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Do it by lottery.
https://www.vox.com/future-perfect/22878118/jury-duty-citizens-assembly-lottocracy-open-democracy
I think this could work on a smaller scale with smaller systems, and in places where there is more homogeneous population. Not so sure I would want to try it on a national scale.
Here's a funny thing - I lived in the UK as a citizen for 35 years, and then in Canada for 6 years, and never once got called for jury duty.
I get selected every single year over here, despite being ineligible.
We don't have this "jury" thing, which I find sad in some ways and good in others.
All in all, I'd weigh the advantages of having juries higher than the disadvantages.