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In 1997 a panel of the Court of Appeals for the Second Circuit, in an opinion in United States v. Shonubi ("Shonubi IV"), struck down a sentencing judge's use of certain statistics to estimate the amount of heroin that the defendant in that case allegedly imported. (United States v. Shonubi, 103 F.3d 1085 (2d Cir., 1997).) Shonubi IV is not particularly important or interesting because of what it portends for the future use of statistical evidence. Shonubi IV is probably little more than a blip on the landscape of the law concerning the use of statistical evidence: it is unlikely to significantly inhibit or retard -- much less reverse -- the long-standing trend in favor of the admissibility of statistical evidence and argument in federal litigation. The opinion of the court of appeals is interesting, important, and--above all--depressing because of what it suggests about the difficulties that many judges may have when they confront statistical methods and statistical evidence: it suggests that quite a few judges--including some very eminent and intelligent ones--still may not have a grasp of some basic characteristics of probabilistic and statistical methods and arguments.

Charles O. Shonubi, a resident of the United States but a Nigerian citizen, was arrested at John F. Kennedy International Airport while allegedly trying to import heroin. At the time of his arrest--December 10, 1991 -- there were -- it was later determined -- 427.4 grams of heroin in his stomach. Before arriving at JFK Shonubi or someone else had inserted that heroin into 103 balloons and, some time later, Shonubi had swallowed those heroin-filled balloons. Shonubi had apparently made previous trips in which he had used this balloon-swallowing method. On those previous trips he had escaped detection. This time, however, his balloon-swallowing modus operandi failed, and he was arrested.

Shonubi was later tried in a federal district court. He was convicted of possessing and importing heroin on December 10, 1991. However, at both the trial and the sentencing hearing, evidence was presented that Shonubi had made at least seven other drug-smuggling trips. Moreover, the sentencing judge, Jack B. Weinstein, specifically made a finding that Shonubi had made seven other heroin-smuggling trips from Nigeria to the United States, via JFK International Airport. This finding of fact, through all the subsequent proceedings involving Shonubi, was never questioned or challenged.

Under the applicable federal sentencing guidelines the severity of Shonubi's sentence for possessing and importing heroin on December 10, 1991, depended in part, not only on the quantity of heroin that Shonubi possessed and imported on December 10, 1991, but also on the quantity of heroin that Shonubi possessed and imported during his seven other known drug-smuggling trips; the severity of his sentence depended in part, that is, on the aggregate weight (in grams) of the heroin that Shonubi imported during all eight of his known drug-smuggling trips from Nigeria. For example, if Shonubi was found to have imported 1000 grams of heroin or more, and not just 427.4 grams, his sentence would be "enhanced," and if it was found that he imported 3000 grams of heroin or more, his sentence would be enhanced yet more. The question at the sentencing hearing -- or so it was assumed -- then became, roughly, the following:

What was the aggregate amount of heroin (in grams) that Shonubi imported in all eight of drug-smuggling trips that Shonubi was known to have made?

To answer this question, the federal probation service and Judge Weinstein adopted a simple expedient: they multiplied by eight (8) the amount of heroin that Shonubi was determined to have been carrying at the time of his arrest. This procedure yielded the product 3419.2 grams. Furthermore, according to Judge Weinstein (in an opinion that I shall call "Shonubi I"), this multiplication procedure--together with other evidence-- showed by a preponderance of the evidence, that "the defendant did import at least 3419.2 grams of heroin" in his eight drug-smuggling trips taken together. (See United States v. Shonubi, 802 F. Supp. 859 (E.D.N.Y., 1992) ("Shonubi I").)

Shonubi appealed his sentence. The Court of Appeals for the Second Circuit, in Shonubi II, vacated the sentence imposed by Judge Weinstein and it remanded the matter to Judge Weinstein for resentencing. It did so in part because, it said, there was no "specific evidence" in the record to support the finding that Shonubi had imported 3419.2 grams of heroin in his eight drug-smuggling trips. (See United States v. Shonubi, 998 F.2d 84 (2d Cir, 1993) (Oakes, Newman & Cardamone, JJ.) ("Shonubi II").)

At the resentencing the prosecution offered certain data collected by the United States Customs Service. This data consisted of the quantities of heroin found in the possession of 117 other drug smugglers who were arrested at the JFK airport between September 1, 1990 and December 10, 1991, which were the dates of Shonubi's first and last known drug-smuggling trips. Those other drug smugglers, like Charles Shonubi, were Nigerian citizens who transported illegal heroin by mixing heroin with another substance to make a kind of paste, stuffing the heroin-larded paste into balloons, and then swallowing the balloons.

There was considerable discussion during the sentencing proceedings (by several sets of experts and by the attorneys for the parties) about the proper use of the customs service data, but--to make a long story appropriately short --Judge Weinstein relied on the customs service data, as well as on other evidence (including, for example, the testimony of an expert on the economics of heroin smuggling and trafficking), to reach the conclusion and make the finding that the aggregate amount of heroin that Shonubi had imported during his eight known drug-smuggling trips was between 1000 and 3000 grams. Stated differently, given that it had been established that Shonubi had imported 427.4 grams on his eighth and final trip, Judge Weinstein found that it was more probable than not that Shonubi had imported at least 572.6 grams in all seven of his remaining known drug-smuggling trips. Judge Weinstein wrote a lengthy opinion (see United States v. Shonubi, 895 F.Supp. 460 (E.D.N.Y.) ("Shonubi III"))--more than 70 printed pages long--setting forth the justification for this factual finding, and, more generally, "explaining how a sentencing judge--and a trier of fact generally--reaches a decision." Judge Weinstein relied on this finding in sentencing Shonubi. Had Judge Weinstein found either that Shonubi had imported only 427.4 grams or that Shonubi had imported less than 1000 grams, Shonubi would have received a lesser sentence.

Shonubi again appealed his sentence. In Shonubi IV the Second Circuit again vacated the sentence imposed by Judge Weinstein. Judge Newman, speaking for an eminent three-judge panel that included Judges Cardamone and Calabresi, said that Judge Weinstein's "comprehensive opinion is a valuable addition to the legal literature on the subject of evidence in particular and judicial decision-making in general." It is not entirely clear that the same can be said of Judge Newman's opinion.

In vacating the sentence imposed by Judge Weinstein, the Second Circuit did not assert that there had to be "direct" evidence of the amount of heroin that Shonubi may have carried during the smuggling trips that he carried out. Judge Weinstein's preemptive discussion of that bankrupt idea had prevented the Second Circuit from adopting it. Nonetheless, the Second Circuit, in Shonubi IV, reiterated its earlier view that a finding of the quantity of heroin that Shonubi had carried on the seven smuggling trips during which he was not arrested had to be supported by "specific evidence." The court now further asserted that the customs service data did not constitute "specific evidence" of that quantity' it said, that is, that the data about the quantities of heroin imported by other balloon-swallowing Nigerian drug smugglers was not specific evidence of the amount of heroin that Shonubi had imported during his first seven known drug-smuggling trips.

The reasoning of the court of appeals in Shonubi IV has a kind of surface plausibility. (I have tried to couch the thesis of Shonubi IV regarding evidentiary specificity in the most appealing way possible.) But, in truth, the opinion of the court of appeals in Shonubi IV is not a distinguished one. Although there are various grounds on which one might reasonably question Judge Weinstein's final judgment about the total amount of heroin that Shonubi imported during his eight smuggling trips, the Second Circuit's view that the statistical evidence relied upon by Weinstein was defective because it was not "specific" is most unfortunate. The notion that evidence of a person's actions must be somehow "specific," either to that person or to his behavior on a specific occasion, is, at best, otiose and, at worst, nonsensical.

One possible way to try to make sense out of Judge Newman's opinion is to view it as a condemnation of statistical evidence in general. On this reading of Shonubi IV, Judge Newman was trying to say that statistical evidence, by its nature, is never "specific" to the matter in issue. There is some support for the interpretation of Shonubi IV: Judge Newman is plainly wary of statistical evidence, at least in sentencing proceedings. But there are two problems with the view that Shonubi IV is, at bottom, a repudiation of statistical evidence and statistical methods. First, Judge Newman, in Shonubi IV, argues that some of the non-statistical evidence in the case is worthless because it is not "specific evidence" of the quantity of heroin Shonubi carried on the seven known drug smuggling trips that Shonubi managed to make without being arrested or detected. Second, Judge Newman, in Shonubi IV, seems to accept the use of statistics and statistical methods for some purposes in drug sentencing proceedings.

But if Judge Newman and the Second Circuit do not wish to make a blanket condemnation of statistics and statistical methods, they are caught in a quandary. Having accepted the thesis that statistics can be legitimately used as a basis for inferences about at least some unknown maters or events -- and having also said that non-specific evidence about an unknown matter is unacceptable --, Judge Newman and the Second Circuit must now embrace at least the following proposition:

Whenever a valid inference can be drawn from statistics, the statistics on which the inference rests are necessarily, somehow, "specific" to the particular unknown or unobserved matter that is in issue.

But this proposition -- alas! -- makes no sense at all.

The central point of gathering statistics for the purpose of drawing inferences about unknown matters is to gather and summarize data about what is known in order to lay a basis for drawing conclusions about the unknown. That means, in principle, that statistics, when offered as a basis for inferences about unknown matters, are never "specific" to the matter about which an inference is to be made. The validity of drawing inferences on the basis of statistics, thus, never rests on the "specificity" of the statistical evidence to the unknown matter in question. What assures the potential inferential value of the statistics one chooses to use is, rather, the perceived similarity of the known or observed events or matters observed to the unknown or unobserved matter or event about which a conclusion is sought to be reached.

The last point can also be expressed in the following way: what matters (according to some statistical theorizing) is that the person or persons entrusted with drawing an inference about some unknown matter or event choose an appropriate "reference class" as a basis for arguments and inferences about that unknown matter or event. It is never the case, however, that the chosen reference class is, in Judge Newman's words, "specific" to the unknown matter or event about which an inference is to be drawn. The premise of the procedure that includes the selection of a reference class (for the purpose of making an inference about some unknown matter or event) is that matters or events that are distinct from, but not significantly different from, the unknown matter or event in question may be a basis for drawing an inference about the unknown matter or event. Given that Judge Newman purports (if only grudgingly) to accept the use of statistics as a basis for drawing inferences about unknown matters, he cannot coherently require that the statistical evidence that a fact finder uses have a "specific" connection or relationship to the unknown matter or event in question.

It might be argued that the "true ground" for the decision of the court of appeals in Shonubi IV was its unarticulated suspicion that Judge Weinstein's use of drug-smuggling balloon swallowing Nigerians other than Shonubi as a reference class for drawing inferences about Shonubi was unjustified. If the court of appeals had chosen to rest its condemnation of Judge Weinstein's use of the customs service data on that ground, the court of appeals might have been able to develop a plausible argument about why Judge Weinstein was unjustified in assuming that the behavior of the 117 other drug Nigerian drug smugglers between 1989 and 1991 was sufficiently like Shonubi's behavior to be regarded as "representative" of Shonubi's (unknown) behavior and why Judge Weinstein was, thus, unjustified in thinking that the behavior of those other drug smugglers was an adequate basis for drawing conclusions about Shonubi's behavior during the seven drug-smuggling trips when he was not caught.

The trouble is that, although the court of appeals could have said these sorts of things, it did not do so, but instead chose to say that there was no "specific" evidence of Shonubi's behavior. And by saying what it did say, the court of appeals implied (inappropriately!) that evidence about the behavior of a group or another individual can never be the basis for inferences about the behavior of an individual. Worse yet--although the court of appeals itself clearly failed to see this--, by saying what it did say, the court of appeals implied--inappropriately!--that statistics can never be the basis for drawing an inference about any matter or event that is not already contained in the statistics submitted to the sentencing court.

If one takes the logic of Shonubi IV seriously, worse things yet may follow. In particular, the Second Circuit's apparent belief in the absolute necessity of "specific evidence" for valid inference implies that one matter or thing or event can never be evidence of, or a sign of any other matter or thing or event. Astonishingly enough, the court of appeals practically says as much when it asserts, for example, that an analysis of the economics of the narcotics trade and information about Shonubi's attitudes toward risk do not constitute "specific evidence" of Shonubi's behavior on the seven drug-smuggling trips that he took without being arrested. The court of appeals explains this strange conclusion by asserting that, although such matters may be specific as to Shonubi (the man), they are not specific as to his conduct during his seven prior trips. But if matters such as personal attitudes toward risk are not "specific evidence," it is hard to avoid the conclusion that the only sufficiently specific evidence of what Shonubi did during his first seven drug-smuggling trips is what Shonubi did during his first seven drug-smuggling trips. Any other matters are, practically by definition, not "specific" to Shonubi's conduct during those particular trips!

It is hard to say whether it is worse to view Shonubi IV as a case about statistical evidence or as a case about the properties and characteristics of evidence and inference in general. If Shonubi IV is about evidence and inference in general, Judge Weinstein, one of the country's most eminent evidence scholars, was quite right in saying,

What the [federal] Rules [of Evidence] do not do is categorize, for exclusionary purposes, forms of relevant evidence as direct, circumstantial, and '"specific." The new vaguely defined classification of "specific evidence" relied upon by the court of appeals in Shonubi II and Shonubi IV is not only unauthorized by controlling case law and the federal Rules of Evidence, it runs counter to our modern theory of forensic evidence. The unique Second Circuit rule represents a retrogressive step towards the practice relied upon from the Middle Ages to the late Nineteenth century, which often limited the use and weight of evidence by category of evidence and type of case.

(United States v. Shonubi, 962 F. Supp. 370, 375 (E.D.N.Y. 1997) ("Shonubi V"(!).)

But if Shonubi IV is not about evidence and inference in general, and if it is "only" about statistical evidence, we are not much better off. I say this for two reasons. First, as the Second Circuit itself seems to recognize, it is not apparent how the logic of Shonubi IV can be limited to statistical evidence. Second, in Shonubi IV the court of appeals chose the worst possible ground for repudiating Judge Weinstein's use of statistics. Statistical evidence and statistical methods have many potential weaknesses. But the allegedly "non-specific" character of the statistics that Judge Weinstein used in the resentencing of Shonubi is not one of the possible reasons for the possible infirmity of the statistics that Judge Weinstein used. For if that were the true basis for the infirmity of the statistics that Judge Weinstein used, almost all statistical evidence would have to be considered worthless. (If statistical evidence is inherently worthless in sentencing proceedings, it is hard to see why it would have any more value when it is offered in other proceedings or in civil or criminal trials.)

Quite a long time ago I heard an eminent statistician lecture--hector, really--a large group of eminent law teachers about the importance of statistical theory and about the need for lawyers, law teachers, and judges to understand the rudiments of statistical evidence and argument. I prefer to phrase his basic point in the following way:

It is very important for the judiciary and the legal profession as a whole to develop a better understanding of the rudiments of probability theory and the logic of inference and proof.

I can only hope that Shonubi IV is not representative of the general state of the judiciary's understanding of such matters. Speaking in the vernacular of statistical theory, I might express my hope this way: I very much hope that the Second Circuit's opinion in Shonubi IV is not a reference class or a part of a reference class that should serve as a basis for predictions about how other courts (or the Second Circuit itself) will deal with statistical evidence and statistical inference in the future. In short, I fervently hope that the Second Circuit's opinion in Shonubi IV is thoroughly unrepresentative and atypical.

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This comment is a portion of a draft of a paper published in the Cardozo Law Review. See P. Tillers, Introduction: Three Original Contributions to Three Important Problems in the Law of Evidence, 18 Cardozo L. Rev. 1875 (1997). Most footnotes and references have been stripped from this online comment.

I am, in general, quite critical of the Second Circuit's handling of Shonubi. I am particularly critical of the Second Circuit's opinion in Shonubi IV. In fairness, however, I must disclose that I was a member of the two-member "panel of experts" that Judge Weinstein appointed to assist him after the remand to Judge Weinstein for resentencing following Shonubi II. (David Schum was the other member of this court-appointed panel.) But I believe that my critical comments about Judge Newman's opinion in Shonubi IV are not attributable to a wounded ego or ruffled feelings. Judge Weinstein's opinion in Shonubi was, of course, his and not mine (or David Schum's), and Judge Weinstein certainly did not embrace all of the views that David Schum and I put forward in our affidavits and reports. I might also note that the Second Circuit--to my great chagrin--cited one of the Schum-Tillers reports in support of its thesis that "specific evidence" was necessary. Shonubi IV, 103 F.3d at 1091. I won't argue here that the Second Circuit's interpretation of the Schum-Tillers reports was unreasonable or unjustified, but I do wish to say--for the historical record--that I certainly did not mean to say what the Second Circuit thought we were saying.