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The criminal burden of proof (ie beyondA reasonable doubt) is famously attributed to “Blackstone’s Ratio”:

It is better that ten guilty persons escape than that one innocent suffer.

I’m not sure if my maths and/or semantics computations are way off, but in order for the probability percentage threshold to be calibrated so as to satisfy this formulation, it seems to me that for every one proper conviction one would want (for lack of a better word.. maybe “guarantee” or “ensure”?) to have 10 false acquittals, out of a total of 11 (1+10) cases. As 1/11=0.09090909…, or 9.1%, is the numerical definition of a reasonable doubt that of 9.1% probability or above?

I’ve often seen it quoted as 99% certainty but what would be the basis of this formulation?

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    "for every one proper conviction one would want to have 10 false acquittals": that's not what this means at all. First, it is a statement about the relative desirability of false acquittals and false convictions, not proper convictions. Maybe the ratio of false acquittals to proper convictions is 1:1,000,000. Second, it's not a statement about an ideal rate. Someone who says "I'd rather have ten wilted salads than a glass of bad milk" does not seek to guarantee that every glass of bad milk is somehow "balanced" by allowing a number of salads to wilt; ideally they'd have none of either.
    – phoog
    Dec 7, 2023 at 12:07

2 Answers 2

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I'm not aware of any jurisdiction that defines it numerically.

The guidance is that the jury is directed like this:

The prosecution must prove that D is guilty. D does not have to prove anything to you. D does not have to prove that he/she is innocent. The prosecution will only succeed in proving that D is guilty if you have been made sure of D’s guilt. If, after considering all of the evidence, you are sure that D is guilty, your verdict must be ‘Guilty’. If you are not sure that D is guilty, your verdict must be ‘Not Guilty’.

If reference has been made to ‘beyond reasonable doubt’ by any advocate, the following may be added:

You have heard reference to the phrase ‘beyond reasonable doubt’. This means the same as being sure.

See the Crown Court Compendium, which provides guidance and draft directions in relation to points of law and practice, with case references.

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Reasonable doubt is not a quantifiable concept. It is an error in law to instruct a jury to consider it in the manner you describe.

Reasonable doubt is not amenable to mathematical calculation or even analogy to probability. It is a wholly different kind of threshold. Reasonable doubt is binary, not a matter of degree. It is an error for a judge to liken reasonable doubt to a degree of certainty; doing so warrants a new trial (R. v. Bisson, [1998] 1 S.C.R. 306).

This is not a probabilistic exercise. No matter what probability threshold one might set, there would be doubts greater than that threshold that would nonetheless not be reasonable doubts if they were not based in the evidence or lack of evidence. The quality and source of the doubt, not merely its magnitude, are critical to determining the reasonableness of the doubt.

The Supreme Court of Canada has explained (R. v. Lifchus, [1997] 3 S.C.R. 320):

the standard of proof beyond a reasonable doubt is inextricably intertwined with that principle fundamental to all criminal trials, the presumption of innocence;

the burden of proof rests on the prosecution throughout the trial and never shifts to the accused;

a reasonable doubt is not a doubt based upon sympathy or prejudice;

rather, it is based upon reason and common sense;

it is logically connected to the evidence or absence of evidence;

it does not involve proof to an absolute certainty; it is not proof beyond any doubt nor is it an imaginary or frivolous doubt; and

more is required than proof that the accused is probably guilty ‑‑ a jury which concludes only that the accused is probably guilty must acquit.

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    FWIW, Canadian law and the law of every U.S. jurisdiction is in accord on this point with one small exception, which is that some U.S. jurisdictions have adopted a statutory rule that a DNA test meeting certain standards that shows or rules out the existence of a genetic relationship with a probability in excess of X% is proof beyond a reasonable doubt of what it shows. It can only be overcome with proof of the existence of a genetically identical sibling, a comparable DNA test that reaches a contrary result or fraud. In reality, such tests are usually either 99.999%+ certain, or inconclusive.
    – ohwilleke
    Dec 6, 2023 at 19:22

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