Criminal defendants are found guilty if the finder of fact determines that they are guilty beyond reasonable doubt based on the data provided. This is analogous to the concept I am more familiar with, that of accepting or rejecting scientific hypotheses based on if an analysis of the data suggests a likelihood of greater or lesser than some threshold, usually denoted as alpha. This is frequently p < 5% for frequentest p values, meaning that the analysis determines that if the null hypothesis is true one would expect a result as far from expected under that hypothesis as observed no more than 1 in 20 times you looked.

I think I can confidently say the reasonable doubt alpha is below 50%. This is based on the threshold in civil trials being balance of probabilities and reasonable doubt being defined (by wiki at least) as being more stringent than that. Is there any other actual numerical bounds we can put on the reasonable doubt alpha? Either bound would be valid, as in it must be below 50% but it must be above 1/1,000,000 because X. Also any jurisdiction would be interesting.

How this differs from other questions

Other questions have asked "What is reasonable doubt mathematically", eg.Probabilistic justice or what is reasonable doubt. The core difference is that I am asking "What can we say about it" rather than "What is the value", such that <50% would be a valid answer to my question (if indeed it is) and not these others. Also I am asking globally and historically, so a common answer of "not in this jurisdiction now" is less useful. For example one question mentions "Blackstone’s Ratio". If there was a jurisdiction that explicitly included Blackstone’s Ratio in their law code, or some judgement that included Blackstone’s Ratio in case law then this would be a valid answer. Any such pronunciation at any time in history would be a valid answer.

To phrase this a different way, if I am the finder of fact, say a juror, and I assign a probability of "they did it" of 51% then I unambiguously should acquit. This is because I am aware of a bound on the reasonable doubt alpha of 50%. Is there any such statement I can make for any number other than 50% for any place and time?

  • 1
    Similar questions have been asked and answered before. E.g. law.stackexchange.com/questions/97794/…. The law doesn't consider "reasonable doubt" in this way.
    – Lag
    Commented May 8 at 11:22
  • @Lag see edit. Any example anywhere would do.
    – User65535
    Commented May 8 at 11:31
  • @Trish The core difference is I am asking "what can we say about it" rather than "what is it".
    – User65535
    Commented May 8 at 11:40
  • "Has there been a law or judgment that includes Blackstone's Ratio?" Look up N Guilty Men by Alexander Volokh, which cites a number of cases.
    – Lag
    Commented May 8 at 11:49
  • 3
    As the answers below suggest, anyone who tries to quantify reasonable doubt in this way is going to walk away dissatisfied. My understanding is that this is a concept generally confined to common-law countries, and that those countries have always rejected mathematical approaches to defining it.
    – bdb484
    Commented May 8 at 13:18

2 Answers 2


You ask:

Is there any such statement I can make for any number other than 50% for any place and time

Yes: in Canada, today, we can say for all values, it would be an error of law to instruct a jury to use that value as a threshold.

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.

Blackstone's ratio is an aphorism about the ideals of outcomes of the entire criminal legal system - from the right to counsel, procedural fairness, disclosure requirements, rules of evidence (which is what Blackstone was actually writing about in that particular sentence), etc. Don't get stuck on it as a way to come up with a probabilistic threshold.



Proving the accused’s guilt beyond reasonable doubt is the standard of proof the Crown must achieve before you can convict them and the words mean exactly what they say — proof beyond reasonable doubt. When you finish considering the evidence in the trial and the submissions made by the parties you must ask yourself whether the Crown has established the accused’s guilt beyond reasonable doubt.

The words mean exactly what they say. There is no numeric formula only the words - proof beyond reasonable doubt. When you are a juror, you decide if the Crown has done that.

  • I am still reading it, but N Guilty Men seems to contradict this, in some places and times.
    – User65535
    Commented May 8 at 12:55

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