One of the key constituencies of causal reasoning is the effect of action.  Action is important, both because it concerns behavior in the actual, physical world and because it is involved when we think about other worlds as we do when we fantasize, imagine, or predict.  Thinking about an alternative world involves acting on our model of the world to change it in whatever way our fantasy or image dictates.  More fundamentally, causal relations are by definition those relations that support action in the form of intervention.  This is the upshot of some compelling recent philosophy (Woodward, 2003, offers a comprehensive review).  Very roughly, A is a cause of B if intervening on A would change the value of B, if other things were held constant in the right way.  The gravitational pull of the Earth causes the moon’s orbit in the sense that if the gravitational pull could somehow be changed, without changing other things, the moon’s orbit would change too.

The logic of intervention is unique and does not fall naturally out of conventional propositional logics, even probabilistic logics.  Consider an event or property whose value is normally determined by some set of causes.  For instance, the height of a blade of grass is normally determined by the amount of sunshine and rainfall, the quality of its soil, etc.  Normally, knowing the value of a variable is diagnostic of the value of its causes.  If the blade is tall, that suggests more rainfall and richer soil conditions than if the blade is short.  But this diagnostic relation fails under intervention.  If someone intervenes on the event or property by setting it to some value, the value reveals nothing about its normal causes.  If I cut the blade of grass so that it’s very short, you should not infer from its height that there’s been little rainfall.  I call this an undoing effect because the causal linkage to a variable being intervened on from its normal causes must be cut for the sake of inference.  A formal discussion of inference from intervention is offered by Pearl(2000) who introduces the DO operator as a mathematical tool for representing intervention.  Spirtes, Glymour, and Schienes (1993) present a more general analysis of intervention.

Both common sense and psychological data suggest that people are sensitive to the logic of intervention.  But other data demonstrate that people use their own actions as signals, often as signals to themselves about their own nature and dispositions, signals that violate the undoing prescription of interventional logic.  My purpose here is to discuss where people’s reasoning about intervention goes right and where it goes wrong in hopes of revealing something about the nature of human causal reasoning.

The psycho-logic of intervention

Evidence that people are appropriately sensitive to the logic of intervention when reasoning comes from experiments in which people are given a causal structure and then asked to reason about the causes of an effect that has been intervened on.  For instance, in an intervention condition, Sloman and Lagnado (2005) gave people the following causal scenario:

All rocketships have two components, A and B.  Movement of component A causes component B to move.  In other words, if A, then B.  Both are moving.

And then asked them the following questions:

i. Suppose Component A were prevented from moving, would Component B still be moving?

ii. Suppose Component B were prevented from moving, would Component A still be moving?

The simple causal model underlying this scenario looks like this:

            Movement of                           Movement of

            Component A  -----------------> Component B

and both components are moving. 

To answer question (i), one should mentally intervene on Component A by imagining its movement stopped and note that Component B would then be stopped.  The vast majority of Sloman and Lagnado’s (2005) participants followed this logic and concluded that “no, Component B would not be moving.”

But question (ii) is different.  Here, one must imagine the intervention downstream, on Component B.  This requires simplifying the causal model by removing any links into the prevented component because the reasoner is setting its value, its normal causes are not.  This has no effect when A is prevented because A has no normal causes.  But when B is prevented, we must disconnect it from A:

            Movement of                           Movement of

             Component A                         Component B

As there is no longer any linkage between the components, it is apparent that Component A’s movement is now independent of B’s movement and therefore the logic of intervention predicts the undoing effect, that component B’s lack of movement is not diagnostic of A.  In other words, people should infer that A would still be moving and respond “yes” to the second question.  Again, this is what the vast majority of people said.

In contrast, when Components A or B are observed to not be moving, as opposed to being intervened on, lack of movement in B does suggest that A is not moving just as A’s lack of movement suggests that B is not moving.  In other words, when asked what to expect after observing no movement:

i. Suppose Component A were observed to not be moving, would Component B still be moving?

ii. Suppose Component B were observed to not be moving, would Component A still be moving?

participants should respond “no” to both questions, and that’s just what the great majority did.  Corroborating data can be found in Waldmann and Hagmayer (2005).

People also show sensitivity to the logic of intervention when making decisions (Hagmayer & Sloman, 2005).  Imagine an action that has some desirable causal consequence (e.g., doing the chores improves health by providing exercise).  This knowledge should and does increase people’s willingness to do the chores.  But you might be told instead that the action and consequence are correlated by virtue of a common cause with no direct causal relation between them (e.g., doing the chores and good health are correlated because both are consequences of a caring attitude found in only some people).  In this case, doing the chores does not increase the chance of good health.  In fact, the choice to do the chores is an intervention that renders the chores independent of one’s degree of health.  So this causal model should not affect one’s willingness to do the chores and, in line with the logic of intervention, it had little influence on Hagmayer and Sloman’s participants.  A general review of studies demonstrating sensitivity to the logic of intervention can be found in Hagmayer et al. (in press). 

There is also strong evidence that intervention facilitates learning relative to mere observation both in children and adults (for a review, see Lagnado et al., in press).  The advantage of intervention in learning may be in part a result of implicit temporal cuing or attentional cues rather than the model-changing informational value of intervention due to undoing (Lagnado & Sloman, 2004).

Failures of interventional logic: Signaling

The undoing effect is not consistently observed in human inference.  Violations are seen in the form of instances of signaling (Bodner & Prelec, 2002).  Quattrone and Tversky (1984) asked a group of students to hold their arms in very cold water for as long as they could. Half of the group was told that people can tolerate cold water for longer if they have a healthy type of heart, while the other half was told that the healthy heart causes lower tolerance.  The first group held their arms in the water for longer than the second even though both groups claimed that they were not influenced by knowledge of the link to heart quality.  In other words, they used their tolerance for cold water as a signal that they were healthy by not being aware of or denying the influence of the heart hypothesis on their action.  They acted as if they had not intervened when in fact they had.  On the assumption that participants were making every effort to be honest, and really did not believe that the hypothesis influenced them, signaling in this case was a form of self-deception.  People deceived themselves into believing they had not intervened in order to use their action as a signal that they were healthy.  The signal may have been directed only toward participants themselves; there may have been no one else they cared to convince.

Shafir and Tversky (1992) report another violation of interventional logic.  They gave participants a real-life version of Newcomb’s paradox (Nozick, 1969).  In brief, people were given a choice between two prizes where the second prize was always larger than the first (the second dominated the first), although the amount of the prizes was uncertain.  They were told that a computer had used earlier choices they had made as a basis for predicting their choice between the first and second prize and if it predicted that they would choose the small prize, there would be much more money available for both prizes than if it predicted that they would choose the larger prize.  Participants always chose after the prediction was made so their choice could not influence the prediction.  Nevertheless, 65% of participants chose the small prize, giving up money in the hope that their action would render a prediction of their choice accurate.  Choice is an intervention in the sense that it is an action that renders a selection independent of its normal causes, in this case rendering the amount chosen independent of the prediction.  So participants acted as if their choice signaled a prediction that it could not possibly have influenced.

The rationality of signaling

Is signaling an error by virtue of violating interventional logic?  Clearly, people are behaving non-optimally in the examples just cited.  The Quattrone and Tversky (1984) example is a case of an action performed merely for its signaling value (to convince the participant, experimenter, or both that the participant has a good heart) and yet the very act reduces the value of the signal (because it is designed to convince rather than reveal the participant’s actual heart type).  The Shafir and Tversky (1992) study demonstrates how decisions made for their signal value can lead to nonconsequentialism.  People gave up money in an obviously futile effort to gain more money.

But a couple of examples don’t condemn all cases of signaling.  A nickel has negligible value yet stealing a nickel remains an outrageous act, not because of its consequences but because of its meaning:  It signals (to oneself if no one else knows about it) that one is a thief.  The symbolic value of certain acts provides sufficient justification for those acts even in the absence of desirable causal consequences of the action (see, e.g., Nozick, 1995).

Moreover, our decisions can give us information about ourselves.  I might not be aware that I prefer one type of beverage or location or partner, yet I might notice that I am consistent in my choices, and this tells me something about myself.  Some people consistently choose partners who dominate them and learn by this about their own desire to be submissive.  People’s choices can have multiple determinants and one can sometimes learn about those determinants by observing one’s own choices.  Self-signaling is not an error when it tells us something about ourselves that we do not already know.

Nevertheless signaling remains problematic.  It can even lead to paradox when an action is performed merely for the sake of its signaling value (Campbell & Sowden, 1985).  Consider someone who is not altruistic yet wishes they were.  They might donate money to charity to signal that they are altruistic, yet their action is not a result of altruism but the desire to signal altruism.  Of course, the act itself is altruistic, so how should we judge the person?  In this case, there’s no causal link from the individual’s conscience to their action, although the diagnostic value of the act suggests such a link.  As Bodner and Prelec (2002) point out, examples of self-handicapping have a parallel logic.  Someone might not study for an exam, or might dress inappropriately for an important meeting, in order to have a ready excuse when they do not meet expectations.

Conclusion

These examples do not invalidate the logic of intervention. But they do force some care in deciding what is and isn’t an intervention.  Alternatively, we can distinguish different types of intervention.  To see which interventions should and which need not follow the logic of intervention, we need to distinguish the process of decision making (a cognitive activity) from the process of choice (determining the state of the world via the action of selecting an option from a set).  The process of decision making takes information from the world and analyzes it to select a course of action.  Choice is an action that is either fully determined by the decision-making process or else affected by other factors as well.

Let’s first consider choices that are fully governed by the decision-making process, for example, my choice on a multiple-choice multiplication test.  I do my calculations and they determine my choice, nothing else affects it.  In such a case, the process of choice cannot teach us anything that we do not already know.  I chose my answer because I did my calculations and decided that was the right answer.  I cannot learn anything new from my answer about what the question was or how I answered it.  I knew as much about those things before I chose my answer as I do immediately afterward.  Call cases where the decision-making process fully determines choice deliberate intervention.  Such cases are fully consistent with the logic of intervention -- with undoing -- inasmuch as the choice itself does not reveal anything new about its determinants.

But not all choices are completely deliberate.  My willingness to donate to charity might not be fully governed by my decision-making process.  There are likely social pressures that I’m not aware of, pressures that charitable organizations are likely to exploit.  The amount that I donate may be affected by the way options are listed on the donation form, by halo effects, by recent memories, indeed by a host of subtle influences that may affect me unwittingly. My final contribution cannot inform me about those factors that entered my decision-making process because, by definition, I knew about them before making my choice.  But my final contribution can inform me about those other factors that influenced me that were not taken into account by my decision-making process because I may not have known about them.  I might even be surprised by the amount of my own donation, in which case it’s likely that one or more of these “hidden” causes are driving me.  The choice is not diagnostic of the input into my decision-making process, but it is diagnostic of these other causes of my choice.

In sum, a rational analysis of intervention requires distinguishing causes of action that influence the decision-making process and causes of action that do not.  A choice should be construed as an intervention only to the degree that the choice is governed by the process of decision making and not by other factors.  Deliberate interventions entail treating choices as non-diagnostic of their causes; other interventions entail this kind of undoing only to the degree that choice is governed by decision making.  But note that normative considerations demand that my beliefs about those factors that do govern the decision-making process are not influenced by choice; such beliefs are governed by undoing because the decision-maker already knows as much about them before choice as he or she does after choice.

The conclusions so far have focused exclusively on decision making.  But the same distinctions arise when reasoning in the absence of a decision.  To answer a question like “what would be the optimal intervention in such-and-such a situation?” I might use a causal model to think about the situation.  To the degree that my answer is governed by my thinking, any intervention I consider should be construed as a deliberate intervention and not diagnostic of its normal causes.  But to the degree that my answer is governed by factors that don’t enter my causal model, like an unconscious desire to intervene in a specific way, the intervention is diagnostic of those factors.  This situation is really not so different than decision making and might just be a special case of it.

However, if I am given an intervention and asked to reason about it, then I must always treat it as a deliberate intervention.  To answer the question “what would happen if I intervened on X?” a reasoner always has complete control over the variable intervened on because what we imagine to be true just is true in our imaginary world.  In that sense, imagined interventions in reasoning should always obey undoing; they reveal nothing about causes other than the intervention because the intervention uniquely determines their value.

Whether or not people are obeying the logic of intervention when reasoning and decision making, their thinking always seems to be guided by causal beliefs.  Even the signal value of actions derives from belief in a causal mechanism determining the action.  Without the belief that heart type causes more or less tolerance for pain, participants would not have been motivated to hold their hands in water for more or less time.  So even when people are violating the logic of intervention, a causal model guides their actions.

Note.  This essay has benefited from the comments of York Hagmayer.

References

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Campbell, R. & Sowden, L. (1985).  (Eds.), Paradoxes of Rationality and Cooperation: Prisoner's Dilemma and Newcomb's Problem.  Vancouver: University of British Columbia Press.

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