Some judges and commentators have characterized all evidence as ultimately “probable,” but other writers have criticized this view as trading on the ambiguities inherent in our ordinary usage of probable to convey an epistemic hedge or uncertainty.  How successful is the probabilistic program in the law?  In the context of assessing causation, many courts have succumbed to the temptation to substitute risk for causation.  Other courts have noticed the difference between a prospective risk and a retrospective factual determination that a risk factor actually participated in bringing about the caused result.  In any event, judicial skepticism about probabilistic evidence, in many contexts, has found its expression in holdings and in dicta of common law courts.  The following is a chronological listing of some pertinent cases that rejected or limited the use of overtly probabilistic evidence. There are only two cases involving epidemiological evidence before 1970 on the list.

Day v. Boston & Maine R.R., 96 Me. 207, 217–218, 52 A. 771, 774 (1902) (“Quantitative probability, however, is only the greater chance. It is not proof, nor even probative evidence, of the proposition to be proved. That in one throw of dice, there is a quantitative probability, or greater chance, that a less number of spots than sixes will fall uppermost is no evidence whatever that in a given throw such was the actual result. Without something more, the actual result of the throw would still be utterly unknown. The slightest real evidence would outweigh all the probability otherwise.”)

Toledo, St. L. & W. R. Co. v. Howe, 191 F. 776, 782-83 (6th Cir. 1911) (holding that evidence at issue was not probabilistic, but noting in dictum that “[n]o man’s property should be taken from him on the mere guess that he has committed a wrong. . . because of a probability among other probabilities that the accident for which recovery is sought might have happened in the way charged.”)

People v. Risley, 214 N.Y. 75, 86, 108 N.E. 200, 203 (1915) (holding that probability calculations were improper when “the fact to be established in this case was not the probability of a future event, but whether an occurrence asserted by the people to have happened had actually taken place”)

Lampe v. Franklin Am. Trust, 339 Mo. 361, 384, 96 S.W.2d 710, 723 (1936) (“verdict must be based upon what the jury finds to be facts rather than what they find to be ‘more probable’.”)

Sargent v. Massachusetts Accident Co., 307 Mass. 246, 250, 29 N.E.2d 825, 827 (1940) (the preponderance standard requires more than showing that the chances mathematically favor a fact in dispute; the proponent must prove the proposition in dispute such that the jurors form an actual belief in the truth of the proposition) (“It has been held not enough that mathematically the chances somewhat favor a proposition to be proved; for example, the fact that colored automobiles made in the current year outnumber black ones would not warrant a finding that an undescribed automobile of the current year is colored and not black, nor would the fact that only a minority of men die of cancer warrant a finding that a particular man did not die of cancer. The weight or preponderance of the evidence is its power to convince the tribunal which has the determination of the fact, of the actual truth of the proposition to be proved. After the evidence has been weighed, that proposition is proved by a preponderance of the evidence if it is made to appear more likely or probable in the sense that actual belief in its truth, derived from the evidence, exists in the mind or minds of the tribunal notwithstanding any doubts that may linger there.”)

Smith v. Rapid Transit, 317 Mass. 469, 470, 58 N.E.2d 754, 755 (1945) (evidence that defendant was the only bus franchise operating in the area where the accident took place was not sufficient to establish that the bus that caused the accident belonged to the defendant where private or chartered buses could have been in the area; it is not enough that mathematically the chances somewhat favor the proposition to be proved)

Kamosky v Owens-Illinois Co., 89 F. Supp. 561, 561-62 (M.D.Pa. 1950) (directing verdict in favor of defendant; statistical likelihood that defendant manufactured the bottle that injured plaintiff was insufficient to satisfy plaintiff’s burden of proof)

Mahoney v. United States, 220 F. Supp. 823, 840 41 (E.D. Tenn. 1963) (Taylor, C.J.) (holding that plaintiffs had failed to prove that their cancers were caused by radiation exposures, on the basis of their statistical, epidemiological proofs), aff’d, 339 F.2d 605 (6th Cir. 1964) (per curiam)

In re King, 352 Mass. 488, 491-92, 225 N.E.2d 900, 902 (1967) (physician expert’s opinion that expressed a mathematical likelihood, unsupported by clinical evidence, that claimant’s death from cancer was caused by his accidental fall was legally insufficient to support a judgment)

Garner v. Heckla Mining Co., 19 Utah 2d 367, 431 P.2d 794, 796 97 (1967) (affirming denial of compensation to family of a uranium miner who had smoked cigarettes and had died of lung cancer; statistical evidence of synergistically increased risk of lung cancer among uranium miners is insufficient to show causation of decedent’s lung cancer, especially considering his having smoked cigarettes)

Whitehurst v. Revlon, 307 F. Supp. 918, 920 (E.D. Va. 1969) (holding that challenged evidence was not probabilistic, and noting in dictum that probability evidence of negligence evidence would leave verdict based upon conjecture, guess or speculation)

Guenther v. Armstrong Rubber Co., 406 F.2d 1315, 1318 (3d Cir. 1969) (holding that defendant cannot be found liable on the basis that it supplied 75-80% of the kind of tire purchased by the plaintiff; any verdict based on this evidence “would at best be a guess”)

Crawford v. Industrial Comm’n, 23 Ariz. App. 578, 582-83, 534 P.2d 1077, 1078, 1082-83 (1975) (affirming an employee’s award of no compensation because he was exposed to disease producing conditions both on and off the job; a physician’s testimony, expressed to a reasonable degree of medical certainty that the working conditions statistically increased the probability of developing a disease does not satisfy the reasonable certainty standard)

Olson v. Federal American Partners, 567 P.2d 710, 712 13 (Wyo. 1977) (affirming judgment for employer in compensation proceedings; cigarette smoking claimant failed to show that his lung cancer resulted from workplace exposure to radiation, despite alleged synergism between smoking and radiation).

Heckman v. Federal Press Co., 587 F.2d 612, 617 (3d Cir. 1977) (statistical data about a group do not establish facts about an individual)

Bazemore v. Davis, 394 A.2d 1377, 1382 n.7 (D.C. 1978) (if verdicts were determined on the basis of statistics indicating high probability of alleged facts, more often than not they would be correct guesses, but this is not a sufficient basis for reaching verdicts)

Kaminsky v. Hertz Corp., 94 Mich. App. 356 (1979) (dictum; reversing summary judgment)

Sulesky v. United States, 545 F. Supp. 426, 430 (S.D.W.Va. 1982) (swine flu vaccine GBS cases; epidemiological studies alone do not prove or disprove causation in an individual)

Robinson v. United States, 533 F. Supp. 320, 330 (E.D. Mich. 1982) (finding for government in swine flu vaccine case; the court found that that the epidemiological evidence offered by the plaintiff was not probative, and that it “would reach the same result if the epidemiological data were entirely excluded since statistical evidence cannot establish cause and effect in an individual”)

Iglarsh v. United States, No. 79 C 2148, 1983 U.S. Dist. LEXIS 10950, *10 (N.D.Ill. Dec. 9, 1983) (“In the absence of a statistically valid epidemiological study, even the plaintiff’s treating physician or expert witness, or any clinician for that matter, is unable to attribute a plaintiff’s injury to the swine flu vaccination.”)

Johnston v. United States, 597 F. Supp. 374, 412, 425-26 (D.Kan. 1984) (although the probability of attribution increases with the relative risk, expert must still speculate in making an individual attribution; “a statistical method which shows a greater than 50% probability does not rise to the required level of proof; plaintiffs’ expert witnesses’ reports were “statistical sophistry,” not medical opinion)

Kramer v. Weedhopper of Utah, Inc., 490 N.E.2d 104, 108 (Ill. App. Ct. 1986) (Stamos, J., dissenting) (“Liability is not based on a balancing of probabilities, but on a finding of fact.  While the majority contends that the measure of what is considered sufficient evidence [to support submitting a case to the jury] resolves itself into a question of probability, a review of case law … reveals that a theoretical probability alone cannot be the basis for [a prima facie case].  There must be some evidence in addition to the abstraction which will enable a jury to choose between competing probabilities.”)

Washington v. Armstrong World Industries, 839 F.2d 1121 (5th Cir. 1988) (affirming grant of summary judgment on grounds that statistical correlation between asbestos exposure and disease did not support specific causation)

Thompson v. Merrell Dow Pharm., 229 N.J. Super. 230, 244, 551 A.2d 177, 185 (1988) (epidemiology looks at increased incidences of diseases in populations)

Norman v. National Gypsum Co., 739 F. Supp. 1137, 1138 (E.D. Tenn. 1990) (statistical evidence of risk of lung cancer from asbestos and smoking was insufficient to show individual causation, without evidence of asbestos fibers in the plaintiff’s lung tissue)

Smith v. Ortho Pharmaceutical Corp., 770 F. Supp. 1561, 1576 (N.D. Ga. 1991) (“The court notes that, in an individual case, epidemiology cannot conclusively prove causation; at best, it can establish only a certain probability that a randomly selected case of birth defect was one that would not have occurred absent exposure (or the ‘relative risk’ of the exposed population).”)

Smith v. Ortho Pharmaceutical Corp., 770 F. Supp. 1561, 1573 (N.D. Ga. 1991) (“However, in an individual case, epidemiology cannot conclusively prove causation; at best, it can only establish a certain probability that a randomly selected case of disease was one that would not have occurred absent exposure, or the ‘relative risk’ of the exposed population.  Epidemiology, therefore, involves evidence on causation derived from group-based information, rather than specific conclusions regarding causation in an individual case.”)

Howard v. Wal-Mart Stores, Inc., 160 F.3d 358, 359–60 (7th Cir. 1998) (Posner, C.J.)

Krim v. pcOrder.com, Inc., 402 F.3d 489 (5th Cir. 2005) (rejecting standing plaintiffs’ standing to sue for fraud absent a showing of actual tracing of shares to the offending public offering; statistical likelihood of those shares having been among those purchased was insufficient to confer standing)