predictions by the statistical view and the causal mechanism view on some intuitive examples
Even successfully tracked covariation, however, does not equal causation, as we illustrated earlier and as every introductory statistics text warns. None of these cases can be explained by the AP rule in Eq. (7.1 ). For example, even if the AP for rooster crowing is 1, nobody would claim that the crowing caused the sun to rise. Although the candidate cause, crowing, covaries perfectly with the effect, sunrise, there is an alternative cause that covaries with the candidate: Whenever the rooster crows, the Earth's rotation is just about to bring the farm toward the sun. Our intuition would say that because there is confounding, one cannot draw any causal conclusion. This pattern of information fits the overshadowing design. If crowing is the more salient of the two confounded cues, then RW would predict that crowing causes sunrise.
Let us digress for a moment to consider what the causal mechanism view predicts. Power theorists might argue that the absence of a plausible mechanism whereby a bird could influence the motion of stellar objects, rather than anything that has to do with covariation, is what prevents us from erroneously inducing a causal relation. In this example, in addition to the confounding by the Earth's rotation, there happens to be prior causal knowledge, specifically, of the noncausality of a bird's crowing with respect to sunrise. Tracing the possible origin of that knowledge, however, we see that we do have covariational information that allows us to arrive at the conclusion that the relation is noncausal. If we view crowing and sunrise at a more general level of abstraction, namely, as sound and the movement of large objects, we no longer have the confounding we noted at the specific level of crowing and sunrise. We have observed that sounds, when manipulated at will so alternative causes do occur independently of the candidate, thus allowing causal inference, do not move large objects. Consequently, crow ing belongs to a category that does not cause sunrise (and does not belong to any category that does cause sunrise), and the confounded covariation between crowing and sunrise is disregarded as spurious.
Our consideration shows that, contrary to the causal mechanism view, prior knowledge of noncausality neither precludes nor refutes observation-based causal discovery. Thagard (2000) gave a striking historic illustration of this fact. Even though the stomach had been regarded as too acidic an environment for viruses to survive, a virus was inferred to be a cause of stomach ulcer. Prior causal knowledge may render a novel candidate causal relation more or less plausible but cannot rule it out definitively. Moreover, prior causal knowledge is often stochastic. Consider a situation in which one observes that insomia results whenever one drinks champagne. Now, there may be a straightforward physiological causal mechanism linking cause and effect, but it is also plausible that the relation is not causal; it could easily be that drinking and insomnia are both caused by a third variable - for example, attending parties (cf. Gopnik et al., 2004).
Returning to the pitfall of statistical and associative models, besides the confounding problem, we find that there is the overdetermination problem, where two or more causes covary with an effect, and each cause by itself would be sufficient to produce the effect. The best-known illustration of overdetermination is provided by Mackie (1974): Imagine two criminals who both want to murder a third person who is about to cross a desert; unaware of each other's intentions, one criminal puts poison in the victim's water bottle, while the other punctures the bottle. Each action on its own co-varies perfectly with the effect, death, and would have been sufficient to bring the effect about. However, in the presence of the alternative cause of death (a given fact in this example), so that there is no confounding, varying each candidate cause in this case makes no difference; for instance, the AP for poison with respect to death, conditional on the presence of the puncturing of the water canteen, is 0! So, Mackie's puzzle goes, which of the two criminals should be called the murderer? Presumably, a lawyer could defend each criminal by arguing that their respective deed made no difference to the victim's ultimate fate - he would have died anyway as a result of the other action (but see Katz, 1989; also see Ellsworth, Chap. 28; Pearl, 2000; and Wright, 1985, on actual causation). Mackie turned to the actual manner of death (by poison or by dehydration) for a solution. But, suppose the death is discovered too late to yield useful autopsy information. Would the desert traveler then have died without a cause? Surely our intuition says no: The lack of covariation in this case does not imply the lack of causation (see Ellsworth, Chap. 28; Spellman & Kin-cannon, 2001, for studies on intuitive judgments in situations involving multiple sufficient causes). What matters is the prediction of the consequences of actions, such as poisoning, which may or may not be revealed in the covariation observed in a particular context.
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