If you are presumed innocent, it makes sense that OVERWHELMING evidence against you can result in a VERY LOW posterior probability of you being innocent. This sounds reasonable.
However a “balance of probabilities” sounds like something completely different, i.e. “one thing is more likely than the other”. How does this go along with presumption of innocence, where to my understanding the burden of proof beyond reasonable doubt should be on the prosecution rather than defence?
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Suppose you suspect someone drives drunk. You might be right, you might be wrong.
What you *do* with that suspicion depends on how bad it would be
* to think they do it when they don’t, and
* to think they don’t do it when they do.
In some situations, it’s really important to be *very sure* before we treat them as guilty. Eg, if they’re going to jail for it – our justice system is *very wary* of sending innocent people to jail. The idea of “innocent until proven guilty” comes from this.
In other situations, it’s important to be *very sure* before we treat them as innocent: eg, if we’re hiring them as a long haul truck driver.
In other situations, both mistakes are about equally bad: we want to take action on the thing that’s *more likely* to be true. Eg, if they’re suing someone who got them fired by spreading rumours about them driving drunk. The idea of “balance of probabilities” comes from this.
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