A Note on Causes of Effects Judea Pearl

• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2014
• Subjects: Greenland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.475.3370; http://ftp.cs.ucla.edu/pub/stat_ser/r439.pdf

Interest in applying counterfactual logic to legal settings has resulted in disagreements re-garding the proper interpretation of the legal term “but for, ” as in “It is more probable than not that the injury would not have occurred but for the defendant action ” (Robertson, 1997). Let A = 1 stands for the defendant’s action, R = 1 for the observed response (e.g., injury or damage), and R0 (respectively R1) for the value that R would have had the action not taken (A = 0). The standard interpretation of the “but for ” criterion is captured by the inequality PN ≥ 0 where PN stands for counterfactual probably PN = P (R0 = 0|A = 1, R = 1) (1) termed “probability of necessity ” in Pearl (2000a). The same interpretation was used by Greenland and Robins (1988); Balke and Pearl (1994a,b); Pearl (1999); Tian and Pearl (2000). Equation (1) is a direct translation of the “but for ” test into counterfactual language, saying that R would not have occurred in the absence of A, given that R and A did in fact occur. Implicit in PN is the understanding that the probability P is defined relative to a reference class of individuals who are exchangeable with the defendant. In other words, P embeds all other information we have about the incident, for example, that the defendant is a red hair lawyers who owns a black Mercedes, and that the claimant was a reckless driver. Ironically, Eq. (1) was also used in Pearl (2000b)to demonstrate that counterfactuals can handle CoE-type questions, while Dawid dismissed counterfactuals as “metaphysical” concepts that “can lead to distorted understandings and undesirable practical consequences” (Dawid, 2000, p. 408). “I challenge Dawid to express Query II [“My headache has gone. Is it because I took aspirin?”], let alone formulate conditions for its estimation in a counterfactual-free language (Pearl, 2000b, p. 429).