanting’ of the reward.

5 For a good survey of neurological theories of drug dependence and drug habituation, see Kauer and Malenka (2007).

6 Adjacent complementarity here means a relation between two temporally ordered events and the interdependence of the later event on the earlier event. In specific for addiction, consider two drug consumptions, happening apart from each other (maybe the two drug consumption experiences happen two nights in a row). The second drug consumption experience will be affected by the first drug consumption experience. The second night the person will be sensitized to the drug a bit more and of course tolerance will happen as well. This relation is known as an adjacent complementarity.

7 As should be evident in the next paragraph on tolerance, the necessary reinforcement condition is not a sufficient condition for a good being addictive.

8 Note that this formulation of the addiction concept applies equally well to beneficial or harmful addictions. BM distinguish beneficial and harmful addictions based upon whether or not the addiction has a positive or negative impact on total utility of the individual and/or earnings of the individual (1988, 684). The obvious candidate for a distinction between harmful and beneficial addictions (welfare of the individual) is not pursued by BM. According to Rogeberg, doing so would rule out their possibility for adopting the as-if stance (2003).

9 There is also the possibility for the phenomenon of reverse tolerance. It is possible that by taking a substance, it is not necessary to take an equipotent dose in the future to achieve the same intensity of drug effects. Rather, it is possible to take less in the future than was required in the past. This occurs in substances that cause long-term biochemical changes (either in enzymatic pathways or receptor upregulation or some similarly isomorphic effect).

10 This formula would be used in order to prove a good as addictive (if past consumption reinforced future consumption and tolerance effects were noted, then the good could be considered addictive).BM note that this point is necessary but far from sufficient to explain what addiction is (1988, 681). In addition, one would have to show the addictive good displays aspects of tolerance.

11 Becker and Murphy call this number the “exogenous rate of disappearance of the physical and mental effects of past consumption of C” (1988, 677). This rate will be specific to each individual, since the particular psychological traits of the individual will influence the rate that the stock of the good diminishes (i.e. some people will remain more addicted to a substance based on past consumption than other people).

12 This ‘unlimited-wealth-present-biased’ addict would be reminiscent of experiments of a mouse with unlimited access to cocaine. The mouse (and the theoretical addict) would quickly drop all other activities (including food and sleep) and pursue the consumption of their addictive good to the point of death.

13 There are other constraints that could be added: familial/societal constraints, time constraints, intelligence constraints, etc (for the purpose of the mathematical formulae below wealth is the only constraint of this type added). I take it that a complete RTA framework would have to incorporate these constraints to properly predict behavior. Therefore, a final formula is necessary in order to situate RTA in a ‘real-world’ context: a formula that delineates the interaction between wealth (and the other mentioned constraints) and rising utility the individual possesses toward the addictive good. For sake of room here I will not go into this complex formula. It is enough to note that the individual has a ‘real world’ constraint (wealth) on the amount of consumption of the addictive good they can exercise (and embedded here is a normative dimension of what one ought to do given their preferences for using compared to their overall wealth level and the necessity to use wealth to maintain basic life functions: eating, sleeping, etc). The individual is constantly balancing current use with a plan for future use.

14 This model is based on Becker and Murphy’s model (adapted from Fehr and Zych’s interpretation, 1998, 646).

15 X could designate, for instance, social constraints (familial or workplace constraints). The point is that wealth constraints are not the only type of constraints worth taking into account.

16 X could designate, for instance, social constraints (familial or workplace constraints). The point is that wealth constraints are not the only type of constraints worth taking into account.


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