Postscript: Abandonment of Causal Power.

Abstract

What does it mean when causal power is greater than 0 but less than 1? Cheng and Novick (2005) argue that when a reasoner represents a potential cause at an inappropriately high level (e.g., citrus fruit instead of the true cause, oranges), true causal power can be between 0 and 1 even when all the required assumptions still hold. In our comment, we argued that such a case involves confounding (properties of oranges are confounded with properties of citrus fruit) and thus causal power cannot be computed according to the power PC theory. Cheng and Novick (2005) disagree and include an illustration that they claim demonstrates the contradiction inherent in our claim. In their example, P(e|i), or P(repelling bugs|citrus fruit), is 0.5 (three oranges repel bugs, three lemons do not), but when re-expressed as qi P(a|i) qa qi P(a|i) qa, they claim P(e|i) should be 0.5 0.5 1 0.5 0.5 1 0.75, which does not match the observed value. Note that this expression uses a value of 0.5 for qi (i.e., causal power of citrus fruit) on the basis of application of Equation 5 (Cheng & Novick, 2005, p. 701). From our perspective, this estimate is erroneous because the situation is confounded, and thus Equation 5 cannot be used. Another way to explain that the value of 0.5 for qi of citrus fruit is not a normatively accurate estimate of causal power is the following. Note that the probabilistic causal power estimate in this case is equivalent to the ratio between the frequency of true cause (e.g., oranges) and the frequency of the broader category (e.g., citrus fruits). It should be clear then that these probabilities are not “invariant properties of relations” (Cheng, 2000, p. 227) because they could easily vary (e.g., there is no natural law that constrains the proportion of oranges in citrus fruits). If we travel to a new context in which citrus fruits are common but oranges are rare, the estimated causal power of citrus fruit will change. This test (suggested in Cheng, 2000) indicates that the estimate of the causal power of citrus fruit (i.e., 0.5 in the above illustration) is not context-free and thus an inaccurate estimate of causal power. Thus, this example fails to show that “a probabilistic causal power can be obtained when all of the power PC assumptions are met if candidate cause c is an imperfect hypothesis, even for a reasoner who assumes causal determinism” (Cheng & Novick, 2005, p. 701). That is, our claim that incorrectly categorized causes violate the no-confounding assumption remains valid. These difficulties associated with confounds imply that accurate computation of causal power requires a tremendous amount of accurate knowledge, much of which reasoners are unlikely to possess (Cheng & Novick, 2005). We agree that this poses a problem for accurately judging causal power and that such situations are yet another obstacle to valid causal inferences (including the successful computation of causal power). Indeed, one could argue that “no causal inference should ever occur” (Cheng & Novick, 2005, p. 702). Therefore, the fact that people are not paralyzed in their causal inferences can actually be taken as evidence against the power PC theory itself (or any other model that requires equally stringent assumptions). Beyond the problem of confounding, we have also argued that each of the assumptions required to compute causal power is difficult to obtain (Luhmann & Ahn, 2005). To deal with these difficulties, Cheng and Novick’s (2005) reply heavily emphasizes the claim that contextualized causal power (Cheng, 2000) is consistent with the power PC theory. Yet, Cheng and Novick still argue that during causal judgments, one possible goal of reasoners (perhaps a particularly important goal) is to compute causal power. They state, “aiming for causal power and accepting contextual power is as ‘contradictory’ as aiming for a gold medal and accepting silver” (Cheng & Novick, 2005, p. 703), implying that causal power (i.e., the gold medal) is the reasoner’s ultimate goal. How-