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One instance that I am familiar with is "innocent unless proven guilty beyond a reasonable doubt." So if you think that someone is "probably" guilty, but have a "reasonable doubt" covering, say 5%-10% of possible outcomes, my understanding is that you're supposed be give the defendant the "benefit of the doubt" and vote to acquit.

In a civil case, where the burden of proof is "preponderance of evidence," the standard of proof is more like 50-50. In this case, you might give someone the benefit of the doubt if you felt that that party was 50% or more in the right.

So is "benefit of the doubt" tied to a quantitative measure or probability? That the party receives the benefit of a very small doubt in the criminal case, and "50%" in the civil case?

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    Every time I've had jury duty the judge provides explicit guidance on how their jurisdiction interprets "reasonable doubt," despite how the attorneys involve might disagree. – jeffronicus Sep 1 '20 at 16:22
  • @jeffronicus: The jury instructions about "reasonable doubt" that I've seen in discussions of cases seem to be deliberately vague, rather than trying to articulate a clear position. Better IMHO would be something like "You must find that there is no plausible explanation for the evidence you've seen that would be consistent with the defendant's innocence, bearing in mind that witnesses sometimes lie, but generally do not do so without cause." If the primary evidence against someone is an eyewitness who would stand to benefit if the defendant is convicted, ... – supercat Sep 1 '20 at 19:17
  • ...and if the witness shows signs of evasiveness or untruthfulness, then it might be plausible that the witness might be lying for the purpose of falsely convicting the defendant. If twenty unrelated people all prevent cell phone video of a defendant committing a crime, it might be theoretically possible that all twenty could have falsified their videos, but it wouldn't really be plausible. If the criminal was seen using a rare object that matches one the defendant has, it might be possible that the crime was committed by someone who happens to have such an object, but it wouldn't... – supercat Sep 1 '20 at 19:20
  • ...generally be plausible. If, however, such an object had recently been stolen in the area where the crime took place, then it would be plausible that someone other than the defendant stole the object and used it to commit the crime. – supercat Sep 1 '20 at 19:22
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    The mathematical theory of probability deals in precisely quantified probabilities, and jurors and judges in these sorts of deliberations generally don't, but a mathematician named I.J. Good wrote a book on certain aspects of the mathematical theory of probability and gave it the title Weight of Evidence, and I suspect that is the only reason a copy of it ended up in the University of Minnesota's law library. – Michael Hardy Sep 1 '20 at 19:35
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Normally, the term "benefit of the doubt", if it was used, would mean that ambiguities should be resolved in favor of the person entitled to it. This could be applied to contract interpretation or to statutory interpretation. Here is an example:

When dealing with restrictions on campaign spending and speech, a court's construction must “give the benefit of the doubt to speech, not censorship. The First Amendment's command that ‘Congress shall make no law ... abridging the freedom of speech’ demands at least that.

Colorado Educ. Ass'n v. Rutt, 184 P.3d 65, 75–76 (Colo. 2008) (ultimately holding that union activities to organize volunteers to walk precincts with a political candidate did not constitute a "campaign expenditure" of a union within the meaning of a state law restriction campaign contributions by unions).

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"The benefit of the doubt" describes who gets the benefit in the case where there is doubt. It does not describe in any way what qualifies as "doubt". In some cases, a preponderance of evidence is all that's needed for there to be "no" doubt, while in others, it requires a conclusion to be reached "beyond a reasonable doubt" or "beyond a shadow of a doubt". These phrases are related to the certainty (or in some way, probability) of doubt. But in any case, when there is doubt (at whatever specified level of uncertainty), the benefit of the doubt goes to the accused (in systems where you are innocent until proven guilty).

I'll also note that even though this term itself is unrelated to probabilities, the legal standards of proof also do not have fixed probability values that can be compared against. So, while a "preponderance of evidence" allows for a higher level of uncertainty than "beyond a reasonable doubt", there is no set probability level that distinguishes one from another.

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