The way courts and juries work (in the US, but probably other Western democracies too) is very much a reflection of the system in general.
In a pure tyranny you'd have a king or some sort of ruler who 'decides'. In a "democracy", supposedly we all have equal control or whatever, but in practice those with the most money and/or connections will lobby the political bodies and essentially be the ruling class.
Similarly, when juries get together to deliberate, anyone who is persuasive and good at influencing what other people think will have a disproportionate influence over the outcome.
For this reason I really, really hate the idea of jury deliberation and believe it to be a lowkey horrible thing.
But how else? As long as you have random people who would rather be at their jobs or with their families but are only here because of the threat of punishment if they don't show up, you probably kind of have to keep a close eye on them and apply some sort of pressure.
But if instead there was a natural incentive to do the job well, then you could get rid of deliberation.
Imagine if people were individually focused on judging the outcome and had some sort of built in incentive to do it correctly.
It may sound like an introvert's pipe dream, but judging a nuanced situation is an inherently introverted thing, and shouldn't be warped into anything else.
The best method that I can think of for giving people incentive to judge correctly is a reward for ruling in the majority.
If you witness a trial from an isolated booth, and you aren't allowed to talk to the other jurors or even have any idea who they are, then your only strategy for ruling in the majority would be to try to rule correctly. Because you know they're watching the same trial and trying to do the same thing.
To simplify it, imagine they put a color on display. And you had to rule in the majority whether it was blue or green or red or what. You know nothing about the other jurors. Your strategy will always be to answer correctly; there's never a reason to be like "well, it's blue, but I just feel like the other people are gonna say green".
You can take it a step further and even keep records of who the best jurors are. And then on the more important cases, you bring in the best people.
Or actually, it would probably be more like: On the more important cases, you raise the reward, and more people apply, and you're able to select from the best people.
So that's one way that you could have courts (judgments) without forcing people to be there and encouraging them to do a vaguely decent job by lecturing them about how important this is or whatever.
I'd like someone to create a blockchain that rules on court cases.
A free market in courts is mindblowing to almost everyone. But we could even stick with the existing infrastructure of government courts (for now) and eventually just swap out juries for the blockchain jury system.