how to affect effectively undesirable effects?

HOW TO AFFECT EFFECTIVELY UNDESIRABLE EFFECTS? by David Navon

University of Haifa, Israel

This paper presents an attempt to formulate universal, context-free normative rules for selecting remedies for undesirable events like diseases, malfunctions, conflicta etc. A formal model meant to compare remedies in view of a number of properties of the effect, the causes, and the remedies, is developed. Several conclusions that do not depend on assessments of costs and probabilities are derived. Two of them are incompatible with two myths of everyday thinking: (a) that preventing is better than curing, 6) that it is best to strike at the root of an evil.

KEY WORDS: causation, decision-making, intuition, prevention, remedy TYPE OF ARTICLE: mathematical model DIMENSIONS AND UNITS: none

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HOST OF DECISIONS is related t o A, ttempts to minimize the potency, prevalence or likelihood of some undesirable events. A prominent way to do this is through preventive measures. These include the control of something that is believed to affect an undesirable event. Even if the event is already happening a t decision time, i t s durability may depend on the future presence of its cause. Thus, controlling the cause could influence the occurrence of the event. For example, experts who try to combat diseases, psychological disorders, mechanical malfunctions, ecological nuisances, or undesirable economic states often take measures t o reduce the probability of their occurrence, recurrence, or endurance.

However, causes are often multiple, and a1 w ay s r esul t-th em selve s-by some other causes. I t is impractical, and in most cases even impossible, to t r ea t all of them. Accordingly, the decision-maker has t o choose a particular cause ta be treated, or to be given high priority in resource allocation. The decision is, of course, based on much technical, domain- specific knowledge (which is of no

concern here). But perhaps the rationale for the choice is common across domains. Experts presumably use their common sense, intuition, experience, or learned rules. They do not use any prescriptive theory or general guidelines for applying their technical knowledge in a principled manner.

In this paper I examine the feasibility of formulating such guidelines. The possible advantage of this activity is not so much in the possibility that the theory would conflict with common sense, but ra ther in the prospect of systematizing intuitive reasoning. This may prove useful when some psychological factors might lead intuition astray. Several examples are discussed below. The range of applications for such a theory is so broad, t ha t even a very small contribution t o the procedure of decision-making may turn out to have a considerable value.

TERMINOLOGY Let any domain of analysis be

conceived of as a network of nodes called events interrelated by arcs that stand for causal relationships (CRs for short). The CRs are binary relationships relating a cause t o (one of) its direct outcomes1.

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182 NAVON

They may be either facilitative (namely when the cause s t rengthens the outcome) or inhibitory (namely when the cause weakens the outcome). I t is not necessary to elaborate at this stage on the nature and meaning of causality (see Bunge, 1979, for a review): Let a causal relationship be simply assumed to exist whenever experts agree that i t does.

The elements of any given network are not necessarily atomic. That is, any CR or event may in turn subsume an indefinitely complex causal network. The elements being referred to may vary with the level of discourse and available knowledge. For example, the network representing immunological analysis may be quite different from the one representing epidemiological analysis.

A network may be augmented by factitious events. The kind of factitious events this paper is concerned with are remedies. A remedy is used to reduce the strength or likelihood of a particular outcome. There are two main types of remedy, antidotes and prophylactics. Antidotes are meant to counteract the effect of one or more causes by bringing to bear another cause, t h a t has the adversary effect on the same outcome. Prophylactics act by blocking or a t tenuat ing a certain CR, or by providing a remedy t o a cause. For example, an antidote for a headache caused to the driver of a car by inhaling smoke from a leaky exhaust system may be an aspirin tablet . The causal relationship between the smoke and the headache may be moderated by installing a suction fan in the car. And finally, the cause itself may be treated by repairing the exhaust system. The latter two are examples of prophylactics.

Events are characterized by three basic dimensions: longevity, which is the span of time the event takes place, or is effective; causal multifariousness, which is the num er of events that may possibly cause it &; and fertility, which is the number of events it may cause.

An event may be undesirable to an

individual or a group, namely it may be associated with subjective loss. To be comparable across events, let the loss be defined with respect to a given unit of time. Then, the compounded subjective loss of a n event is t h e loss it bears during its lifetime. In the simple case where subjective loss is stationary, compounded subjective loss equals longevity times subjective loss.

Other a t t r ibutes of events will be defined later. Let us turn now to causal relationships.

CRs are explicit relationships between events that within a given network are conceived of as directly causally related. However, causation is transitive, so that even events that are not close neighbors within the network may be implicitly causally related. Causal relationships between events are characterized by their immediacy, which is the inverse of the number of CRs, namely explicit arcs, in the path connecting the cause to the outcome. A CR is, of course, a causal relationship having the highest degree of immediacy.

CRs have the i r latency periods, namely the average t ime from the moment the cause is in effect t o the moment the outcome i s generated. Conceivably, some maturation time from the generation of a n event may be required before that event is potentially effective, namely ready t o generate its own outcomes. For simplicity, let this possibility be ignored for the time being. Thus, let it be assumed that if a cause is in effect at t ime t l , and the latency period of the corresponding CR is x, then the outcome will both be generated and be potentially effective at t l+ x. Also, it seems possible that a cause will not act t o generate the outcome until some other event has occurred. Again, for t he t ime being le t intr icate interactions between factors be ignored. In this analysis a cause is assumed to be always sufficient for generating the outcome. The latency of a causal relationship which comprises more than


one CR is, under the above assumptions, the sum of the latencies of t he component CRs.

Similarly, each remedy has its latency period, which is the average time from the moment the remedy is applied to the moment the generation of the undesirable event i s inhibited. That period must depend both on the latencies of the CRs involved and on the time necessary for the remedy to have i t s effect (namely, to establish or to block a CR).

A causal relationship i s also characterized by its potency, which is the probability that the cause starts the process which gives rise to the outcome within a given uni t of time, provided tha t the la t ter has not been already happening a t the time i t would have been generated by t h a t cause. The potency of an implicit causal relationship equals the product of the potencies of the CRs comprising the path connecting the cause to the outcome, given that none of the events along the path h a s been already happening at the time it was to be set off (cf. Costner & Leik, 1964; Einhorn & Hogarth, 1986). The compounded potency is the probability that the cause gives rise to the outcome during the lifetime of the cause. That is, if p i s t he potency, and n is the longevity of t he cause, then the compounded potency equals 1 - (1- p)", given that potency is stationary.

Within a given environment, and at a certain time to, an event has a certain incidence 1 ikelihood. Incidence likelihoods depend on incidence at time t-1, on the incidence likelihoods of the possible causes, and on the potencies of the causal relationships. A formal expression for incidence likelihoods is presented below.

Remedies vary on their effectiveness. The effectiveness may be measured by the amount of decrement in the incidence likelihood of the undesirable outcome due to the use of the remedy. Effectiveness of a prophylactic remedy

depends both on the remedy and on the causal relationship being t reated. Different remedies meant to act on the same CR may, of course, not be equally strong. Also, some CRs may be more robust than others, namely their potency may be harder t o reduce by equally strong remedies. Effectiveness of an antidote depends on the balance of potencies of the CR corresponding to the antidote itself and the other CRs leading to the undesirable event being treated.

Another characteristic of remedies is their cost. The cost of using remedies over a given period may be called the compounded cost. The compounded benefit resulting from using a remedy over a given period is the decrement in the loss associated with the undesirable outcome being treated. I t depends on the effectiveness of the remedy and the loss of the outcome.

Another characteristic of events is their drive force. Some events may not be just passive vehicles for transmitting causality. They may "have to" cause something. A prominent example is a psychological drive: I t may cause various courses of behavior; if some are precluded, others will be taken, with the constraint t h a t the drive h a s to be gratified. This may be represented as a kind of robustness that characterizes not a single CR but rather the class of all possible CRs emanat ing from a cause. The implication must be that the potencies of those CRs a r e context- dependent, since when the potency of one CR i s reduced, t he potency of another one is augmented. The only way to combat the effects of such a cause is to provide remedies for all its possible outcomes, or to look for a remedy for the cause itself. The latter is, for example, the logic of psychotherapies based on psychoanalytic theories (see, e.g., Freud, 1940f 1949).

If, indeed, some causes have nonzero drive forces, then events may be said to be characterized by sibling heritability, which i s t he probability t h a t t he


184 NAVON

incidence likelihood of the event manifests a trade-off with the incidence likelihoods of other undesirable events, so tha t when the former i s reduced, some of the latter increases.

The various characteristics of events, causal relationships, and remedies are listed for convenience in Table 1.

Table 1. A list of characterlstlcs of events, casual

relatlonshlps, and remedies

Events longevity casual multifariousness fertility loss cornpound loss incidence likelihood drive force sibling heritability

Casual Relatlonshlps immediacy latency potency compound potency robustness

Remedles strength effectiveness latency cost compound cost compound benefit

A NORMATIVE MODEL It is not evident what should be the

desiderata of a model for t rea t ing undesirable effects. What is the overall goal of such a model? Of course, it would be ideal to try to minimize losses across the whole system. However, t he difficulties are clear. First, the system may be open or at least very complex; side effects may interrelate systems that apparently are separate. Second, human

attempts to treat undesirable effects are never done as a part of a concerted effort to reduce all evil. The resources, human as well as economic, a re simply too scarce. Effects are usually treated one at a time. Accordingly, a realistic goal may be the following :

G1. Focus on one undesirable event, 0, and try to minimize losses due to it at the minimum cost.

Accomplishing th i s goal calls for considering both causes and possible remedies. Causes with high compounded potency are good candidates for being treated, bu t the availability of cost- effective remedies might modify the priorities. I t seems tha t a reasonable strategy is the following:

62. Choose a period of time T ; then maximize over T the compounded benefit in t e rms of 0 minus the compounded cost across all known remedies and all possible causes.

Yet, this may not be enough, since any intervention might produce other consequences that are due either to side effects of applying the remedies or to changes in the incidence likelihoods of other outcomes due t o sibling heritability. I t seems advisable to look for possible consequences like these, to the extent that they are foreseeable by the expert. This leads to the following strategy:

G3. Minimize, across all known remedies and all possible causes, increases in loss compounded over T due to undesirable effects other than 0. If the losses are comparable, this implies that those increases are to be deducted from the compound benefit considered for G2.

Yet, G143 are quite rudimentary. The next question i s whether it i s possible t o derive guidelines for decision tha t a re more specific. Those might

Behavioral Science, Vdume 37,1992

follow from possible contingencies between characterist ics of causes, outcomes, causal relationships, and remedies.

The f i rs t step is to specify formal expressions for the variables mentioned in G2and 63.

Let ~ O E denote the longevity of event E, and let 1 tAB denote the latency of the causal relationship relating event A to even B. Let IE,tO denote the incidence of event E at time to. Let CA B t

at t ime to , where in the case t h a t 1 tA B is positive, t O represents the time of gineration of A. Whenever the specific time in the latter term is substituted with an interval, i t indicates that the causing occurs at least once during that interval. The symbol Q denotes the union of all events. In the following, I assume stochastic independence among conjoined events.

Under the simplifying assumption t h a t incidence i s all-or-none, t he incidence likelihood of event E at t O equals

(l-prob @Q,E [t - 1 0 ~ t-11)) prob (CQ 9 , E Q) &>

denote the causing of event A by evknt #

prob (CQ,E,[Q-~OE, t-11) +

’

where prob(CQ,E,to equals

where ca. denotes a cause of E, and m denotes tde number of possible causes of E. Note that the probability of C is the potency of the correspon&$g’w Potencies of inhibitory CRs a r e represented as “negative” probabilities in this expression.

The use of a remedy modifies the system in a way t h a t affects the incidence likelihood of E. An antidote serves to add a cause ca* which has an inhibitory effect on E, or to increase its incidence likelihood I,,j,[tO-ltcaj ,E) I. A

prophylactic works by reducing the potency of a certain facilitative CR, namely the probability Ccaj8,tP for a certain cause can. or bv re ucine the

Y

incidence likelihooa‘ Icaj,&-lhaj,~) I, for a certain cause cao

The effectiveness of a remedy R for

prOb(Ig,b I no remedy used) prOb(1g I R used) (3)

The compounded cost of us ing a th l is

event E at time to equals

remedy R during a period [ t denoted by CCR [tl, th] and equa 11’ s

COR (th-tl+ 1) (4)

where COR denotes the cost of remedy R.

The compounded benefit from using remedy R for event E during a period Ftl, th] is denoted by CBR E [t 1 . It IS the reduction in ex’pkcte’$?oss resulting from tha t event, namely i t equals

SlE hc+’tR’E [prob(IE,t j 1 no remedy used)

where slE denotes the subjective loss associated with event E, and 1 tR E denotes the latency corresponding ’to remedy R and event E. Note that what is being summed by the C sign are the momentary effectiveness measures of the remedy over the period of its use .

The compounded benefits for all the events t h a t a r e seen to be possibly affected by the use of remedy R, including the undesirable event being remedied, may be summed, in the case t h a t the losses a r e comparable. Of course, some “benefits” may be negative. The sum is, thus, the change in overall loss due to the use of the remedy. The special s t a tus of t he event being remedied may be preserved by weighting i t more heavily, but i t is not clear that this has any advantage. The emphasis

j=l=ltR,E prOb(IE,t j I R used)] (5 )

Behavioral Science, Vdume 37,1992

186 NAVON

on that event automatically follows from the simple fact that one would probably never be able to take into account all side-effects.

Hence, t he net gain from using a remedy R during a period [ tl , %I equals

n

CBR,E ,[t 1,th 1 - ccR,[tl ,th 1 (6) i d

where n denotes the number of considered events.

Alternative remedies for the same undesirable event may be compared using the expression in (6). Thus, this can serve as a blueprint for a general method for choosing a way t o reduce losses of undesirable effects.

CONCLUSIONS A formal approach for comparing the

usefulness of various treatments for an undesirable event, subject t o some simplifying as sump ti on s , h a s been proposed here. The natural next step would be t o discuss the ecological validity of the simplifying assumptions, the loss in resulting generality, and the possibility of relaxing them. However, first we have to consider how practical the proposed algorithm is. In my view, the difficulties-methodological as well a s technical-in measuring t h e parameters a r e too grea t t o allow immediate applications. In passing, i t should be noted that in this respect the proposed model is not much different from some other normative models, such as expected utility theory (von Neumann & Morgenstern, 1947).

On the other hand, the analysis in the las t section may lead t o general conclusions t h a t do not depend on precise measurements of a l l t he parameters. In other words, although it may be hard to determine the most preferable option for remedying a given undesirable outcome, i t may be nonetheless possible t o infer t h e dependence of effectiveness on some parameters or parameter combination. This may show how a change in the

value of a certain parameter would affect the relative merit of the options.

PROPHYLACTICS VS. ANTIDOTES Folk wisdom has it that prevention is

better than the cure. I t is unclear to what extent experts actually follow this rule of thumb. Anyhow, let us now examine such accepted wisdom within the framework of the present analysis.

I t seems t h a t a tendency t o prefer preventive measures res t s on th ree implicit assumptions. One, antidotes cannot effectively reduce the undesirable event. Two, the event is not causally multifarious, namely it is caused by a few causes, o r even j u s t one. Three, prophylactics a re strong, in tha t the relevant CR can be effectively attenuated, or the cause itself can be effectively remedied.

The validity of the first assumption depends, of course, on the particular problem, and a generalization i s improper without an extensive survey.

The second assumption i s crucial. Even when a prophylactic is very effective in treating one cause, the utility of that treatment would be limited, if there a re other causes t h a t a r e not treated, as can be readily seen from expression (2). However, armchair exploration makes one wonder what is the basis for this assumption. Events that are caused by just one immediate cause appear to be rare. In the case that an event has a few causes, each one of the causes has to be treated for efficient prevention, and the cost of that may be high.

The third assumption is even more problematic. First, in the case that the prophylactic works by at tenuat ing a facilitative CR, it is yet to be established empirically t h a t such attenuation i s generally, or a t least on the average, more effective than introducing a n inhibitory CR. But more importantly, if prevention is attempted via remedying a cause, then it does not make sense that causes can be remedied more effectively


causes can be remedied more effectively than outcomes: If the remedy for the cause is a cause antidote, then why should it be more effective in principle than the antidote for the outcome? If the remedy for the cause is a cause prophylactic, then it might be more effective if indeed prophylactics were much more effective than antidotes, but that is exactly the issue examined here.

Another problem with prophylactics is that their contribution to the overall uti l i ty may be offset by sibling heritability. If a CR is attenuated and the corresponding cause has some drive force, then the potencies of other CRs emanat ing from t h a t cause may increase. To the extent t h a t t he outcomes are undesirable, that may be harmful on the whole. I t is reasonable t o assume, tha t the cause would not respond in the same manner t o the administration of an antidote, since no CR emanating from it is being affected by that.

Perhaps t h e reason, other t han wishful thinking, t ha t prevention is often preferred, is that i t is associated with cases in which foresight or caution manage to avoid any damages due t o the unwelcome event. Curing is, in contrast, associated with realizing the evil af ter i t h a s already s tar ted. However, this is not necessarily true. An undesirable event may be anticipated, and an antidote may be supplied as it starts. On the other hand, prophylactics a re often used not for forestalling an event before it starts but rather for minimizing its recurrence or endurance after it already has occurred or h a s s tar ted. Thus, whenever a deliberate choice is made at a given point in time, prophylactics do not have any a priori advantage over antidotes in terms of lag with respect to the onset of the event being remedied.

IMMEDIACY OF THE TREATED CAUSE Another prevalent stance is that it is

best t o t r e a t t he ul t imate cause if

possible. The corollary appears to be that the more remote the cause being treated, the better. Let us examine whether this is warranted in light of what has been said above.

The potency of a causal relationship is defined here as the product of the potencies of the CRs comprising the path connecting the cause t o the outcome. Since potencies are fractions, it follows quite naturally that the potency of an immediate cause cannot be smaller, and is in many cases larger, than the potency of a remote cause. What is, then, the basis for the belief that i t is bet ter to treat a remote cause?

A remote cause might be worth treating in one particular case-when it is orphan, namely, when all its possible causes have ceased to exist. This is in contrast t o the typical case in which t reatment is a continual enterprise, since the causes are regenerated. Thus, the compounded c o s t of t rea t ing a n orphan cause is relatively small.

In the extreme case t h a t each CR along the path has a potency of unity, the potencies of the causal relationships corresponding to all the causes along the path, including the most remote one, are unity. Since the combination rule for potencies is multiplicative, any small potency depreciates considerably from the potency associated with remote causes.

In another extreme case tha t each event along the path has only one cause, the incidence likelihood of each event is affected considerably by treating any of the causes regardless of its immediacy. However, when events a r e causally multifarious, the effect of treating a cause on the incidence likelihood of an event is directly re la ted t o the immediacy of the cause.

I t seems safe to estimate, t h a t i t would be quite diffkult t o find orphan remote causes the causal relationships that have potencies close to unity and comprise minimally multifarious events along the path. Hence, in the more usual


188 NAVON

cases, i t seems advisable t o focus on immediate causes.

Another case in which it makes sense to treat a remote cause is when it has a high-drive force. In such a case, attempts to treat should be oriented not towards a single undesirable event but ra ther , more than ever , towards a configuration of events that has similar causes. If an event can cause a range of undesirable outcomes, and attenuating one causal relationship emanating from i t would resu l t in increasing the incidence likelihood of alternative ones, then i t seems prudent t o remedy the event itself. Thus, it is reasonable for a theory that regards a set of phenomena as compensatory symptoms of a single “deep” state to prescribe treating that s ta te . In contrast , a theory t h a t construes the occurrence of the same phenomena as totally independent may justifiably advocate that any of these phenomena be t rea ted without necessarily treating its cause.

THE TWO TYPES OF PROPHYLACTIC

One might contend that when people advocate treating remote, rather than immediate causes, they really mean that preventing should be done by remedying a cause rather than by attenuating the CR emanating from it. Is there a basis for such a generalization?

What is required in order that a cause actually acts to generate an outcome is the conjunction of its own incidence and the materialization of its potential effect, as is represented in Expression (2). The probability of this conjunction is the product of two probabilities, which are the corresponding incidence likelihood (Icaj ,[to-ltcaj,E I) and potency (cca ,E,tO)* Hence, manipulations t hat cut potency o r incidence likelihood by the same proportions must be equally effective as remedies.

Thus, the claim that attenuating a CR is be t te r than remedying the cause would be true, if manipulations meant to

reduce potencies were on the average more successful than manipulations meant to reduce incidence likelihoods. How plausible is this condition? The latter manipulations may be done in either of two ways. One is by providing an antidote for the cause. I t cannot be determined tha t as a rule, o r on the average, that would affect the incidence likelihood of the cause less than any manner of reducing the potency of the CR would affect t h a t potency. The second way of manipulat ing the incidence likelihood of the cause is by using a cause prophylactic. Since the cause may in itself be causally multifarious, a cause prophylactic cannot be superior, and is often inferior, to a cause antidote (see arguments in the section “prophylactics vs. antidotes”). Hence, by transitivity, that way probably does not help to reduce the incidence likelihood of the cause more than any manner of reducing the potency of the CR does.

Thus, there is no a priori advantage to remedying a cause over attenuating a CR. If anything, of the two types of prophylactic, the former seems more risky.

HOW ABOUT OTHER PARAMETERS?

Other implications from the analysis seem more straightforward, but i t is useful to mention them briefly.

The incidence likelihood of a cause affects directly the incidence likelihood of t h e outcome, as can be seen in Expression (2). Thus, if the incidence likelihoods of all the immediate causes of an undesirable event are known, then other things being equal, the one with the highest likelihood should be treated. As can be seen in Expression ( l ) , the incidence likelihood of an event depends in a direct manner on its longevity, on i t s causal multifariousness, on the potencies of the CRs generating it, and on the incidence likelihoods of i t s causes. Hence, all of these parameters

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AFFECTING UNDE~IRABLE EFFECTS 189

causes should be considered for the decision.

As can be seen in expression (2), the potency of a CR also has a direct effect on the incidence likelihood of an outcome. Thus, other things being equal, causal relationships having higher potencies should be treated.

It is obviously better to focus on CRs that are less robust, since a high potency is indeed a good target for treatment only in case i t can be effectively curtailed.

The drive force of causes is relevant for the following reason: If a CR emanating from a forceful cause was attenuated, a t least part of the gain would be offset by the increase in potencies of CRs leading t o other undesirable events. This is rendered inadmissible by G3. Hence, other causes would rather be treated. The alternative is to remedy the forceful cause itself.

The loss associated with the cause itself may sometimes be pertinent for the decision. If several causes are equivalent in terms of all other considerations, it may obviously be advisable to treat the one with the highest compounded loss. However, it seems that most often the loss associated with an undesirable outcome that is worth being treated is much greater than any of the losses associated with i ts causes; hence the choice will probably be determined by other parameters.

The latency of a causal relationship may become relevant only when immediate treatment is called for and there are no antidotes. If the short-term compounded loss is deemed critical, a small and quick reduction in it may be preferred to a larger but slower measure.

A SHORT SUMMARY In sum, grave doubts are cast on two

possible myths in everyday thinking. The myths are (a) that preventing is better than curing, and (b) that it is best

to strike at the root of an evil. It is not clear how widespread those beliefs are. But regardless of whether or not they are prevalent, it is important to lay the theoretical ground for evaluating them. This in itself is a good reason for formulating the theory presented here. Providing a possible framework for evaluating options for combatting an undesirable effect is another one.

FOOTNOTES

1. The word “effect” is reserved in this paper (except for the title) for the causal relationship itself. (e.g., one might say that a cause C has a strong effect on an outcome 0.)

2. Causal multifariousness may assume, of course, any positive integer as a value, but interestingly it may even assume the value 0 . At some moment, an event may exist while all of i t s possible causes have ceased to exist (of course, this would occur much less of ten with generic events, like having flat tires, than with particular events, like the flat tire Mr. X had yesterday). Such an event may be called an orphan event.

REFERENCES Bunge, M. Causality and modern science.

New York:Dover, 1979. Costner, H.L., & Leik, R.K.Deductions

from “axiomatic theory”. American Sociological Review, 29, 1964, 819-835.

Einhorn, H.J., & Hogarth, R.M. Judging probable cause. Psychological Bulletin, 99, 1986,3-19.

Freud, S. An outline of psychoanalysis (translated by J. Strachey), New York: W.W. Norton, 1949. (Original work published 1940)

(Manuscript received April 18, 1991)


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