Reconceptualizing the burden of proof

Yale Law Journal

Volumn 122, Issue 5, 2013, Pages 1254-1279

  Cheng, Edward K ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

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EID: 84875096022     PISSN: 00440094     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (56)

1. E.g., Brown v. Bowen, 847 F.2d 342, 345 (7th Cir. 1988) (stating that under the preponderance standard, "the trier of fact rules for the plaintiff if it thinks the chance greater than 0.5 that the plaintiff is in the right").
2. Althen v. Sec'y of Dep't of Health & Human Servs., 58 Fed. Cl. 270, 283 (2003) "[J]udges often express [preponderance of evidence] mathematically by saying the plaintiff must establish the facts necessary to her [or his] case by a probability greater than 0.5 or greater than 50%. "
3. Dan B. Dobbs, The Law of Torts 360 (2000) (alterations in original).
4. E.g., Brown, 847 F.2d at 345-46 (characterizing the beyond-a-reasonable-doubt standard as 0.9 or higher).
5. See Peter Tillers & Jonathan Gottfried, Case Comment, United States v. Copeland, 369 F. Supp. 2d 275 (E.D.N.Y. 2005).
6. A Collateral Attack on the Legal Maxim that Proof Beyond a Reasonable Doubt Is Unquantifiable?, 5 Law Probability & Risk 135, 135-36 (2006) (collecting cases).
7. See, e.g., Michael S. Pardo, Second-Order Proof Rules, 61 Fla. L. Rev. 1083, 1102 n.111 (2009) (classifying the Conjunction Paradox as an "analytical problem[]... for probabilistic rules").
8. See generally Ronald J. Allen & Sarah A. Jehl, Burdens of Persuasion in Civil Cases: Algorithms v. Explanations, 2003 Mich. St. L. Rev. 893 (suggesting that the Conjunction Paradox cannot be resolved by a theory or algorithm alone, but rather requires an additional substantive explanation).
9. * P (B) < P(B).
10. See generally Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. Rev. 401, 404-15 (1986) (reviewing the critiques of probabilistic models of evidence).
11. Richard Lempert, The New Evidence Scholarship: Analyzing the Process of Proof, 66 B.U. L. Rev. 439, 450-67 (1986) (summarizing the criticisms against probabilistic models and the responses to them).
12. Michael S. Pardo & Ronald J. Allen, Juridical Proof and the Best Explanation, 27 Law & Phil. 223 (2008) (describing inference to the best explanation and its advantages over probabilistic models).
13. Nancy Pennington & Reid Hastie, A Cognitive Theory of Juror Decision Making: The Story Model, 13 Cardozo L. Rev. 519 (1991).
14. See, e.g., Thomas A. Mauet, Trial Techniques 24 (8th ed. 2010) ("A theory of the case is a clear, simple story of 'what really happened' from your point of view.... Trials are in large part a contest to see which party's version of 'what really happened' the jury will accept as more probably true. ").
15. Louis Kaplow, Direct Versus Communications-Based Prohibitions on Price Fixing, 3 J. Legal Analysis 449, 451 (2011).
16. E.g., E.L. Lehmann & Joseph P. Romano, Testing Statistical Hypotheses 56-57 (3d ed. 2005) (defining the hypothesis-testing problem as being between a class H and an alternative class K).
17. Readers familiar with classical hypothesis testing may immediately note that classical hypothesis testing strongly favors the null hypothesis, a preference at odds with the usual practice in civil litigation. This preference is not always the case. For example, as described below, the null hypothesis can be given no specific preference. These complications, however, should not detract from the basic point, which is that hypothesis testing is typically comparative, just like in the story model.
18. The explanation derives from a useful presentation by Jonathan Rougier. See Jonathan Rougier, Statistics 2: Bayesian Hypothesis Testing, U. of Bristol Sch. of Mathematics (Dec. 2008), http://www.maths.bris.ac.uk/~mazjcr/stats2/HOBayes2.pdf.
19. 2, I have simply followed the Type I (false positive)/Type II (false negative) distinction commonly used, using the defendant's story as the baseline.
20. Kevin M. Clermont, Death of Paradox: The Killer Logic Beneath the Standards of Proof, 88 Notre Dame L. Rev. (forthcoming 2013) (manuscript at 55-56) (on file with author). A natural response, however, is that if the defendant fails to provide a narrative, the jury will simply substitute the best narrative it can construct in favor of the defendant.
21. To be precise, the plaintiff might prove one element to p > 0.71 and the other to p < 0.71 so long as their product is still greater than 0.5, but the point is the same.
22. P(AB) = 0.24, P(AB) = 0.24, and P(AB) = 0.16. See Charles Nesson, The Evidence or the Event? On Judicial Proof and the Acceptability of Verdicts, 98 Harv. L. Rev. 1357, 1389-90 (1985) (developing this conjunction argument).
23. See generally Ronald J. Allen, Factual Ambiguity and a Theory of Evidence, 88 Nw. U. L. Rev. 604, 609-12 (1994) (discussing the aggregation problem for relative plausibility theory).
24. See, e.g., Richard A. Posner, Antitrust Law 40-41 (2d ed. 2001) (identifying the "fundamental" distinction between "collusive practices" and "exclusionary practices").
25. See, e.g., Richard A. Posner, Antitrust Law 40-41 (2d ed. 2001) (identifying the "fundamental" distinction between "collusive practices" and "exclusionary practices").
26. The subsequent exposition is a relatively standard one found in texts or outlines on Bayesian statistics. See, e.g., George Casella & Roger L. Berger, Statistical Inference 414 (2d ed. 2002).
27. E.g., Ronald Christensen, Testing Fisher, Neyman, Pearson, and Bayes, 59 Am. Statistician 121, 123 (2005) ("The absence of a clear source for the prior probabilities seems to be the primary objection to the Bayesian procedure. ").
28. Here, I use the term "likelihood" for its precise statistical meaning, which is the probability of seeing the observed data under an assumed model. "Likelihood" should not, as in common parlance, be conflated with probability more generally.
29. See, e.g., Richard A. Posner, Antitrust Law 40-41 (2d ed. 2001) (identifying the "fundamental" distinction between "collusive practices" and "exclusionary practices").
30. As it turns out, this assumption-that the burden of production is met-may be quite critical, for it excludes extreme cases in which both the plaintiff's and the defendant's narratives are ridiculous or unlikely. In those cases, juries (or perhaps the court on summary judgment) will find for the defendant regardless of the ratios.
31. Δ{pipe}E) in the strict mathematical sense. Rather, the expression is merely what the legal system uses as an estimate of the true value.
32. Indeed, flipping the conditional is often called the "transposition fallacy, " and is an error to be avoided. In this case, however, setting the prior odds to 1 leads to the result.
33. 58 N.E.2d 754 (Mass. 1945).
34. Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv. L. Rev. 1329, 1340-41 & n.37, 1346-50 (1971).
35. Jonathan B. Baker, Vertical Restraints with Horizontal Consequences: Competitive Effects of "Most-Favored-Customer" Clauses, 64 Antitrust L.J. 517, 531-32 (1996).
36. In an extreme case in which the defendant disclaimed owning any blue buses at all, the fact that the plaintiff was hit by the defendant's bus on the dark night might provide some sort of existence proof, but that is not the inquiry here.
37. This market share inference may also explain why some people who are uncomfortable with finding liability based on an 80 percent market share change their position when the numbers become 99 percent or 99.9 percent.
38. L. Jonathan Cohen, The Probable and the Provable 74-81 (1977).
39. Allan G. King, "Gross Statistical Disparities" as Evidence of a Pattern and Practice of Discrimination: Statistical Versus Legal Significance, 22 Lab. Law. 271, 272 (2007).
40. Michael G. Collins, Article III Cases, State Court Duties, and the Madisonian Compromise, 1995 Wis. L. Rev. 39, 136.
41. In this context, the defendant's negation would not appear to violate the rule requiring a specific story, since a substance is either capable of causing the disease or not. Even if one were to substitute a more specific story-e.g., that the plaintiff's disease was caused by some other known causal agent-the ultimate conclusion should still hold.
42. See, e.g., Richard A. Posner, Antitrust Law 40-41 (2d ed. 2001) (identifying the "fundamental" distinction between "collusive practices" and "exclusionary practices").
43. See, e.g., Richard A. Posner, Antitrust Law 40-41 (2d ed. 2001) (identifying the "fundamental" distinction between "collusive practices" and "exclusionary practices").
44. Amos Tversky & Daniel Kahneman, Evidential Impact of Base Rates, in Judgment Under Uncertainty: Heuristics and Biases 153, 156-57 (Daniel Kahneman et al. eds., 1982).
45. This discussion of res ipsa was in part inspired by David Kaye, Probability Theory Meets Res Ipsa Loquitur, 77 Mich. L. Rev. 1456 (1979), which looks at res ipsa through the perspective of probability theory.
46. See, for example, Dupont v. Fred's Stores of Tenn., Inc., 652 F.3d 878, 882-84 (8th Cir. 2011), where a customer allegedly sustained a head injury when plastic bins fell off of a shelf.
47. See Chris Guthrie et al., Inside the Judicial Mind, 86 Cornell L. Rev. 777, 808-09 (2001) (discussing base rate issues in the res ipsa context).
48. See Jonathan J. Koehler, When Do Courts Think Base Rate Statistics Are Relevant?, 42 Jurimetrics J. 373, 377 (2002) (describing cases in which courts have found base rates irrelevant).
49. Josh Bowers, Physician, Heal Thyself: Discretion and the Problem of Excessive Prosecutorial Caseloads, A Response to Adam Gershowitz and Laura Killinger, 106 Nw. U. L. Rev. 143, 152 n.34 (2011) ("[E]mbedded in the prosecutor's burden of proof beyond a reasonable doubt is a normative abhorrence for Type I errors (wrongful convictions) as compared to Type II errors (wrongful acquittals). ").
50. Gregory M. Gilchrist, Plea Bargains, Convictions and Legitimacy, 48 Am. Crim. L. Rev. 143, 147 (2011) ("The presumption of innocence and the government's burden of proof beyond a reasonable doubt cause the evidence to be weighed in a manner that favors, by design, wrongful acquittals over wrongful convictions. ").
51. See Boaz Sangero & Mordechai Halpert, Proposal To Reverse the View of a Confession: From Key Evidence Requiring Corroboration to Corroboration for Key Evidence, 44 U. Mich. J.L. Reform 511, 544-46 (2011) (demonstrating how the reasonable doubt standard can be quantified in order to limit the number of wrongful convictions to a predetermined level).
52. See Peter Tillers & Jonathan Gottfried, Case Comment, United States v. Copeland, 369 F. Supp. 2d 275 (E.D.N.Y. 2005).
53. This analogy between the criminal burden of proof and classical hypothesis testing is often found in the statistics literature for purposes of illustration. See, e.g., Michael W. Trosset, Criminal Law and Statistical Hypothesis Testing (1997) (unpublished technical report), http://www.stat.purdue.edu/~yuzhu/stat514s2006/Supplement/law.ps.
54. But see Tung Liu & Courtenay C. Stone, Law and Statistical Disorder: Statistical Hypothesis Test Procedures and the Criminal Trial Analogy (Dept. of Econ., Ball State Univ., Working Paper No. 200601, 2006), http://econfac.iweb.bsu.edu/research/workingpapers/bsuecwp200601r1liu.pdf (expressing concerns about using such analogies in attempting to teach statistics).
55. See generally Michael J. Saks & Samantha L. Neufeld, Convergent Evolution in Law and Science: The Structure of Decision-Making Under Uncertainty, 10 Law Probability & Risk 133 (2011) (showing the uncanny convergence in approach between statistical hypothesis testing and criminal adjudication).
56. J. Neyman & E. S. Pearson, On the Problem of the Most Efficient Tests of Statistical Hypotheses, 231 Phil. Transactions Royal Soc'y London Series A 289 (1933).