33rd & 424th District Courts

Consider Judge Jack B. Weinstein, a leading authority on the American law of evidence.
He has long advocated more extensive forensic use of statistical methods. If any
reputable judge were to advocate quantification of the reasonable doubt standard, one
might expect that Weinstein would be the one to do so. A search of Weinstein’s judicial
record does show that Weinstein has written two opinions that discuss quantification of
the reasonable doubt standard. See United States v. Fatico, 458 F. Supp. 388, 409-11
(E.D.N.Y. 1978) and Vargas v. Keane, 86 F.3d 1273, 1281-84 (2d Cir., 1996) (Weinstein,
J., concurring, sitting “by designation” – i.e., temporarily – on the United States Court of
Appeals for the Second Circuit). However, neither of these opinions directly embraces
quantification of the reasonable doubt standard. In these opinions Weinstein reports the
results of two surveys that were conducted under his auspices. In both surveys – one
survey canvassed some federal trial judges; the other, jurors – the respondents were asked
to use numbers (in the form of percentages) to express their judgment of the amount of
certainty that is required for conviction of crime under the reasonable doubt standard.15
To the extent that the actual language of Fatico and Vargas is a true barometer of
Schum, Quantifying Burdens of Proof: A Likelihood Ratio Approach, 27 Jurimetrics Journal 383 (1987);
David Hamer, Probabilistic Standards of Proof, Their Complements, and the Errors That Are Expected to
Flow from Them, 1 The University of New England Law Journal 71 (2004).
15 In Vargas the respondents – jurors – were asked to use quantitative mathematical language – the
language of percentages – to describe how sure they had to be of the guilt of the defendant under different
non-numerical formulations of the reasonable doubt standard.
Weinstein’s motivations for conducting those surveys, Weinstein was investigating how
judges and jurors view the reasonable doubt standard, not because he was working
toward the day when the fuzzy legal concept of reasonable doubt would be replaced with
a crisp mathematical formulation, but because he wanted to “precisiate”16 the reasonable
doubt standard – to explain, precisely, how the fuzzy concept of reasonable doubt works
in trials. If even math-friendly judges such as Jack Weinstein do not endorse the use of
numbers in criminal trials to clarify or reformulate the reasonable doubt standard, the
prospects for mathematical quantification at trial of the reasonable doubt standard would
seem to be virtually nonexistent.

But what are we to make of another decision by the very same Jack B. Weinstein: United
States v. Copeland, 369 F. Supp. 2d 275 (E.D.N.Y., 2005)? In Copeland Weinstein used
a numerical probability (expressed as a percentage) to quantify a standard of persuasion
(“reasonable probability”). Is Copeland compatible with the prevailing rule that
reasonable doubt cannot be quantified in trials? If “substantial probability” can and
should be quantified, why can’t and why shouldn’t “reasonable doubt” be quantified?
Does Copeland amount to a collateral attack on the rule prohibiting quantification of the
reasonable doubt standard?

Is Judge Weinstein’s quantification of the “reasonable probability” standard (together
with his quantification of the complementary “clear and convincing evidence” standard17)
compatible or incompatible with the customary legal maxim that the standard of “proof
beyond a reasonable doubt” is not quantifiable? Wags have noted that lawyers are trained
to distinguish the indistinguishable. Viewed from a technical legal perspective,
Weinstein’s decision in Copeland III is not directly inconsistent with the customary legal
rule barring quantification of reasonable doubt.18 Broadly viewed, however, Copeland III
raises serious questions about the soundness of the well-entrenched legal maxim that the
reasonable doubt standard is unquantifiable. If standards such as “reasonable probability”
and “clear and convincing evidence” can be quantified, why can’t reasonable doubt be
quantified? What is it, precisely, that allegedly makes it impossible or inadvisable to
quantify reasonable doubt?