I like the idea, however your problem is you will always come across trolls on the internet, or people who just like screwing up systems. I would say this percentage on facebook is quite sizable, so i would propose these alterations(to be taken individually or all together or mix/match):
Assign a trustability value to each juror, that is hidden and modified in one of two ways(or both):
Have a pool of pre-existing cases(I'm sure facebook has tons of examples stored in their history banks).
In this situation facebook knows what the outcome should be according to their standards.
Have any prospective juror have a mix of "real" cases and these pre-existing cases mixed together for a trial period, say that first 20 cases they review have an unknown mix. This way they can't guess which ones are appropriate or not.
Use their verdicts on these existing cases to assign a juror a "reliability" factor on their verdicts on the non-example cases in their batch.
That way jurors who don't quite get the rules, or are causing problems, are easily weeded out and their vote counts less in the total verdict weight on their real cases.
Alternatively:
Trustability starts at 50%, so new jurors get half votes.
whenever a juror disagrees with the majority opinion by the polar opposite choice, lower their trustability rating.
Likewise when they are in the majority and it is not a middleground, increase their trustability.
Both of these improvements will lower the odds of troll or mob mentality, even if the control a decent size of the juror pool because their individual votes will be worth less, while being invisible enough to the end-user that they won't be able to tell they aren't being effective.