D.H. Kaye [*]
Notice: This document is the introduction to an article published in The Journal of Criminal Law & Criminology, Vol. 85, No. 3, Pp. 676-695, 1995, © 1995 by Northwestern University School of Law.
Keywords: evidence, forensic DNA, binning, likelihood ratio
The basic concepts are always the hardest. This is particularly true in the study of evidence. Relevant evidence is evidence that alters the probability of a fact that matters, and relevant evidence generally is admissible unless it is too prejudicial.  Despite this seemingly simple formulation, questions of relevance relating to DNA evidence -- even to the most elementary concept of a "match" between two DNA samples -- can be confusing.
Well established methods of molecular biology permit laboratories to compare DNA from a crime scene to DNA from a defendant.  If the DNA in these samples appears to be similar, the match usually is powerful evidence that the incriminating DNA came from the defendant. To describe the incriminating effect of the resemblance, scientists may use numbers. The numbers most frequently seen in criminal cases are estimates of the relative frequency of other people whose DNA also would match the crime scene DNA according to the criteria the laboratory uses for declaring a match -- in a word or two, the match frequency. 
In court the most successful objection to these numbers has been that the standard computational method does not account adequately for "population structure."  Arguments targeting the criteria for declaring a match have fared less well.  In a recent article in this journal on the "DNA War," Professor William C. Thompson seeks to correct this situation. Already a veteran of a few skirmishes in the war,  Professor Thompson believes that when a defendant argues that "the match criteria should have been drawn in a narrower manner that excludes him," the finding of a match "could properly be excluded under Federal Rule 403."  At the very least, he thinks, the court should allow expert testimony to the jury that the match criteria are too inclusive.  In contrast, I have argued that:
Disputes over the strictness of particular windows or the optimal match window -- when there is no such thingÄmay confuse and perplex the jury when it considers the probative value of a match. As a result, such proof generally should not be allowed. 
This article shows that Professor Thompson's call for exclusion of DNA evidence or for expert testimony on the definition of a match is not responsive to the concern that animates and underlies his proposal. If anything, a more radical responseÄrejecting the very notion of a simple "match" -- may be in order. To reach these conclusions, Parts I and II describe the basic ideas of "matching" and "binning" that are central to the usual analysis of DNA evidence. Part III outlines a theory of probative value that illuminates the limitations of match-binning. With these fundamentals in place, Parts IV and V address Professor Thompson's concern and demonstrate that, depending on circumstances yet to be established, it could warrant a modification in the way that DNA evidence is presented, though not necessarily the one that Professor Thompson endorses.
The analysis demands a careful definition of probative value and a clear understanding of the matching process and its statistical properties. These can be obtained only in the currency of some mathematical notation and concepts. This price, however, is well worth paying. At the most practical level, the exercise promises to improve the presentation of DNA evidence. In addition, it illuminates the workings of a theory of probative value and inductive proof that evidence scholars have been propounding for the some time. 
* Regents' Professor, Arizona State University, College of Law, Box 877906, Tempe AZ 85287-7906 (480) 965-2922, firstname.lastname@example.org). I am grateful to Bruce Budowle, Jay Koehler, William Thompson, Bruce Weir, and especially David Balding for comments on a draft of this paper. [BACK]
1. See Fed. R. Evid. 401 (" Relevant evidence' means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence."); Fed. R. Evid. 402 ("All relevant evidence is admissible, except as otherwise provided . . . ."); Fed. R. Evid. 403 ("Although relevant, evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence."). [BACK]
2. The DNA at the crime scene may come from the defendant's blood, semen or saliva. In other cases, the victim's DNA may be found on the defendant's property. See, e.g., State v. Bible, 858 P.2d. 1152 (Ariz. 1993); People v. Castro, 545 N.Y.S.2d 985 (Sup. Ct. 1989). Although the discussion here explicitly refers only to the former situation, the analysis applies to both methods of linking a defendant to a crime. [BACK]
3. Some courts seem to require such testimony. E.g., Nelson v. State, 628 A.2d 69, 76 (Del. 1993) (trial court's exclusion of match frequency "inherently inconsistent" with its admission of testimony of a match, because "without the necessary statistical calculations, the evidence of the match was 'meaningless' to the jury."); State v. Brown, 470 N.W.2d 30 (Iowa 1991) (expert testimony that "the likelihood of a person matching in all four fragments . . . would be one in several billion" admissible, since "[w]ithout statistical evidence, the ultimate results of DNA testing would become a matter of speculation."); State v. Vandebogart, 616 A.2d 483, 494 (N.H. 1992) ("A match is virtually meaningless without a statistical probability expressing the frequency with a match could occur."). It would not, however, be "meaningless" to inform the jury that two samples match and that this match makes it more probable, in an amount that is not precisely known, that the DNA in the samples comes from the same person. Nor, when all estimates of the frequency are in the millionths or billionths, would it be meaningless to inform the jury that there is a match that is known to be extremely rare in the general population. D.H. Kaye, The Forensic Debut of the National Research Council's DNA Report: Population Structure, Ceiling Frequencies, and the Need for Numbers, 34 Jurimetrics J. 369, 380-82 (1994). [BACK]
4. United States v. Jakobetz, 747 F. Supp. 250, 263 (D. Vt. 1990) ("substructure is arguably the weakest link of the DNA profiling chain"), aff'd, 955 F.2d 786 (2d Cir. 1992), cert. denied, 113 U.S. 104 (1992). See also Committee on DNA Technology in Forensic Science, National Research Council, DNA Technology in Forensic Science 79 (1992) [cited as NRC Report] ("whether actual populations have significant substructure for the loci used" is "the key question"). "Substructure" refers to the presence of subgroups that have distinctive DNA patterns and that tend to mate among themselves. For the view that courts sometimes have erred in excluding the estimates on this ground, see D.H. Kaye, DNA Evidence: Probability, Population Genetics, and the Courts, 7 Harv. J. L. & Technology 101 (1993). [BACK]
5. See Kaye, supra note 4; William C. Thompson, Evaluating the Admissibility of New Genetic Identification Tests: Lessons from the "DNA War," 84 J. Crim. L. & Crimin. 22, 50-51 (1993) ("Only one court has held that the dispute over the FBI's matching procedure precludes the admissibility of the test under Frye."). [BACK]
6. Thompson, supra note 5. [BACK]
7. See, e.g., People v. Simpson, No. BA097211 (Los Angeles County Superior Court, Motion to Exclude DNA Evidence, Oct. 4, 1994); State v. Anderson, No. CR 46255 (Dist. Ct., Bernalillo County, Memorandum in Opposition to the Introduction of the FBI's DNA Evidence, Apr. 3, 1990). [BACK]
8. Thompson, supra note 5, at 60. Professor Thompson recommends exclusion only when "the defendant makes a strong showing prior to trial that the observed discrepancies are unlikely to have arisen if the 'matching' prints have a common source." Id. [BACK]
9. Id. at 60 n.171. [BACK]
10. Kaye, supra note 4, at 114-15 (footnotes omitted). [BACK]
11. Although this theory has deep roots in the works of logicians, philosophers, psychologists and statisticians, much of the exposition and development in the legal literature has come from the Michigan Law School. See, e.g., Richard Lempert, The New Evidence Scholarship: Analyzing the Process of Proof, 66 B.U. L. Rev. 439 (1986), reprinted in Probability and Inference in the Law of Evidence: The Limits and Uses of Bayesianism 61 (Peter Tillers & Eric C. Green eds., 1988); Richard D. Friedman, Character Impeachment Evidence: Psycho-Bayesian [!?] Analysis and a Proposed Overhaul, 38 UCLA L. Rev. 637 (1991); Richard D. Friedman, A Close Look at Probative Value, 66 B.U. L. Rev. 733 (1986). The "Michigan School," however, emphasizes Bayes's rule for combining new information with prior probabilities of hypotheses. The approach used here focuses on the concept of relative likelihood which can be embraced without a commitment to Bayesian reasoning in general. See, e.g., D.H. Kaye, Introduction: What is Bayesianism? in Tillers & Green, supra, at 1. There are critics of the Michigan School, but they do not always offer clear alternatives. See, e.g., Ronald J. Allen, Factual Ambiguity and a Theory of Evidence, 88 Nw. U. L. Rev. 604, 627-28 (1994) (sketching a "theory of juridical evidence" that "reduces to the proposition that a disinterested fact finder reconstructs the past based on all the observational inputs available at the moment of judging"). [BACK]
last updated 11/24/98