1 For a collection of the literature on this issue, see the collected conference papers devoted to the subject in 13 Cardozo L. Rev., nos. 2–3 (1991) and 66 Boston Univ. L. Rev. (1986).

2 Nesson, C., “The Evidence or the Event? On Judicial Proof and the Acceptability of Verdicts” (1985) 98 Harv. L. Rev. 1357CrossRefGoogle Scholar; Tribe, L.H., “Trial by Mathematics: Precision and Ritual in the Legal Process” (1971) 84 Harv. L. Rev. 1329.CrossRefGoogle Scholar See also the rebuttal of Saks, M. and Kidd, R., “Human Information Processing and Adjudication: Trial by Heuristice” (1980–1981) 15 L. & Society Rev. 123, 125.CrossRefGoogle Scholar For an interesting review of a forerunner of this discussion in Scots jurisprudence, see Harira, Abu, “An Early Holistic Conception of Judicial Factfinding” 1986 Juridical Rev. 79.Google Scholar

3 Oxford Univ. Press (1977) (hereinafter cited as “Cohen”).

4 For a reaction to this approach from the mathematical community, see Wagner, G., Book Review: “The Probable and the Provable” 1979 Duke L. J. 1071.CrossRefGoogle Scholar

5 See Carnap, R., Logical Foundations of Probability (Univ. of Chicago Press, 2d ed. 1962) 24Google Scholar (hereinafter “Carnap”).

6 Carnap, supra n. 5, at 25.

7 Shapiro, B., Probability and Certainty in Seventeenth Century England (Princeton Univ. Press, 1983) 3–14.Google Scholar

8 Daston, L. J., “The Domestication of Risk: Mathematical Probability and Insurance 1650–1830” in Kruger, L. et al. , eds., The Probabilistic Revolution, vol. 2 (Cambridge, MIT Press, 1987) 237.Google Scholar

9 To use this formula the events must be independent. The mistake of using this formula for dependent events was made in the now famous case People v. Collins, 68 Cal. 2d 319, 438 P.2d 33, 66 Cal. Rptr. 497 (1968), in which significantly dependent events were viewed as independent.

10 For the formula proof, see Brook, J., A Lawyer's Guide to Probability and Statistics (Toronto, Carswell, 1990) 71–77.Google Scholar

11 For a sample of the vast literature on the subject, see Levi, Issac, Gambling with Trust – An Essay on Induction and the Aim of Science (Cambridge, MIT, 1967)Google Scholar; Pollock, J.L., Nomic Probability and the Foundations of Induction (Oxford, Oxford Univ. Press, 1990)Google Scholar; and the somewhat unusual approach of Chattopadhyaya, D.P., Induction, Probability and Skepticism (Albany, SUNY Press, 1991).Google Scholar

12 Brilmayer, L. and Kornhauser, L., “Review: Quantitative Methods and Legal Decisions” (1978) 46 U. Chi. L. Rev. 116CrossRefGoogle Scholar (hereinafter cited as “Brilmayer & Kornhauser”).

13 See discussion of the example in part VIII(l) “Weight”, infra.

14 Compare Nozick's System of credibility values in Nozick, R., The Nature of Rationality (Princeton Univ. Press, 1993) 84–85.Google Scholar

15 See the discussion of “Weight', infra, section VIII(1).

16 Kuhn, T.S., The Structure of Scientific Revolutions (Univ. of Chicago Press, 1962).Google Scholar

17 Daubert v. Merrell Dow Pharmaceuticals, lne, 509 U.S. 579, 113 S. Ct. 2785 (1993) at 2978; and see discussion of this case, infra.

18 For works describing the historical as well as philosophical development of the concept, see Cox, R.R., Schutz's Theory of Relevance (The Hague, Martinus Nijhoff, 1978)Google Scholar; Webb, R.B., The Presence of the Past (Gainesville, Univ. of Florida, 1976).Google Scholar

19 Sperber, D. and Wilson, D., Relevance (Cambridge, Harvard Univ. Press, 1987).Google Scholar

20 Ayer, A. J., “The Legacy of Hume” in Probability and Evidence (New York, Columbia Univ. Press, 1972).CrossRefGoogle Scholar

21 Cohen, L.J., “The Role of Evidential Weight in Criminal Proof” (1986) 66 Boston U. L. Rev. 635.Google Scholar

22 Lempert, R., “Modeling Relevance” (1977) 75 Michigan L. Rev. 1021CrossRefGoogle Scholar (cited hereinafter as “Lempert”).

23 Lempert, supra n. 22, at 1028.

24 Federal Rules of Evidence, Rule 410. On these rules generally, see Green, E. and Nesson, C., Problems, Cases and Materials on Evidence (Boston, Little, Brown & Co., 1983) 50–91.Google Scholar

25 509 U.S. 579 (1993).

26 Frye v. U.S., 293 F. 1013 (1923).

27 Cohen, supra n. 3, at 96–97.

28 Ibid., at 99.

29 Ibid., at 100.

30 Brilmayer & Kornhauser, supra n. 12, at 143.

31 See ibid.

32 Nagel, E., Principles of the Theory of Probability (Chicago, University Of Chicago Press, 1957) at 47.Google Scholar

33 Keynes, J.M., A Treatise on Probability (London, McMillan, 1921, reprinted 1963), at 42.Google Scholar

34 See, e.g., Pattern Jury Instructions – Civil Cases llth District (St. Paul, West, 1990), at 14: “If proof fails to establish any essential part of the plaintifFs claim by a preponderance of the evidence – you should find for the defendant as to that claim.” For criminal trials, see Pattern Criminal Jury Instructions 6th Circuit (St. Paul, West, 1991), at 6, stating that the “government must prove every element of the crime beyond a reasonable doubt.”

35 See also Lempert, R., “The New Evidence Scholarship: Analyzing the Process of Proof” (1986) 66 Boston Univ. L. Rev. 439.Google Scholar

36 Nesson, supra n. 2, at 1388.

37 Cohen, supra n. 3, at 266.

38 For a general discussion of decisionmaking in judicial panels, see Ben-Shahar, O., Non-dichotomous Choice Problems in Collegial Courts (LLM thesis, Harvard Law School, 1991, unpublished).Google Scholar

39 These are the real facts of an Israeli case, Tassa v. State of Israel, 1419/86 CA. (T.A.), 1988(1) P.M. 309.

40 As required by article 80 of the Israel Courts Law (combined version) 1984, as amended in 1992. See discussion in Feller, S.Z., “Majority and Dissent – Means of Concretization” (1988) 15 Iyunei Mishpat 31Google Scholar (in Hebrew).

41 These, too, are the facts of a real case decided by the Supreme Court of Israel, Afenger v. State of Israel (1979) 33(iii) P.D. 141.

42 Kornhauser, L.A., “Modeling Collegial Courts II. Legal Doctrine” (1992) 8 J. of L. Econ & Org. 441.Google Scholar

43 Cohen, supra n. 3, at 68–73.

44 Although Cohen quotes Wigmore to the contrary, ibid., at 69.

45 Cohen, supra n. 3, at 270.

46 Hastie, R., Pennington, N., “A Cognitive Theory of Juror Decision-making: The Story Model” (1991) 13 Cardozo L. Rev. 519, at 546.Google Scholar

47 See Brilmayer & Kornhauser, supra n. 12, at 142.

48 Putnam, H., “Three-valued Logic” in Mathematics, Matter and Method – Philosophical Papers, vol. 1 (Cambridge, Cambridge Univ. Papers, 2d ed. 1979), at 166.CrossRefGoogle Scholar

49 Cohen, L.J., The Implications of Induction (London, Methuen, 1970) at 155–70.Google Scholar

50 For the legal formulation, see 9 Wigmore, Evidence, section 2497.

51 Cohen, supra n. 3, at 247–49.

52 Ibid., at 132.

53 In a recent decision, a U.S. appellate court accepted 99% as the standard for reasonable doubt. United States v. Hannigan, 27 F.3d 890 (3d Cir., 1994).

54 For an explanation of the civil cases model see Kaye, D.H., “The Limits of the Preponderance of the Evidence Standard: Justifiable Naked Statistical Evidence and Multiple Causation” (1982) American Bar Foundation Research Journal 487–516Google Scholar, reprinted in Twining, William and Stein, Alex, eds., Evidence and Proof (Aldershot, England, Dartmouth Publishing Co., 1992).Google Scholar

55 For this doctrine, see Caldwell v. Mississippi 472 U.S. 320 (1985); Sawyer v. Smith 497 U.S. 227 (1990).

56 See Langbein, J.H. “The German Advantage in Civil Procedure” (1985) 52 U. Chi. L. Rev. 823.CrossRefGoogle Scholar

57 Cohen, L.J., “The Role of Evidential Weight in Criminal Proof” (1986) 66 Boston U. L. Rev. 635.Google Scholar

58 Brilmayer & Kornhauser, supra n. 12, at 144.

59 Levi, , Gambling with Truth, supra n. 11, at 140–41.Google Scholar

60 Kaye, D.H., “Comment – Do We Need Calculus of Weight” (1986) 66 Boston Univ. L. Rev. 657.Google Scholar

61 For a discussion of the law on this point, see Salzburg, S., “A special Aspect of Relevance: Counteracting Negative Inferences Associated with the Lack of Evidence” (1978) 66 Calif. L. Rev. 1011.CrossRefGoogle Scholar

62 See Lindley, and Eggleston, , “The Problem of Missing Evidence” (1983) Law Q. Rev. 86.Google Scholar

63 Allen, R., “Tne Nature of Juridical Proof” (1991) 13 Cardozo L. Rev. 373, at 378.Google Scholar

64 Jeffrey, R., Probability and the Art of Judgment (Cambridge Univ. Press, 1992), at 208.CrossRefGoogle Scholar

65 Ibid. Jeffrey makes this point in relating to a future result to be determined. Along similar lines, Nesson, supra n. 2, argues against Pascalian probability in legal factfinding.

66 Cohen, supra n. 3, at 87–92.

67 For a counterargument, see Nesson, supra n. 2, at 1361.

68 A logical (if somewhat cruel) answer to this Problem would be to punish the factfinder if a mistake is found, thus making him bear the risk.

69 Cohen, L.J., “Tne Role of Evidential Weight in Criminal Proof” (1986) 66 Boston Univ. L. Rev. 625, at 645.Google Scholar

70 Cohen, L.J., The Implications of Induction (London, Methuen, 1970), at 10.Google Scholar

71 Zuckerman, A.A.S., “Law, Fact or Justice” (1986) 66 Boston Univ. L. Rev. 487.Google Scholar

72 Freud, S., “The Expert Opinion in the Halsmann Case” (1926) Standard Edition Complete Psychological Works of Sigmund Freud, vol. XXI, 251–53.Google Scholar

73 Dray, W., Laws and Explanation in History (Westport, Greenwood Press, 1957).Google Scholar

74 Hart, and Honore, , “Causal Judgment in History and in the Law” in Dray, W., ed., Philosophical Analysis and History (Westport, Greenwood Press, 1966) 219.Google Scholar

75 Ibid.

76 Porter, T.M., The Rise of Statistical Thinking 1820–1900 (Princeton Univ. Press, 1986) 149–71.Google Scholar