This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation. We further investigate the circumstances under which such bounds can emerge, and the philosophical dilemma associated with determining individual cases from statistical data.
BalkeA.PearlJ.. 1994a. “Counterfactual Probabilities: Computational Methods, Bounds, and Applications.” Pp. 46–54 in Uncertainty in Artificial Intelligence 10, edited by de MantarasR. L.PooleD.. San Mateo, CA: Morgan Kaufmann.
2.
BalkeA.PearlJ.. 1994b. “Probabilistic Evaluation of Counterfactual Queries.” Pp. 230–37 in Proceedings of the Twelfth National Conference on Artificial Intelligence, edited by B. Hayes-Roth and R. E. Korf, vol. I. Menlo Park, CA: MIT Press.
3.
CaiZ.KurokiM.. 2006. “Variance Estimators for Three ‘Probabilities of Causation.’”Risk Analysis25:1611–20.
4.
ColeP.1997. “Causality in Epidemiology, Health Policy, and Law.”Journal of Marketing Research27:10279–85.
5.
DawidA.2000. “Causal Inference Without Counterfactuals (with Comments and Rejoinder).”Journal of the American Statistical Association95:407–48.
6.
DawidA.FienbergS.FaigmanD.. 2014. “Fitting Science into Legal Contexts: Assessing Effects of Causes or Causes of Effects?”Sociological Methods and Research43:359–90.
7.
DuncanO.1975. Introduction to Structural Equation Models. New York: Academic Press.
8.
FreedmanD. A.StarkP. B.. 1999. “The Swine U Vaccine and Guillain-Barré Syndrome: A Case Study in Relative Risk and Specific Causation.”Evaluation Review23:619–47.
9.
GallesD.PearlJ.. 1998. “An Axiomatic Characterization of Causal Counterfactuals.”Foundation of Science3:151–82.
10.
GreenlandS.1999. “Relation of Probability of Causation, Relative Risk, and Doubling Dose: A Methodologic Error That Has Become a Social Problem.”American Journal of Public Health89:1166–69.
11.
JewellN. P. 2014“Assessing Causes for Individuals: Comments on Dawid, Faigman, and Fienberg.”Sociological Methods and Research54:391–395.
12.
HaavelmoT.1943. “The Statistical Implications of a System of Simultaneous Equations.”Econometrica11:1-12. Reprinted in HendryD. F.MorganM. S., eds. 1995. The Foundations of Econometric Analysis, pp. 477–90. Cambridge, UK: Cambridge University Press.
13.
HalpernJ.1998. “Axiomatizing Causal Reasoning.” Pp. 202–10 in Uncertainty in Artificial Intelligence, edited by CooperG.MoralS.. San Francisco, CA: Morgan Kaufmann. Also, Journal of Artificial Intelligence Research12:17–37, 2000.
14.
PearlJ.1993. “Comment: Graphical Models, Causality, and Intervention.”Statistical Science8:266–69.
15.
PearlJ.2000a. Causality: Models, Reasoning, and Inference. New York: Cambridge University Press.
16.
PearlJ.2000b. “Comment on A. P. Dawid’s, Causal Inference Without Counterfactuals.”Journal of the American Statistical Association95:428–31.
17.
PearlJ.2009. Causality: Models, Reasoning, and Inference. 2nd ed. New York: Cambridge University Press.
18.
PearlJ.2011. “The Algorithmization of Counterfactuals.”Annals of Mathematics and Artificial Intelligence61:29–39.
19.
PearlJ.2012. “The Causal Foundations of Structural Equation Modeling.” Pp. 68–91 in Handbook of Structural Equation Modeling, edited by HoyleR.. New York: Guilford Press.
20.
PearlJ.2013. “The Curse of Free-will and the Paradox of Inevitable Regret.”Journal of Causal Inference1:255–57.
21.
PearlJ.2014. “Causes of Effects and Effects of Causes (Extended Version).”Tech. Rep. R-431-L. Los Angeles: Department of Computer Science, University of California. Accessed October 6, 2014, http://ftp.cs.ucla.edu/pub/statser/r431-L.pdf.
22.
RobertsonD.1997. “The Common Sense of Cause in Fact.”Texas Law Review75:1765–800.
23.
RobinsJ.GreenlandS.. 1989. “The Probability of Causation under a Stochastic Model for Individual Risk.”Biometrics45:1125–38.
24.
ShpitserI.PearlJ.. 2009. “Effects of Treatment on the Treated: Identification and Generalization.” Pp. 514–21 in Proceedings of the Twenty-fifth Conference on Uncertainty in Artificial Intelligence, edited by BilmesJ.NgA.. Corvallis, OR: AUAI Press.
25.
TianJ.PearlJ.. 2000. “Probabilities of Causation: Bounds and Identification.”Annals of Mathematics and Artificial Intelligence28:287–313.
26.
WrightS.1921. “Correlation and Causation.”Journal of Agricultural Research20:557–85.
27.
YamamotoT.2012. “Understanding the Past: Statistical Analysis of Causal Attribution.”American Journal of Political Science32:237–56. doi:10.1111/j.1540–5907.2011.00539.x.
