I think there's another problem which would be indistinguishable from this one. The realms of behavioral science show we're inordinately vulnerable to priming, and to various forms, conscious and unconscious, of peer pressure.
Well, it turns out we've screwed up any semblance of a 'presumption of innocence' by intermingling that concept with forced group dynamics.
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From a previous post - https://news.ycombinator.com/item?id=8546354 :
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...Because it is not voting in the sense of other voting. A criminal jury verdict has to be unanimous, but we send them to a sealed room and tell them 'Come back when you have a unanimous verdict.', rather than "Oh, you voted and disagreed? Well, Not Guilty then."
There is a strong understanding among the populace that a jury is a majoritarian body, that unanimity is a legal fiction, and that juries which can't effectively suppress dissenting opinions are failures in their social function, and we demand both extended "deliberation", and a completely new trial to correct their issue.
We even reinforce this understanding in caselaw; A last-ditch effort to un-"hang" a jury is termed an Allen Charge, which is apparently when the judge instructs the jury's minority vote that their position isn't reasonable while glaring at them menacingly.
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How does a "Presumption of innocence" held by one member, survive that group dynamic? A juror who is unconvinced by the case the prosecution makes doesn't have to say "I'm unconvinced", they have to actively fight for the defendant in deliberation, and convince the other people to change their votes, in order to leave the room. The holders of minority opinions are entrained to see themselves as inconveniencing every other member of the jury, keeping them from work and families. If they do not feel strongly about the verdict one way or another, the ideals of the justice system say that this is an absolute case for dismissal, because 'better ten guilty men go free than for one man to be wrongfully convicted', but faced with these social incentives, what do you expect them to do?
We've created a system where we may as well tell jurors: "If not all of you believe strongly in the verdict, forget the presumption of innocence and go with the decision of whichever among you has the strongest opinions that are the least persuadable".
If you want a system that preserves a presumption of innocence, switch to a unanimity-which-fails-to-acquittal or a supermajority-which-fails-to-acquittal standard rather than a unanimity-which-fails-to-another-vote standard.