First the disclaimer: I am not a lawyer.
Now, as I understand it, in Canada, there are three levels of deciding guilt in a court of law, depending on the seriousness of the crime.
Preponderance of Evidence
Is there more evidence against the accused, or more evidence for him? This is used in the least serious cases--the accused may, or may not be guilty, even if there is more evidence against him.
This is the most obvious use of the balance that we see blind justice carrying.
Balance of Probabilities
Is it probable, given the evidence, that the accused did commit the crime? A higher test of truth, used in more serious cases, this is closer to an application of common sense than the first.
Again, this is a balance, but it is now of more than just the evidence.
Beyond a Reasonable Doubt to a Moral Certainty
In the most serious cases, like murder, the jury is asked to see beyond the weight of the evidence, the first test, beyond the probability the accused commited the crime, the second, to whether, in their heart of hearts, the jury actually believes the accused committed the crime.
When it is a life in the balance, whether many years in jail, or to end it, this most serious test is used.
But the foundation is still the judgement of peers. Instructed in law by the judge, swayed by the appeals of the opposing counsel, these ordinary people, in the silence of their own conscience, make this most serious decision.